Just Numbers (14 March 2022).pdf

10 21 19 20 14 21 13 2 5 18 19
E. Figaroa (figaroa.numbers@gmail.com)
March 14, 2022
1 Euler Polynomial P(n) = n + n^2 + 41 Page 1
I have further elaborated on this quadratic equation devised by Leonhard Euler in 1772.
This resulted in my own formulas with regard to this quadratic equation.
2 Legendre Polynomial P(n) = 2n^2 + 29 Page 12
This quadratic equation, once discovered or invented by Adrien-Marie Legendre, generates many primes.
I have further elaborated on this equation, resulting in my own formulas.
3 Prime-Generating Polynomial P(n) = 6n^2 + 6n + 31 Page 24
Self-made quadratic equation and related equations that produce prime numbers.
4 Various Prime-Generating Quadratic Polynomials Page 26
Self-invented figures with differently arranged numbers, creating patterns of prime numbers.
I came up with a number of equations that describe the patterns of these prime numbers.
5 Franklin's Magic Squares Page 31
Benjamin Franklin has created some world-famous magic squares.
I have been thinking of some methods that he could possibly have used to make these magic squares.
This also applies to the rediscovered magic squares of Franklin by Paul C. Pasles.
6 Magic Constant Triangle and RS Page 53
Triangle with the numbers entered in zigzag, along with my self-invented formula RS = 2n^2 + 3 (for n ≥ 2).
7 Magic Squares Page 54
I made these magic squares with, among other things, prime numbers.
8 Pi Triangle Page 58
I made this pi triangle by entering the numbers of pi in a zigzag pattern, resulting in several interesting patterns and remarkable observations.
9 Ulam Normal and Zigzag Page 60
In 1963, Stanislaw Ulam devised a spiral that, to his surprise, arranged many prime numbers in a line.
I have entered the numbers in the Ulam spiral in a zigzag which reveals other patterns.
10 Various Figures Page 73
Self-invented figures with different ways of arranging the numbers.
11 Generalized Collatz Problem Page 82
This mathematical problem has been around for years and is still unsolved after 80 years.
I have provided my own take on this with some possible ways to approach this problem without pretending to have found the solution.

Quadratic Prime-Generating Polynomial (Euler 1772): P(n) = n^2 + n + 41
n n^2 41 P(n) = n^2 + n + 41 n n^2 41 P(n) = n^2 + n + 41 n n^2 41 P(n) = n^2 + n + 41
0 0 41 41 167 27889 41 28097 334 111556 41 111931 173 x 647
1 1 41 43 168 28224 41 28433 335 112225 41 112601
2 4 41 47 169 28561 41 28771 336 112896 41 113273 227 x 499
3 9 41 53 170 28900 41 29111 43 x 677 337 113569 41 113947
4 16 41 61 171 29241 41 29453 338 114244 41 114623 83 x 1381
5 25 41 71 172 29584 41 29797 83 x 359 339 114921 41 115301
6 36 41 83 173 29929 41 30143 43 x 701 340 115600 41 115981
7 49 41 97 174 30276 41 30491 341 116281 41 116663
8 64 41 113 175 30625 41 30841 342 116964 41 117347 43 x 2729
9 81 41 131 176 30976 41 31193 343 117649 41 118033
10 100 41 151 177 31329 41 31547 344 118336 41 118721 227 x 523
11 121 41 173 178 31684 41 31903 61 x 523 345 119025 41 119411 43 x 2777
12 144 41 197 179 32041 41 32261 346 119716 41 120103
13 169 41 223 180 32400 41 32621 347 120409 41 120797 113 x 1069
14 196 41 251 181 32761 41 32983 348 121104 41 121493
15 225 41 281 182 33124 41 33347 349 121801 41 122191 71 x 1721
16 256 41 313 183 33489 41 33713 350 122500 41 122891
17 289 41 347 184 33856 41 34081 173 x 197 351 123201 41 123593
18 324 41 383 185 34225 41 34451 47 x 733 352 123904 41 124297
19 361 41 421 186 34596 41 34823 97 x 359 353 124609 41 125003
20 400 41 461 187 34969 41 35197 61 x 577 354 125316 41 125711
21 441 41 503 188 35344 41 35573 355 126025 41 126421
22 484 41 547 189 35721 41 35951 356 126736 41 127133
23 529 41 593 190 36100 41 36331 47 x 773 357 127449 41 127847 173 x 739
24 576 41 641 191 36481 41 36713 358 128164 41 128563
25 625 41 691 192 36864 41 37097 359 128881 41 129281
26 676 41 743 193 37249 41 37483 360 129600 41 130001 71 x 1831
27 729 41 797 194 37636 41 37871 361 130321 41 130723 61 x 2143
28 784 41 853 195 38025 41 38261 362 131044 41 131447
29 841 41 911 196 38416 41 38653 363 131769 41 132173
30 900 41 971 197 38809 41 39047 364 132496 41 132901 347 x 383
31 961 41 1033 198 39204 41 39443 365 133225 41 133631
32 1024 41 1097 199 39601 41 39841 366 133956 41 134363
33 1089 41 1163 200 40000 41 40241 367 134689 41 135097 53 x 2549
34 1156 41 1231 201 40401 41 40643 97 x 419 368 135424 41 135833 41 x 3313
35 1225 41 1301 202 40804 41 41047 369 136161 41 136571 41 x 3331
36 1296 41 1373 203 41209 41 41453 370 136900 41 137311 61 x 2251
37 1369 41 1447 204 41616 41 41861 41 x 1021 371 137641 41 138053
38 1444 41 1523 205 42025 41 42271 41 x 1031 372 138384 41 138797
39 1521 41 1601 206 42436 41 42683 373 139129 41 139543 47 x 2969
40 1600 41 1681 41 x 41 207 42849 41 43097 71 x 607 374 139876 41 140291 53 x 2647
41 1681 41 1763 41 x 43 208 43264 41 43513 53 x 821 375 140625 41 141041
42 1764 41 1847 209 43681 41 43931 197 x 223 376 141376 41 141793
43 1849 41 1933 210 44100 41 44351 377 142129 41 142547
44 1936 41 2021 43 x 47 211 44521 41 44773 378 142884 41 143303 47 x 3049
45 2025 41 2111 212 44944 41 45197 379 143641 41 144061
46 2116 41 2203 213 45369 41 45623 43 x 1061 380 144400 41 144821 97 x 1493
47 2209 41 2297 214 45796 41 46051 381 145161 41 145583 197 x 739
48 2304 41 2393 215 46225 41 46481 53 x 877 382 145924 41 146347
49 2401 41 2491 47 x 53 216 46656 41 46913 43 x 1091 383 146689 41 147113 131 x 1123
50 2500 41 2591 217 47089 41 47347 113 x 419 384 147456 41 147881
51 2601 41 2693 218 47524 41 47783 71 x 673 385 148225 41 148651 43 x 3457
52 2704 41 2797 219 47961 41 48221 386 148996 41 149423
53 2809 41 2903 220 48400 41 48661 387 149769 41 150197
54 2916 41 3011 221 48841 41 49103 388 150544 41 150973 43 x 3511
55 3025 41 3121 222 49284 41 49547 389 151321 41 151751 263 x 577
56 3136 41 3233 53 x 61 223 49729 41 49993 390 152100 41 152531
57 3249 41 3347 224 50176 41 50441 391 152881 41 153313
58 3364 41 3463 225 50625 41 50891 392 153664 41 154097
59 3481 41 3581 226 51076 41 51343 393 154449 41 154883
60 3600 41 3701 227 51529 41 51797 394 155236 41 155671
61 3721 41 3823 228 51984 41 52253 395 156025 41 156461 97 x 1613
62 3844 41 3947 229 52441 41 52711 396 156816 41 157253
63 3969 41 4073 230 52900 41 53171 397 157609 41 158047
64 4096 41 4201 231 53361 41 53633 398 158404 41 158843
65 4225 41 4331 61 x 71 232 53824 41 54097 47 x 1151 399 159201 41 159641 263 x 607
66 4356 41 4463 233 54289 41 54563 400 160000 41 160441
67 4489 41 4597 234 54756 41 55031 113 x 487 401 160801 41 161243 383 x 421
68 4624 41 4733 235 55225 41 55501 402 161604 41 162047 131 x 1237
69 4761 41 4871 236 55696 41 55973 223 x 251 403 162409 41 162853
70 4900 41 5011 237 56169 41 56447 47 x 1201 404 163216 41 163661
71 5041 41 5153 238 56644 41 56923 405 164025 41 164471
72 5184 41 5297 239 57121 41 57401 61 x 941 406 164836 41 165283 197 x 839
73 5329 41 5443 240 57600 41 57881 407 165649 41 166097 163 x 1019
74 5476 41 5591 241 58081 41 58363 408 166464 41 166913 83 x 2011
75 5625 41 5741 242 58564 41 58847 83 x 709 409 167281 41 167731 41 x 4091
76 5776 41 5893 71 x 83 243 59049 41 59333 410 168100 41 168551 41 x 4111
77 5929 41 6047 244 59536 41 59821 163 x 367 411 168921 41 169373
78 6084 41 6203 245 60025 41 60311 41 x 1471 412 169744 41 170197
79 6241 41 6361 246 60516 41 60803 41 x 1483 413 170569 41 171023
80 6400 41 6521 247 61009 41 61297 414 171396 41 171851
81 6561 41 6683 41 x 163 248 61504 41 61793 61 x 1013 415 172225 41 172681
82 6724 41 6847 41 x 167 249 62001 41 62291 167 x 373 416 173056 41 173513 167 x 1039
83 6889 41 7013 250 62500 41 62791 417 173889 41 174347
84 7056 41 7181 43 x 167 251 63001 41 63293 167 x 379 418 174724 41 175183 167 x 1049
85 7225 41 7351 252 63504 41 63797 131 x 487 419 175561 41 176021
86 7396 41 7523 253 64009 41 64303 420 176400 41 176861 47 x 53 x 71 47 x 3763 53 x 3337 71 x 2491
87 7569 41 7697 43 x 179 254 64516 41 64811 421 177241 41 177703 83 x 2141
88 7744 41 7873 255 65025 41 65321 83 x 787 422 178084 41 178547 61 x 2927
89 7921 41 8051 83 x 97 256 65536 41 65833 43 x 1531 423 178929 41 179393
90 8100 41 8231 257 66049 41 66347 424 179776 41 180241
91 8281 41 8413 47 x 179 258 66564 41 66863 425 180625 41 181091 47 x 3853
92 8464 41 8597 259 67081 41 67381 43 x 1567 426 181476 41 181943
93 8649 41 8783 260 67600 41 67901 427 182329 41 182797 53 x 3449
94 8836 41 8971 261 68121 41 68423 53 x 1291 428 183184 41 183653 43 x 4271
95 9025 41 9161 262 68644 41 68947 429 184041 41 184511
96 9216 41 9353 47 x 199 263 69169 41 69473 430 184900 41 185371
97 9409 41 9547 264 69696 41 70001 431 185761 41 186233 43 x 61 x 71 43 x 4331 61 x 3053 71 x 2623
98 9604 41 9743 265 70225 41 70531 251 x 281 432 186624 41 187097 223 x 839
99 9801 41 9941 266 70756 41 71063 179 x 397 433 187489 41 187963
100 10000 41 10141 267 71289 41 71597 434 188356 41 188831
101 10201 41 10343 268 71824 41 72133 53 x 1361 435 189225 41 189701
102 10404 41 10547 53 x 199 269 72361 41 72671 436 190096 41 190573
103 10609 41 10753 270 72900 41 73211 179 x 409 437 190969 41 191447
104 10816 41 10961 97 x 113 271 73441 41 73753 131 x 563 438 191844 41 192323
105 11025 41 11171 272 73984 41 74297 439 192721 41 193201
106 11236 41 11383 273 74529 41 74843 440 193600 41 194081 421 x 461
107 11449 41 11597 274 75076 41 75391 441 194481 41 194963
108 11664 41 11813 275 75625 41 75941 442 195364 41 195847 151 x 1297
109 11881 41 12031 53 x 227 276 76176 41 76493 443 196249 41 196733 113 x 1741
110 12100 41 12251 277 76729 41 77047 444 197136 41 197621
111 12321 41 12473 278 77284 41 77603 71 x 1093 445 198025 41 198511 179 x 1109
112 12544 41 12697 279 77841 41 78161 47 x 1663 446 198916 41 199403
113 12769 41 12923 280 78400 41 78721 447 199809 41 200297
114 12996 41 13151 281 78961 41 79283 448 200704 41 201193
115 13225 41 13381 282 79524 41 79847 449 201601 41 202091 179 x 1129
116 13456 41 13613 283 80089 41 80413 97 x 829 450 202500 41 202991 41 x 4951
117 13689 41 13847 61 x 227 284 80656 41 80981 47 x 1723 451 203401 41 203893 41 x 4973
118 13924 41 14083 285 81225 41 81551 452 204304 41 204797
119 14161 41 14321 286 81796 41 82123 41 x 2003 453 205209 41 205703
120 14400 41 14561 287 82369 41 82697 41 x 2017 454 206116 41 206611 307 x 673
121 14641 41 14803 113 x 131 288 82944 41 83273 455 207025 41 207521
122 14884 41 15047 41 x 367 289 83521 41 83851 71 x 1181 456 207936 41 208433
123 15129 41 15293 41 x 373 290 84100 41 84431 457 208849 41 209347
124 15376 41 15541 291 84681 41 85013 151 x 563 458 209764 41 210263
125 15625 41 15791 292 85264 41 85597 459 210681 41 211181 223 x 947
126 15876 41 16043 61 x 263 293 85849 41 86183 460 211600 41 212101 113 x 1877
127 16129 41 16297 43 x 379 294 86436 41 86771 461 212521 41 213023
128 16384 41 16553 295 87025 41 87361 199 x 439 462 213444 41 213947
129 16641 41 16811 296 87616 41 87953 281 x 313 463 214369 41 214873 151 x 1423
130 16900 41 17071 43 x 397 297 88209 41 88547 464 215296 41 215801
131 17161 41 17333 298 88804 41 89143 97 x 919 465 216225 41 216731
132 17424 41 17597 299 89401 41 89741 43 x 2087 466 217156 41 217663 307 x 709
133 17689 41 17863 300 90000 41 90341 61 x 1481 467 218089 41 218597 47 x 4651
134 17956 41 18131 301 90601 41 90943 199 x 457 468 219024 41 219533
135 18225 41 18401 302 91204 41 91547 43 x 2129 469 219961 41 220471
136 18496 41 18673 71 x 263 303 91809 41 92153 470 220900 41 221411
137 18769 41 18947 304 92416 41 92761 471 221841 41 222353 43 x 5171
138 19044 41 19223 47 x 409 305 93025 41 93371 472 222784 41 223297 47 x 4751
139 19321 41 19501 306 93636 41 93983 473 223729 41 224243 53 x 4231
140 19600 41 19781 131 x 151 307 94249 41 94597 474 224676 41 225191 43 x 5237
141 19881 41 20063 308 94864 41 95213 475 225625 41 226141
142 20164 41 20347 309 95481 41 95831 61 x 1571 476 226576 41 227093
143 20449 41 20633 47 x 439 310 96100 41 96451 477 227529 41 228047 97 x 2351
144 20736 41 20921 311 96721 41 97073 478 228484 41 229003
145 21025 41 21211 312 97344 41 97697 151 x 647 479 229441 41 229961
146 21316 41 21503 313 97969 41 98323 480 230400 41 230921 53 x 4357
147 21609 41 21797 71 x 307 314 98596 41 98951 53 x 1867 481 231361 41 231883 461 x 503
148 21904 41 22093 315 99225 41 99581 482 232324 41 232847
149 22201 41 22391 316 99856 41 100213 483 233289 41 233813 61 x 3833
150 22500 41 22691 317 100489 41 100847 484 234256 41 234781
151 22801 41 22993 318 101124 41 101483 485 235225 41 235751
152 23104 41 23297 319 101761 41 102121 486 236196 41 236723
153 23409 41 23603 320 102400 41 102761 487 237169 41 237697 251 x 947
154 23716 41 23911 321 103041 41 103403 53 x 1951 488 238144 41 238673
155 24025 41 24221 53 x 457 322 103684 41 104047 489 239121 41 239651 367 x 653
156 24336 41 24533 323 104329 41 104693 490 240100 41 240631
157 24649 41 24847 324 104976 41 105341 491 241081 41 241613 41 x 71 x 83 41 x 5893 71 x 3403 83 x 2911
158 24964 41 25163 325 105625 41 105991 83 x 1277 492 242064 41 242597 41 x 61 x 97 41 x 5917 61 x 3977 97 x 2501
159 25281 41 25481 83 x 307 326 106276 41 106643 47 x 2269 493 243049 41 243583
160 25600 41 25801 327 106929 41 107297 41 x 2617 494 244036 41 244571 199 x 1229
161 25921 41 26123 151 x 173 328 107584 41 107953 41 x 2633 495 245025 41 245561
162 26244 41 26447 53 x 499 329 108241 41 108611 313 x 347 496 246016 41 246553 373 x 661
163 26569 41 26773 41 x 653 330 108900 41 109271 113 x 967 497 247009 41 247547
164 26896 41 27101 41 x 661 331 109561 41 109933 47 x 2339 498 248004 41 248543
165 27225 41 27431 332 110224 41 110597 499 249001 41 249541
166 27556 41 27763 333 110889 41 111263 500 250000 41 250541 199 x 1259
326 Prime Numbers 175 Composite Numbers
© E. Figaroa (figaroa.numbers@gmail.com 1

Quadratic Polynomial (Euler 1772): P(n) = n^2 + n + 41
n P(n) = n^2 + n + 41 2n + 2 n P(n) = n^2 + n + 41 2n + 2
0 41 2 251 63293 504 167 x 379
1 43 4 252 63797 506 131 x 487
2 47 6 253 64303 508
3 53 8 254 64811 510
4 61 10 255 65321 512 83 x 787 787 - 709 = 78
5 71 12 256 65833 514 43 x 1531
6 83 14 257 66347 516
7 97 16 258 66863 518
8 113 18 259 67381 520 43 x 1567 1567 - 1531 = 36
9 131 20 260 67901 522
10 151 22 261 68423 524 53 x 1291
11 173 24 262 68947 526
12 197 26 263 69473 528
13 223 28 264 70001 530
14 251 30 265 70531 532 251 x 281 281 281 - 251 = 30
15 281 32 266 71063 534 179 x 397
16 313 34 267 71597 536
17 347 36 268 72133 538 53 x 1361 1361 - 1291 = 70
18 383 38 269 72671 540
19 421 40 270 73211 542 179 x 409
20 461 42 271 73753 544 131 x 563 563 - 487 = 76
21 503 44 272 74297 546
22 547 46 273 74843 548
23 593 48 274 75391 550
24 641 50 275 75941 552
25 691 52 276 76493 554
26 743 54 277 77047 556
27 797 56 278 77603 558 71 x 1093
28 853 58 279 78161 560 47 x 1663
29 911 60 280 78721 562
30 971 62 281 79283 564
31 1033 64 282 79847 566
32 1097 66 283 80413 568 97 x 829
33 1163 68 284 80981 570 47 x 1723 1723 - 1663 = 60
34 1231 70 285 81551 572
35 1301 72 286 82123 574 574 / 41 = 14 41 x 2003
36 1373 74 287 82697 576 41 x 2017 2017 - 2003 = 14
37 1447 76 288 83273 578
38 1523 78 289 83851 580 71 x 1181 1181 - 1093 = 88
39 1601 80 290 84431 582
40 1681 82 82 / 41 = 2 41 x 41 41 41 - 41 = 0 0 spaces between this composite number and the next. 41 + 41 = 82 (2n + 2) 291 85013 584 151 x 563
41 1763 84 41 x 43 43 43 - 41 = 2 2 spaces between this composite number and the next. 41 + 43 = 84 (2n +2) 292 85597 586
42 1847 86 293 86183 588
43 1933 88 294 86771 590
44 2021 90 43 x 47 47 47 - 43 = 4 4 spaces between this composite number and the next. 43 + 47 = 90 (2n + 2) 295 87361 592 199 x 439
45 2111 92 296 87953 594 281 x 313 313 313 - 281 = 32
46 2203 94 297 88547 596
47 2297 96 298 89143 598 97 x 919 919 - 829 = 90
48 2393 98 299 89741 600 43 x 2087
49 2491 100 47 x 53 53 53 - 47 = 6 6 spaces between this composite number and the next. 47 + 53 = 100 (2n + 2) 300 90341 602 61 x 1481
50 2591 102 301 90943 604 199 x 457
51 2693 104 302 91547 606 43 x 2129 2129 - 2087 = 42
52 2797 106 303 92153 608
53 2903 108 304 92761 610
54 3011 110 305 93371 612
55 3121 112 306 93983 614
56 3233 114 53 x 61 61 61 - 53 = 8 8 spaces between this composite number and the next. 53 + 61 = 114 (2n + 2) 307 94597 616
57 3347 116 308 95213 618
58 3463 118 309 95831 620 61 x 1571 1571 - 1481 = 90
59 3581 120 310 96451 622
60 3701 122 311 97073 624
61 3823 124 312 97697 626 151 x 647 647 - 563 = 84
62 3947 126 313 98323 628
63 4073 128 314 98951 630 53 x 1867
64 4201 130 315 99581 632
66 4463 134 317 100847 636
67 4597 136 318 101483 638
68 4733 138 319 102121 640
69 4871 140 320 102761 642
70 5011 142 321 103403 644 53 x 1951 1951 - 1867 = 84
71 5153 144 322 104047 646
72 5297 146 323 104693 648
73 5443 148 324 105341 650
74 5591 150 325 105991 652 83 x 1277
75 5741 152 326 106643 654 47 x 2269
76 5893 154 71 x 83 83 83 - 71 = 12 12 spaces between this composite number and the next. 71 + 83 = 154 (2n + 2) 327 107297 656 656 / 41 = 16 41 x 2617
77 6047 156 328 107953 658 41 x 2633 2633 - 2617 = 16
78 6203 158 329 108611 660 313 x 347 347 347 - 313 = 34
79 6361 160 330 109271 662 113 x 967
80 6521 162 331 109933 664 47 x 2339 2339 - 2269 = 70
81 6683 164 164 / 41 = 4 41 x 163 332 110597 666
82 6847 166 41 x 167 167 - 163 = 4 333 111263 668
83 7013 168 334 111931 670 173 x 647
84 7181 170 43 x 167 335 112601 672
85 7351 172 336 113273 674 227 x 499
86 7523 174 337 113947 676
87 7697 176 43 x 179 179 - 167 = 12 338 114623 678 83 x 1381 1381 - 1277 = 104
88 7873 178 339 115301 680
90 8231 182 341 116663 684
91 8413 184 47 x 179 342 117347 686 43 x 2729
92 8597 186 343 118033 688
93 8783 188 344 118721 690 227 x 523
94 8971 190 345 119411 692 43 x 2777 2777 - 2729 = 48
95 9161 192 346 120103 694
96 9353 194 47 x 199 199 - 179 = 20 347 120797 696 113 x 1069 1069 - 967 = 102
97 9547 196 348 121493 698
98 9743 198 349 122191 700 71 x 1721
99 9941 200 350 122891 702
100 10141 202 351 123593 704
101 10343 204 352 124297 706
102 10547 206 53 x 199 353 125003 708
103 10753 208 354 125711 710
104 10961 210 97 x 113 113 113 - 97 = 16 355 126421 712
105 11171 212 356 127133 714
106 11383 214 357 127847 716 173 x 739 739 - 647 = 92
107 11597 216 358 128563 718
108 11813 218 359 129281 720
109 12031 220 53 x 227 227 - 199 = 28 360 130001 722 71 x 1831 1831 - 1721 = 110
110 12251 222 361 130723 724 61 x 2143
111 12473 224 362 131447 726
112 12697 226 363 132173 728
113 12923 228 364 132901 730 347 x 383 383 383 - 347 = 36
114 13151 230 365 133631 732
115 13381 232 366 134363 734
116 13613 234 367 135097 736 53 x 2549
117 13847 236 61 x 227 368 135833 738 738 / 41 = 18 41 x 3313
118 14083 238 369 136571 740 41 x 3331 3331 - 3313 = 18
119 14321 240 370 137311 742 61 x 2251 2251 - 2143 = 108
120 14561 242 371 138053 744
121 14803 244 113 x 131 131 131 - 113 = 18 372 138797 746
122 15047 246 246 / 41 = 6 41 x 367 373 139543 748 47 x 2969
123 15293 248 41 x 373 373 - 367 = 6 374 140291 750 53 x 2647 2647 - 2549 = 98
124 15541 250 375 141041 752
125 15791 252 376 141793 754
126 16043 254 61 x 263 263 - 227 = 36 377 142547 756
127 16297 256 43 x 379 378 143303 758 47 x 3049 3049 - 2969 = 80
128 16553 258 379 144061 760
129 16811 260 380 144821 762 97 x 1493
130 17071 262 43 x 397 397 - 379 = 18 381 145583 764 197 x 739
131 17333 264 382 146347 766
132 17597 266 383 147113 768 131 x 1123
133 17863 268 384 147881 770
134 18131 270 385 148651 772 43 x 3457
135 18401 272 386 149423 774
136 18673 274 71 x 263 387 150197 776
137 18947 276 388 150973 778 43 x 3511 3511 - 3457 = 54
138 19223 278 47 x 409 389 151751 780 263 x 577
139 19501 280 390 152531 782
140 19781 282 131 x 151 151 151 - 131 = 20 391 153313 784
141 20063 284 392 154097 786
142 20347 286 393 154883 788
143 20633 288 47 x 439 439 - 409 = 30 394 155671 790
144 20921 290 395 156461 792 97 x 1613 1613 - 1493 = 120
145 21211 292 396 157253 794
146 21503 294 397 158047 796
147 21797 296 71 x 307 307 - 263 = 44 398 158843 798
148 22093 298 399 159641 800 263 x 607
149 22391 300 400 160441 802
150 22691 302 401 161243 804 383 x 421 421 421 - 383 = 38
151 22993 304 402 162047 806 131 x 1237 1237 - 1123 = 114
152 23297 306 403 162853 808
153 23603 308 404 163661 810
154 23911 310 405 164471 812
155 24221 312 53 x 457 406 165283 814 197 x 839 839 - 739 = 100
156 24533 314 407 166097 816 163 x 1019
157 24847 316 408 166913 818 83 x 2011
158 25163 318 409 167731 820 820 / 41 = 20 41 x 4091
159 25481 320 83 x 307 410 168551 822 41 x 4111 4111 - 4091 = 20
160 25801 322 411 169373 824
161 26123 324 151 x 173 173 173 - 151 = 22 412 170197 826
162 26447 326 53 x 499 499 - 457 = 42 413 171023 828
163 26773 328 328 / 41 = 8 41 x 653 414 171851 830
164 27101 330 41 x 661 661 - 653 = 8 415 172681 832
165 27431 332 416 173513 834 167 x 1039
166 27763 334 417 174347 836
167 28097 336 418 175183 838 167 x 1049
168 28433 338 419 176021 840
169 28771 340 420 176861 842 47 x 53 x 71 47 x 3763 53 x 3337 71 x 2491
170 29111 342 43 x 677 421 177703 844 83 x 2141 2141 - 2011 = 130
171 29453 344 422 178547 846 61 x 2927
172 29797 346 83 x 359 359 - 307 = 52 423 179393 848
173 30143 348 43 x 701 701 - 677 = 24 424 180241 850
174 30491 350 425 181091 852 47 x 3853 3853 - 3763 = 90
175 30841 352 426 181943 854
176 31193 354 427 182797 856 53 x 3449 3449 - 3337 = 112
177 31547 356 428 183653 858 43 x 4271
178 31903 358 61 x 523 429 184511 860
179 32261 360 430 185371 862
180 32621 362 431 186233 864 43 x 61 x 71 43 x 4331 61 x 3053 71 x 2623 2623 - 2491 = 132
181 32983 364 432 187097 866 223 x 839 4331 - 4271 = 60 3053 - 2927 = 126
182 33347 366 433 187963 868
183 33713 368 434 188831 870
184 34081 370 173 x 197 197 197 - 173 = 24 435 189701 872
185 34451 372 47 x 733 436 190573 874
186 34823 374 97 x 359 437 191447 876
187 35197 376 61 x 577 577 - 523 = 54 438 192323 878
188 35573 378 439 193201 880
189 35951 380 440 194081 882 421 x 461 461 461 - 421 = 40
190 36331 382 47 x 773 773 - 733 = 40 441 194963 884
191 36713 384 442 195847 886 151 x 1297
192 37097 386 443 196733 888 113 x 1741
193 37483 388 444 197621 890
194 37871 390 445 198511 892 179 x 1109
195 38261 392 446 199403 894
196 38653 394 447 200297 896
197 39047 396 448 201193 898
198 39443 398 449 202091 900 179 x 1129
199 39841 400 450 202991 902 902 / 41 = 22 41 x 4951
200 40241 402 451 203893 904 41 x 4973 4973 - 4951 = 22
201 40643 404 97 x 419 419 - 359 = 60 452 204797 906
202 41047 406 453 205703 908
203 41453 408 454 206611 910 307 x 673
204 41861 410 410 / 41 = 10 41 x 1021 455 207521 912
205 42271 412 41 x 1031 1031 - 1021 = 10 456 208433 914
206 42683 414 457 209347 916
207 43097 416 71 x 607 458 210263 918
208 43513 418 53 x 821 459 211181 920 223 x 947 947 - 839 = 108
209 43931 420 197 x 223 223 223 - 197 = 26 460 212101 922 113 x 1877 1877 - 1741 = 136
210 44351 422 461 213023 924
211 44773 424 462 213947 926
212 45197 426 463 214873 928 151 x 1423 1423 - 1297 = 126
213 45623 428 43 x 1061 464 215801 930
214 46051 430 465 216731 932
215 46481 432 53 x 877 877 - 821 = 56 466 217663 934 307 x 709
216 46913 434 43 x 1091 1091 - 1061 = 30 467 218597 936 47 x 4651
217 47347 436 113 x 419 468 219533 938
218 47783 438 71 x 673 673 - 607 = 66 469 220471 940
219 48221 440 470 221411 942
220 48661 442 471 222353 944 43 x 5171
221 49103 444 472 223297 946 47 x 4751 4751 - 4651 = 100
222 49547 446 473 224243 948 53 x 4231
223 49993 448 474 225191 950 43 x 5237 5237 - 5171 = 66
224 50441 450 475 226141 952
225 50891 452 476 227093 954
226 51343 454 477 228047 956 97 x 2351
227 51797 456 478 229003 958
228 52253 458 479 229961 960
229 52711 460 480 230921 962 53 x 4357 4357 - 4231 = 126
230 53171 462 481 231883 964 461 x 503 503 503 - 461 = 42
231 53633 464 482 232847 966
232 54097 466 47 x 1151 483 233813 968 61 x 3833
233 54563 468 484 234781 970
234 55031 470 113 x 487 487 - 419 = 68 485 235751 972
235 55501 472 486 236723 974
236 55973 474 223 x 251 251 251 - 223 = 28 487 237697 976 251 x 947
237 56447 476 47 x 1201 1201 - 1151 = 50 488 238673 978
238 56923 478 489 239651 980 367 x 653
239 57401 480 61 x 941 490 240631 982
240 57881 482 491 241613 984 984 / 41 = 24 41 x 71 x 83 41 x 5893 71 x 3403 83 x 2911
241 58363 484 492 242597 986 41 x 61 x 97 41 x 5917 61 x 3977 97 x 2501 2501 - 2351 = 150
242 58847 486 83 x 709 493 243583 988 3977 - 3833 = 144
243 59333 488 494 244571 990 199 x 1229
244 59821 490 163 x 367 495 245561 992
245 60311 492 492 / 41 = 12 41 x 1471 496 246553 994 373 x 661
246 60803 494 41 x 1483 1483 - 1471 = 12 497 247547 996
247 61297 496 498 248543 998
248 61793 498 61 x 1013 1013 - 941 = 72 499 249541 1000
249 62291 500 167 x 373 500 250541 199 x 1259
250 62791 502

Euler Quadratic Polynomial (P(n) = n^2 + n + 41) And Related Prime-Generating Polynomials
n P(n) = n^2 + n + 41 n P(n) = n^2 + n + 41
0 41 2 251 63293 504 167 x 379
1 43 4 252 63797 506 131 x 487
2 47 6 253 64303 508
3 53 8 254 64811 510
4 61 10 255 65321 512 83 x 787 787 - 709 = 78
5 71 12 256 65833 514 43 x 1531
6 83 14 257 66347 516
7 97 16 258 66863 518
8 113 18 259 67381 520 43 x 1567 1567 - 1531 = 36
9 131 20 260 67901 522
10 151 22 261 68423 524 53 x 1291
11 173 24 262 68947 526
12 197 26 263 69473 528
13 223 28 264 70001 530
14 251 30 265 70531 532 251 x 281 281 281 - 251 = 30
15 281 32 266 71063 534 179 x 397
16 313 34 267 71597 536
17 347 36 268 72133 538 53 x 1361 1361 - 1291 = 70
18 383 38 269 72671 540
19 421 40 270 73211 542 179 x 409
20 461 42 271 73753 544 131 x 563 563 - 487 = 76
21 503 44 272 74297 546
22 547 46 273 74843 548
23 593 48 274 75391 550
24 641 50 275 75941 552
25 691 52 276 76493 554
26 743 54 277 77047 556
27 797 56 278 77603 558 71 x 1093
28 853 58 279 78161 560 47 x 1663
29 911 60 280 78721 562
30 971 62 281 79283 564
31 1033 64 282 79847 566
32 1097 66 283 80413 568 97 x 829
33 1163 68 284 80981 570 47 x 1723 1723 - 1663 = 60
34 1231 70 285 81551 572
35 1301 72 286 82123 574 P(n) = 41n^2 - (n - 1) 574 / 41 = 14 41 x 2003 P(n) = 49n^2 + 35n + 2003
36 1373 74 287 82697 576 P(n) = 41n^2 + (n + 1) 41 x 2017 2017 - 2003 = 14 P(n) = 49n^2 + 63n + 2017
37 1447 76 288 83273 578
38 1523 78 289 83851 580 71 x 1181 1181 - 1093 = 88
39 1601 80 290 84431 582
40 1681 82 P(n) = 41n^2 - (n - 1) 82 / 41 = 2 41 x 41 41 41 - 41 = 0 P(n) = n^2 - n + 41 291 85013 584 151 x 563
41 1763 84 P(n) = 41n^2 + (n + 1) 41 x 43 43 43 - 41 = 2 P(n) = n^2 + 3n + 43 292 85597 586
42 1847 86 293 86183 588
43 1933 88 294 86771 590
44 2021 90 43 x 47 47 47 - 43 = 4 295 87361 592 199 x 439
45 2111 92 296 87953 594 281 x 313 313 313 - 281 = 32
46 2203 94 297 88547 596
47 2297 96 298 89143 598 97 x 919 919 - 829 = 90
48 2393 98 299 89741 600 43 x 2087
49 2491 100 47 x 53 53 53 - 47 = 6 300 90341 602 61 x 1481
50 2591 102 301 90943 604 199 x 457
51 2693 104 302 91547 606 43 x 2129 2129 - 2087 = 42
52 2797 106 303 92153 608
53 2903 108 304 92761 610
54 3011 110 305 93371 612
55 3121 112 306 93983 614
56 3233 114 53 x 61 61 61 - 53 = 8 307 94597 616
57 3347 116 308 95213 618
58 3463 118 309 95831 620 61 x 1571 1571 - 1481 = 90
59 3581 120 310 96451 622
60 3701 122 311 97073 624
61 3823 124 312 97697 626 151 x 647 647 - 563 = 84
62 3947 126 313 98323 628
63 4073 128 314 98951 630 53 x 1867
64 4201 130 315 99581 632
65 4331 132 61 x 71 71 71 - 61 = 10 316 100213 634
66 4463 134 317 100847 636
67 4597 136 318 101483 638
68 4733 138 319 102121 640
69 4871 140 320 102761 642
70 5011 142 321 103403 644 53 x 1951 1951 - 1867 = 84
71 5153 144 322 104047 646
72 5297 146 323 104693 648
73 5443 148 324 105341 650
74 5591 150 325 105991 652 83 x 1277
75 5741 152 326 106643 654 47 x 2269
76 5893 154 71 x 83 83 83 - 71 = 12 327 107297 656 P(n) = 41n^2 - (n - 1) 656 / 41 = 16 41 x 2617 P(n) = 64n^2 + 48n + 2617
77 6047 156 328 107953 658 P(n) = 41n^2 + (n + 1) 41 x 2633 2633 - 2617 = 16 P(n) = 64n^2 + 80n + 2633
78 6203 158 329 108611 660 313 x 347 347 347 - 313 = 34
79 6361 160 330 109271 662 113 x 967
80 6521 162 331 109933 664 47 x 2339 2339 - 2269 = 70
81 6683 164 P(n) = 41n^2 - (n - 1) 164 / 41 = 4 41 x 163 P(n) = 4n^2 + 0n + 163 332 110597 666
82 6847 166 P(n) = 41n^2 + (n + 1) 41 x 167 167 - 163 = 4 P(n) = 4n^2 + 8n + 167 333 111263 668
83 7013 168 334 111931 670 173 x 647
84 7181 170 43 x 167 335 112601 672
85 7351 172 336 113273 674 227 x 499
86 7523 174 337 113947 676
87 7697 176 43 x 179 179 - 167 = 12 338 114623 678 83 x 1381 1381 - 1277 = 104
88 7873 178 339 115301 680
89 8051 180 83 x 97 97 97 - 83 = 14 340 115981 682
90 8231 182 341 116663 684
91 8413 184 47 x 179 342 117347 686 43 x 2729
92 8597 186 343 118033 688
93 8783 188 344 118721 690 227 x 523
94 8971 190 345 119411 692 43 x 2777 2777 - 2729 = 48
95 9161 192 346 120103 694
96 9353 194 47 x 199 199 - 179 = 20 347 120797 696 113 x 1069 1069 - 967 = 102
97 9547 196 348 121493 698
98 9743 198 349 122191 700 71 x 1721
99 9941 200 350 122891 702
100 10141 202 351 123593 704
101 10343 204 352 124297 706
102 10547 206 53 x 199 353 125003 708
103 10753 208 354 125711 710
104 10961 210 97 x 113 113 113 - 97 = 16 355 126421 712
105 11171 212 356 127133 714
106 11383 214 357 127847 716 173 x 739 739 - 647 = 92
107 11597 216 358 128563 718
108 11813 218 359 129281 720
109 12031 220 53 x 227 227 - 199 = 28 360 130001 722 71 x 1831 1831 - 1721 = 110
110 12251 222 361 130723 724 61 x 2143
111 12473 224 362 131447 726
112 12697 226 363 132173 728
113 12923 228 364 132901 730 347 x 383 383 383 - 347 = 36
114 13151 230 365 133631 732
115 13381 232 366 134363 734
116 13613 234 367 135097 736 53 x 2549
117 13847 236 61 x 227 368 135833 738 P(n) = 41n^2 - (n - 1) 738 / 41 = 18 41 x 3313 P(n) = 81n^2 + 63n + 3313
118 14083 238 369 136571 740 P(n) = 41n^2 + (n + 1) 41 x 3331 3331 - 3313 = 18 P(n) = 81n^2 + 99n + 3331
119 14321 240 370 137311 742 61 x 2251 2251 - 2143 = 108
120 14561 242 371 138053 744
121 14803 244 113 x 131 131 131 - 113 = 18 372 138797 746
122 15047 246 P(n) = 41n^2 - (n - 1) 246 / 41 = 6 41 x 367 P(n) = 9n^2 + 3n + 367 373 139543 748 47 x 2969
123 15293 248 P(n) = 41n^2 + (n + 1) 41 x 373 373 - 367 = 6 P(n) = 9n^2 + 15n + 373 374 140291 750 53 x 2647 2647 - 2549 = 98
124 15541 250 375 141041 752
125 15791 252 376 141793 754
126 16043 254 61 x 263 263 - 227 = 36 377 142547 756
127 16297 256 43 x 379 378 143303 758 47 x 3049 3049 - 2969 = 80
128 16553 258 379 144061 760
129 16811 260 380 144821 762 97 x 1493
130 17071 262 43 x 397 397 - 379 = 18 381 145583 764 197 x 739
131 17333 264 382 146347 766
132 17597 266 383 147113 768 131 x 1123
133 17863 268 384 147881 770
134 18131 270 385 148651 772 43 x 3457
135 18401 272 386 149423 774
136 18673 274 71 x 263 387 150197 776
137 18947 276 388 150973 778 43 x 3511 3511 - 3457 = 54
138 19223 278 47 x 409 389 151751 780 263 x 577
139 19501 280 390 152531 782
140 19781 282 131 x 151 151 151 - 131 = 20 391 153313 784
141 20063 284 392 154097 786
142 20347 286 393 154883 788
143 20633 288 47 x 439 439 - 409 = 30 394 155671 790
144 20921 290 395 156461 792 97 x 1613 1613 - 1493 = 120
145 21211 292 396 157253 794
146 21503 294 397 158047 796
147 21797 296 71 x 307 307 - 263 = 44 398 158843 798
148 22093 298 399 159641 800 263 x 607
149 22391 300 400 160441 802
150 22691 302 401 161243 804 383 x 421 421 421 - 383 = 38
151 22993 304 402 162047 806 131 x 1237 1237 - 1123 = 114
152 23297 306 403 162853 808
153 23603 308 404 163661 810
154 23911 310 405 164471 812
155 24221 312 53 x 457 406 165283 814 197 x 839 839 - 739 = 100
156 24533 314 407 166097 816 163 x 1019 P(n) = 25n^2 + 5n + 1019
157 24847 316 408 166913 818 83 x 2011
158 25163 318 409 167731 820 P(n) = 41n^2 - (n - 1) 820 / 41 = 20 41 x 4091 P(n) = 100n^2 + 80n + 4091
159 25481 320 83 x 307 410 168551 822 P(n) = 41n^2 + (n + 1) 41 x 4111 4111 - 4091 = 20 P(n) = 100n^2 + 120n + 4111
160 25801 322 411 169373 824
161 26123 324 151 x 173 173 173 - 151 = 22 412 170197 826
162 26447 326 53 x 499 499 - 457 = 42 413 171023 828
163 26773 328 P(n) = 41n^2 - (n - 1) 328 / 41 = 8 41 x 653 P(n) = 16n^2 + 8n + 653 414 171851 830
164 27101 330 P(n) = 41n^2 + (n + 1) 41 x 661 661 - 653 = 8 P(n) = 16n^2 + 24n + 661 415 172681 832
165 27431 332 416 173513 834 167 x 1039 P(n) = 25n^2 + 45n + 1039
166 27763 334 417 174347 836
167 28097 336 418 175183 838 167 x 1049
168 28433 338 419 176021 840
169 28771 340 420 176861 842 47 x 53 x 71 47 x 3763 53 x 3337 71 x 2491
170 29111 342 43 x 677 421 177703 844 83 x 2141 2141 - 2011 = 130
171 29453 344 422 178547 846 61 x 2927
172 29797 346 83 x 359 359 - 307 = 52 423 179393 848
173 30143 348 43 x 701 701 - 677 = 24 424 180241 850
174 30491 350 425 181091 852 47 x 3853 3853 - 3763 = 90
175 30841 352 426 181943 854
176 31193 354 427 182797 856 53 x 3449 3449 - 3337 = 112
177 31547 356 428 183653 858 43 x 4271
178 31903 358 61 x 523 429 184511 860
179 32261 360 430 185371 862
180 32621 362 431 186233 864 43 x 61 x 71 43 x 4331 61 x 3053 71 x 2623 2623 - 2491 = 132
181 32983 364 432 187097 866 223 x 839 4331 - 4271 = 60 3053 - 2927 = 126
182 33347 366 433 187963 868
183 33713 368 434 188831 870
184 34081 370 173 x 197 197 197 - 173 = 24 435 189701 872
185 34451 372 47 x 733 436 190573 874
186 34823 374 97 x 359 437 191447 876
187 35197 376 61 x 577 577 - 523 = 54 438 192323 878
188 35573 378 439 193201 880
189 35951 380 440 194081 882 421 x 461 461 461 - 421 = 40
190 36331 382 47 x 773 773 - 733 = 40 441 194963 884
191 36713 384 442 195847 886 151 x 1297
192 37097 386 443 196733 888 113 x 1741
193 37483 388 444 197621 890
194 37871 390 445 198511 892 179 x 1109
195 38261 392 446 199403 894
196 38653 394 447 200297 896
197 39047 396 448 201193 898
198 39443 398 449 202091 900 179 x 1129
199 39841 400 450 202991 902 P(n) = 41n^2 - (n - 1) 902 / 41 = 22 41 x 4951 P(n) = 121n^2 + 99n + 4951
200 40241 402 451 203893 904 P(n) = 41n^2 + (n + 1) 41 x 4973 4973 - 4951 = 22 P(n) = 121n^2 + 143n + 4973
201 40643 404 97 x 419 419 - 359 = 60 452 204797 906
202 41047 406 453 205703 908
203 41453 408 454 206611 910 307 x 673
204 41861 410 P(n) = 41n^2 - (n - 1) 410 / 41 = 10 41 x 1021 P(n) = 25n^2 + 15n + 1021 455 207521 912
205 42271 412 P(n) = 41n^2 + (n + 1) 41 x 1031 1031 - 1021 = 10 P(n) = 25n^2 + 35n + 1031 456 208433 914
206 42683 414 457 209347 916
207 43097 416 71 x 607 458 210263 918
208 43513 418 53 x 821 459 211181 920 223 x 947 947 - 839 = 108
209 43931 420 197 x 223 223 223 - 197 = 26 460 212101 922 113 x 1877 1877 - 1741 = 136
210 44351 422 461 213023 924
211 44773 424 462 213947 926
212 45197 426 463 214873 928 151 x 1423 1423 - 1297 = 126
213 45623 428 43 x 1061 464 215801 930
214 46051 430 465 216731 932
215 46481 432 53 x 877 877 - 821 = 56 466 217663 934 307 x 709
216 46913 434 43 x 1091 1091 - 1061 = 30 467 218597 936 47 x 4651
217 47347 436 113 x 419 468 219533 938
218 47783 438 71 x 673 673 - 607 = 66 469 220471 940
219 48221 440 470 221411 942
220 48661 442 471 222353 944 43 x 5171
221 49103 444 472 223297 946 47 x 4751 4751 - 4651 = 100
222 49547 446 473 224243 948 53 x 4231
223 49993 448 474 225191 950 43 x 5237 5237 - 5171 = 66
224 50441 450 475 226141 952
225 50891 452 476 227093 954
226 51343 454 477 228047 956 97 x 2351
227 51797 456 478 229003 958
228 52253 458 479 229961 960
229 52711 460 480 230921 962 53 x 4357 4357 - 4231 = 126
230 53171 462 481 231883 964 461 x 503 503 503 - 461 = 42
231 53633 464 482 232847 966
232 54097 466 47 x 1151 483 233813 968 61 x 3833
233 54563 468 484 234781 970
234 55031 470 113 x 487 487 - 419 = 68 485 235751 972
235 55501 472 486 236723 974
236 55973 474 223 x 251 251 251 - 223 = 28 487 237697 976 251 x 947
237 56447 476 47 x 1201 1201 - 1151 = 50 488 238673 978
238 56923 478 489 239651 980 367 x 653
239 57401 480 61 x 941 490 240631 982
240 57881 482 491 241613 984 P(n) = 41n^2 - (n - 1) 984 / 41 = 24 41 x 71 x 83 41 x 5893 71 x 3403 83 x 2911 P(n) = 144n^2 + 120n + 5893
241 58363 484 492 242597 986 P(n) = 41n^2 + (n + 1) 41 x 61 x 97 41 x 5917 61 x 3977 97 x 2501 2501 - 2351 = 150 P(n) = 144n^2 + 168n + 5917
242 58847 486 83 x 709 493 243583 988 3977 - 3833 = 144
243 59333 488 494 244571 990 199 x 1229
244 59821 490 163 x 367 P(n) = 9n^2 + 3n + 367 495 245561 992
245 60311 492 P(n) = 41n^2 - (n - 1) 492 / 41 = 12 41 x 1471 P(n) = 36n^2 + 24n + 1471 496 246553 994 373 x 661
246 60803 494 P(n) = 41n^2 + (n + 1) 41 x 1483 1483 - 1471 = 12 P(n) = 36n^2 + 48n + 1483 497 247547 996
247 61297 496 498 248543 998
248 61793 498 61 x 1013 1013 - 941 = 72 499 249541 1000
249 62291 500 167 x 373 P(n) = 9n^2 + 15n + 373 500 250541 199 x 1259
250 62791 502

Composite Number Polynomials (A Product Of Two Prime-Generating Polynomials) Related To P(n) = n^2 + n + 41
The Euler (1772) Quadratic Polynomial, P(n) = n^2 + n + 41, produces not only prime numbers but also composite numbers.
P(n) = n^2 + n + 41
P(n) = 41n^2 - (n - 1) P(n) = 41n^2 + (n + 1)
"First Generation" Composite Number Polynomials "First Generation" Composite Number Polynomials
P(n) = (n^2 + n + 41) x (n^2 - n + 41) P(n) = (n^2 + n + 41) x (n^2 + 3n + 43)
P(n) = n^4 + 81n^2 + 1681 P(n) = n^4 + 4n^3 + 87n^2 + 166n + 1763
P(n) = (n^2 + n + 41) x (4n^2 + 163) P(n) = (n^2 + n + 41) x (4n^2 + 8n + 167)
P(n) = 4n^4 + 4n^3 + 327n^2 + 163n + 6683 P(n) = 4n^4 + 12n^3 + 339n^2 + 495n + 6847
P(n) = (n^2 + n + 41) x (9n^2 + 3n + 367) P(n) = (n^2 + n + 41) x (9n^2 + 15n + 373)
P(n) = 9n^4 + 12n^3 + 739n^2 + 490n + 15047 P(n) = 9n^4 + 24n^3 + 757n^2 + 988n + 15293
P(n) = (n^2 + n + 41) x (16n^2 + 8n + 653) P(n) = (n^2 + n + 41) x (16n^2 + 24n + 661)
P(n) = 16n^4 + 24n^3 + 1317n^2 + 981n + 26773 P(n) = 16n^4 + 40n^3 + 1341n^2 + 1645n + 27101
P(n) = (n^2 + n + 41) x (25n^2 + 15n + 1021) P(n) = (n^2 + n + 41) x (25n^2 + 35n + 1031)
P(n) = 25n^4 + 40n^3 + 2061n^2 + 1636n + 41861 P(n) = 25n^4 + 60n^3 + 2091n^2 + 2466n + 42271
P(n) = (n^2 + n + 41) x (36n^2 + 24n + 1471) P(n) = (n^2 + n + 41) x (36n^2 + 48n + 1483)
P(n) = (n^2 + n + 41) x (49n^2 + 35n + 2003) P(n) = (n^2 + n + 41) x (49n^2 + 63n + 2017)
P(n) = (n^2 + n + 41) x (64n^2 + 48n + 2617) P(n) = (n^2 + n + 41) x (64n^2 + 80n + 2633)
P(n) = (n^2 + n + 41) x (81n^2 + 63n + 3313) P(n) = (n^2 + n + 41) x (81n^2 + 99n + 3331)
P(n) = (n^2 + n + 41) x (100n^2 + 80n + 4091) P(n) = (n^2 + n + 41) x (100n^2 + 120n + 4111)
P(n) = (n^2 + n + 41) x (121n^2 + 99n + 4951) P(n) = (n^2 + n + 41) x (121n^2 + 143n + 4973)

Composite Number Generating Polynomials
"First Generation" Composite Number Polynomials Related To P(n) = n^2 + n + 41
n P(n) = (n^2 + n + 41) x (n^2 - n + 41) n^2 x n^2 + n^2 x -n + n^2 x 41 + n x n^2 + n x -n + n x 41 + 41 x n^2 + 41 x -n + 41 x 41 n P(n) = (n^2 + n + 41) x (n^2 + 3n + 43) n^2 x n^2 + n^2 x 3n + n^2 x 43 + n x n^2 + n x 3n + n x 43 + 41 x n^2 + 41 x 3n + 41 x 43
41 x 41 0 41 x 41 n^4 + -n^3 + 41n^2 + n^3 + -n^2 + 41n + 41n^2 + -41n + 1681 0 41 x 43 n^4 + 3n^3 + 43n^2 + n^3 + 3n^2 + 43n + 41n^2 + 123n + 1763
41 x 43 1 43 x 41 1 43 x 47
43 x 47 2 47 x 43 P(n) = n^4 + 81n^2 + 1681 2 47 x 53 P(n) = n^4 + 4n^3 + 87n^2 + 166n + 1763
47 x 53 3 53 x 47 3 53 x 61
53 x 61 4 61 x 53 n = 13 28561 + 13689 + 1681 = 43931 4 61 x 71 n = 11 14641 + 5324 + 10527 + 1826 + 1763 = 34081
61 x 71 5 71 x 61 5 71 x 83
71 x 83 6 83 x 71 223 x 197 = 43931 6 83 x 97 173 x 197 = 34081
83 x 97 7 97 x 83 7 97 x 113
97 x 113 8 113 x 97 8 113 x 131
113 x 131 9 131 x 113 9 131 x 151
131 x 151 10 151 x 131 10 151 x 173
151 x 173 11 173 x 151 11 173 x 197
173 x 197 12 197 x 173 12 197 x 223
197 x 223 13 223 x 197 13 223 x 251
223 x 251 14 251 x 223 14 251 x 281
251 x 281 15 281 x 251 15 281 x 313
281 x 313 16 313 x 281 16 313 x 347
313 x 347 17 347 x 313 17 347 x 383
347 x 383 18 383 x 347 18 383 x 421
383 x 421 19 421 x 383 19 421 x 461
421 x 461 20 461 x 421 20 461 x 503
461 x 503 21 503 x 461
n P(n) = (n^2 + n + 41) x (4n^2 + 163) n^2 x 4n^2 + n^2 x 163 + n x 4n^2 + n x 163 + 41 x 4n^2 + 41 x 163 n P(n) = (n^2 + n + 41) x (9n^2 + 3n + 367) n^2 x 9n^2 + n^2 x 3n + n^2 x 367 + n x 9n^2 + n x 3n + n x 367 + 41 x 9n^2 + 41 x 3n + 41 x 367
41 x 163 0 41 x 163 4n^4 + 163n^2 + 4n^3 + 163n + 164n^2 + 6683 41 x 367 0 41 x 367 9n^4 + 3n^3 + 367n^2 + 9n^3 + 3n^2 + 367n + 369n^2 + 123n + 15047
41 x 167 1 43 x 167 41 x 373 1 43 x 379
43 x 167 2 47 x 179 P(n) = 4n^4 + 4n^3 + 327n^2 + 163n + 6683 43 x 379 2 47 x 409 P(n) = 9n^4 + 12n^3 + 739n^2 + 490n + 15047
43 x 179 3 53 x 199 43 x 397 3 53 x 457
47 x 179 4 61 x 227 n = 11 58564 + 5324 + 39567 + 1793 + 6683 = 111931 47 x 409 4 61 x 523 n = 7 21609 + 4116 + 36211 + 3430 + 15047 = 80413
47 x 199 5 71 x 263 47 x 439 5 71 x 607
53 x 199 6 83 x 307 173 x 647 = 111931 53 x 457 6 83 x 709 97 x 829 = 80413
53 x 227 7 97 x 359 53 x 499 7 97 x 829
61 x 227 8 113 x 419 61 x 523 8 113 x 967
61 x 263 9 131 x 487 61 x 577 9 131 x 1123
71 x 263 10 151 x 563 71 x 607 10 151 x 1297
71 x 307 11 173 x 647 71 x 673
83 x 307 12 197 x 739 83 x 709
83 x 359 13 223 x 839 83 x 787
97 x 359 97 x 829
97 x 419 97 x 919
113 x 419 113 x 967 n P(n) = (n^2 + n + 41) x (9n^2 + 15n + 373) n^2 x 9n^2 + n^2 x 15n + n^2 x 373 + n x 9n^2 + n x 15n + n x 373 + 41 x 9n^2 + 41 x 15n + 41 x 373
113 x 487 113 x 1069
131 x 487 131 x 1123 0 41 x 373 9n^4 + 15n^3 + 373n^2 + 9n^3 + 15n^2 + 373n + 369n^2 + 615n + 15293
131 x 563 n P(n) = (n^2 + n + 41) x (4n^2 + 8n + 167) n^2 x 4n^2 + n^2 x 8n + n^2 x 167 + n x 4n^2 + n x 8n + n x 167 + 41 x 4n^2 + 41 x 8n + 41 x 167 131 x 1237 1 43 x 397
151 x 563 151 x 1297 2 47 x 439 P(n) = 9n^4 + 24n^3 + 757n^2 + 988n + 15293
151 x 647 0 41 x 167 4n^4 + 8n^3 + 167n^2 + 4n^3 + 8n^2 + 167n + 164n^2 + 328n + 6847 151 x 1423 3 53 x 499
173 x 647 1 43 x 179 4 61 x 577 n = 5 5625 + 3000 + 18925 + 4940 + 15293 = 47783
173 x 739 2 47 x 199 P(n) = 4n^4 + 12n^3 + 339n^2 + 495n + 6847 5 71 x 673
197 x 739 3 53 x 227 6 83 x 787 71 x 673 = 47783
197 x 839 4 61 x 263 n = 9 26244 + 8748 + 27459 + 4455 + 6847 = 73753 7 97 x 919
223 x 839 5 71 x 307 8 113 x 1069
223 x 947 6 83 x 359 131 x 563 = 73753 9 131 x 1237
7 97 x 419 10 151 x 1423
8 113 x 487
9 131 x 563
10 151 x 647
11 173 x 739
12 197 x 839
13 223 x 947
n P(n) = (n^2 + n + 41) x (16n^2 + 8n + 653) n^2 x 16n^2 + n^2 x 8n + n^2 x 653 + n x 16n^2 + n x 8n + n x 653 + 41 x 16n^2 + 41 x 8n + 41 x 653 n P(n) = (n^2 + n + 41) x (25n^2 + 15n + 1021) n^2 x 25n^2 + n^2 x 15n + n^2 x 1021 + n x 25n^2 + n x 15n + n x 1021 + 41 x 25n^2 + 41 x 15n + 41 x 1021
41 x 653 0 41 x 653 16n^4 + 8n^3 + 653n^2 + 16n^3 + 8n^2 + 653n + 656n^2 + 328n + 26773 41 x 1021 0 41 x 1021 25n^4 + 15n^3 + 1021n^2 + 25n^3 + 15n^2 + 1021n + 1025n^2 + 615n + 41861
41 x 661 1 43 x 677 41 x 1031 1 43 x 1061
43 x 677 2 47 x 733 P(n) = 16n^4 + 24n^3 + 1317n^2 + 981n + 26773 43 x 1061 2 47 x 1151 P(n) = 25n^4 + 40n^3 + 2061n^2 + 1636n + 41861
43 x 701 3 53 x 821 43 x 1091 3 53 x 1291
47 x 733 4 61 x 941 n = 7 38416 + 8232 + 64533 + 6867 + 26773 = 144821 47 x 1151 4 61 x 1481 n = 7 60025 + 13720 + 100989 + 11452 + 41861 = 228047
47 x 773 5 71 x 1093 47 x 1201 5 71 x 1721
53 x 821 6 83 x 1277 97 x 1493 = 144821 53 x 1291 6 83 x 2011 97 x 2351 = 228047
53 x 877 7 97 x 1493 53 x 1361 7 97 x 2351
61 x 941 8 113 x 1741 61 x 1481
61 x 1013 61 x 1571
71 x 1093 71 x 1721
71 x 1181 71 x 1831
83 x 1277 83 x 2011
83 x 1381 83 x 2141
97 x 1493 n P(n) = (n^2 + n + 41) x (16n^2 + 24n + 661) n^2 x 16n^2 + n^2 x 24n + n^2 x 661 + n x 16n^2 + n x 24n + n x 661 + 41 x 16n^2 + 41 x 24n + 41 x 661 97 x 2351 n P(n) = (n^2 + n + 41) x (25n^2 + 35n + 1031) n^2 x 25n^2 + n^2 x 35n + n^2 x 1031 + n x 25n^2 + n x 35n + n x 1031 + 41 x 25n^2 + 41 x 35n + 41 x 1031
97 x 1613 97 x 2501
113 x 1741 0 41 x 661 16n^4 + 24n^3 + 661n^2 + 16n^3 + 24n^2 + 661n + 656n^2 + 984n + 27101 0 41 x 1031 25n^4 + 35n^3 + 1031n^2 + 25n^3 + 35n^2 + 1031n + 1025n^2 + 1435n + 42271
113 x 1877 1 43 x 701 1 43 x 1091
2 47 x 773 P(n) = 16n^4 + 40n^3 + 1341n^2 + 1645n + 27101 2 47 x 1201 P(n) = 25n^4 + 60n^3 + 2091n^2 + 2466n + 42271
3 53 x 877 3 53 x 1361
4 61 x 1013 n = 7 38416 + 13720 + 65709 + 11515 + 27101 = 156461 4 61 x 1571 n = 7 60025 + 20580 + 102459 + 17262 + 42271 = 242597
5 71 x 1181 5 71 x 1831
6 83 x 1381 97 x 1613 = 156461 6 83 x 2141 97 x 2501 = 242597
7 97 x 1613 7 97 x 2501
8 113 x 1877
"Second Generation" Composite Number Polynomials Related To P(n) = n^2 + n + 41
n (4n^2 + 8n + 167) x (9n^2 + 15n + 373) n (4n^2 + 163) x (25n^2 + 5n + 1019)
163 x 367 0 167 x 373 163 x 1019 0 163 x 1019
167 x 373 1 179 x 397 167 x 1039 1 167 x 1049
167 x 379 2 199 x 439 167 x 1049 2 179 x 1129
179 x 397 3 227 x 499 179 x 1109 3 199 x 1259
179 x 409 4 263 x 577 179 x 1129
199 x 439 5 307 x 673 199 x 1229
199 x 457 199 x 1259
227 x 499
227 x 523 n (4n^2 + 8n + 167) x (25n^2 + 45n + 1039)
263 x 577
263 x 607 n (4n^2 + 163) x (9n^2 + 3n + 367) 0 167 x 1039
307 x 673 1 179 x 1109
307 x 709 0 163 x 367 2 199 x 1229
1 167 x 379
2 179 x 409
3 199 x 457
4 227 x 523
5 263 x 607
6 307 x 709

Quadratic Prime-Generating Polynomial Related To P(n) = n^2 + n + 41
n n^2 P(n) = 41n^2 - (n - 1) n n^2 P(n) = 41n^2 + (n + 1)
0 0 1 0 0 1
1 1 41 1 1 43
2 4 163 2 4 167
3 9 367 3 9 373
4 16 653 4 16 661
5 25 1021 5 25 1031
6 36 1471 6 36 1483
7 49 2003 7 49 2017
8 64 2617 8 64 2633
9 81 3313 9 81 3331
10 100 4091 10 100 4111
11 121 4951 11 121 4973
12 144 5893 71 x 83 12 144 5917 61 x 97
13 169 6917 13 169 6943 53 x 131
14 196 8023 71 x 113 14 196 8051 83 x 97
15 225 9211 61 x 151 15 225 9241
16 256 10481 47 x 223 16 256 10513
17 289 11833 17 289 11867
18 324 13267 18 324 13303 53 x 251
19 361 14783 19 361 14821
20 400 16381 20 400 16421
21 441 18061 21 441 18103 43 x 421
22 484 19823 43 x 461 22 484 19867
23 529 21667 47 x 461 23 529 21713
24 576 23593 24 576 23641 47 x 503
25 625 25601 25 625 25651 113 x 227
26 676 27691 26 676 27743
27 729 29863 27 729 29917
28 784 32117 28 784 32173
29 841 34453 131 x 263 29 841 34511
30 900 36871 30 900 36931
31 961 39371 31 961 39433 47 x 839
32 1024 41953 32 1024 42017
33 1089 44617 33 1089 44683
34 1156 47363 34 1156 47431
35 1225 50191 53 x 947 35 1225 50261
36 1296 53101 36 1296 53173
37 1369 56093 37 1369 56167
38 1444 59167 38 1444 59243
39 1521 62323 39 1521 62401
40 1600 65561 53 x 1237 40 1600 65641 41 x 1601
41 1681 68881 41 1681 68963
42 1764 72283 41 x 41 x 43 41 x 1763 43 x 1681 42 1764 72367
43 1849 75767 43 1849 75853
44 1936 79333 44 1936 79421 43 x 1847
45 2025 82981 45 2025 83071
46 2116 86711 46 2116 86803 61 x 1423
47 2209 90523 47 2209 90617
48 2304 94417 263 x 359 48 2304 94513
49 2401 98393 61 x 1613 49 2401 98491
50 2500 102451 50 2500 102551
51 2601 106591 51 2601 106693
52 2704 110813 52 2704 110917
53 2809 115117 53 2809 115223
54 2916 119503 54 2916 119611
55 3025 123971 151 x 821 55 3025 124081 167 x 743
56 3136 128521 56 3136 128633 307 x 419
57 3249 133153 57 3249 133267 71 x 1877
58 3364 137867 58 3364 137983
59 3481 142663 179 x 797 59 3481 142781 71 x 2011
60 3600 147541 60 3600 147661
61 3721 152501 61 3721 152623
62 3844 157543 62 3844 157667
63 3969 162667 47 x 3461 63 3969 162793 173 x 941
64 4096 167873 64 4096 168001 43 x 3907
65 4225 173161 43 x 4027 65 4225 173291
66 4356 178531 66 4356 178663 53 x 3371
67 4489 183983 251 x 733 67 4489 184117
68 4624 189517 68 4624 189653
69 4761 195133 83 x 2351 69 4761 195271
70 4900 200831 47 x 4273 70 4900 200971
71 5041 206611 307 x 673 71 5041 206753 47 x 53 x 83 47 x 4399 53 x 3901 83 x 2491
72 5184 212473 179 x 1187 72 5184 212617 173 x 1229
73 5329 218417 73 5329 218563 61 x 3583
74 5476 224443 74 5476 224591
75 5625 230551 75 5625 230701 281 x 821
76 5776 236741 61 x 3881 76 5776 236893
77 5929 243013 487 x 499 77 5929 243167
78 6084 249367 78 6084 249523 47 x 5309
79 6241 255803 79 6241 255961
80 6400 262321 80 6400 262481 199 x 1319
81 6561 268921 81 6561 269083 41 x 6563
82 6724 275603 197 x 1399 82 6724 275767
83 6889 282367 41 x 71 x 97 83 6889 282533 359 x 787
84 7056 289213 84 7056 289381
85 7225 296141 43 x 71 x 97 85 7225 296311 199 x 1489
86 7396 303151 86 7396 303323
87 7569 310243 87 7569 310417 43 x 7219
88 7744 317417 53 x 53 x 113 53 x 5989 113 x 2809 88 7744 317593
89 7921 324673 89 7921 324851 563 x 577
90 8100 332011 90 8100 332191
91 8281 339431 197 x 1723 91 8281 339613
92 8464 346933 92 8464 347117 313 x 1109
93 8649 354517 53 x 6689 93 8649 354703
94 8836 362183 373 x 971 94 8836 362371
95 9025 369931 83 x 4457 95 9025 370121
96 9216 377761 96 9216 377953 151 x 2503
97 9409 385673 227 x 1699 97 9409 385867 83 x 4649
98 9604 393667 98 9604 393863
99 9801 401743 99 9801 401941 113 x 3557
100 10000 409901 100 10000 410101 397 x 1033
101 10201 418141 173 x 2417 101 10201 418343
102 10404 426463 347 x 1229 102 10404 426667 131 x 3257
103 10609 434867 103 10609 435073 223 x 1951
104 10816 443353 104 10816 443561
105 11025 451921 105 11025 452131
106 11236 460571 106 11236 460783 197 x 2339
107 11449 469303 107 11449 469517 43 x 61 x 179 43 x 10919 61 x 7697 179 x 2623
108 11664 478117 43 x 11119 108 11664 478333 577 x 829
109 11881 487013 109 11881 487231 97 x 5023
110 12100 495991 47 x 61 x 173 47 x 10553 61 x 8131 173 x 2867 110 12100 496211
111 12321 505051 111 12321 505273 97 x 5209
112 12544 514193 167 x 3079 112 12544 514417
113 12769 523417 113 12769 523643 397 x 1319
114 12996 532723 199 x 2677 114 12996 532951
115 13225 542111 115 13225 542341 197 x 2753
116 13456 551581 116 13456 551813
117 13689 561133 47 x 11939 117 13689 561367
118 13924 570767 131 x 4357 118 13924 571003 47 x 12149
119 14161 580483 199 x 2917 119 14161 580721 53 x 10957
120 14400 590281 223 x 2647 120 14400 590521 179 x 3299
121 14641 600161 383 x 1567 121 14641 600403
122 14884 610123 122 14884 610367 41 x 14887
123 15129 620167 281 x 2207 123 15129 620413
124 15376 630293 41 x 15373 124 15376 630541 53 x 11897
125 15625 640501 439 x 1459 125 15625 640751 47 x 13633
126 15876 650791 673 x 967 126 15876 651043
127 16129 661163 113 x 5851 127 16129 661417
128 16384 671617 43 x 15619 128 16384 671873 71 x 9463
129 16641 682153 129 16641 682411
130 16900 692771 130 16900 693031 43 x 71 x 227 43 x 16117 71 x 9761 227 x 3053
131 17161 703471 131 17161 703733
132 17424 714253 439 x 1627 132 17424 714517
133 17689 725117 661 x 1097 133 17689 725383 421 x 1723
134 17956 736063 134 17956 736331 61 x 12071
135 18225 747091 347 x 2153 135 18225 747361
136 18496 758201 136 18496 758473 151 x 5023
137 18769 769393 61 x 12613 137 18769 769667 313 x 2459
138 19044 780667 138 19044 780943 113 x 6911
139 19321 792023 139 19321 792301
140 19600 803461 140 19600 803741
141 19881 814981 53 x 15377 141 19881 815263 701 x 1163
142 20164 826583 142 20164 826867
143 20449 838267 607 x 1381 143 20449 838553
144 20736 850033 144 20736 850321 131 x 6491
145 21025 861881 145 21025 862171
146 21316 873811 53 x 16487 146 21316 874103
147 21609 885823 147 21609 886117
148 21904 897917 419 x 2143 148 21904 898213
149 22201 910093 149 22201 910391 383 x 2377
150 22500 922351 150 22500 922651 43 x 43 x 499 43 x 21457 499 x 1849
94 Prime Numbers 57 Composite Numbers 91 Prime Numbers 60 Composite Numbers

Formula "P(m) = m^2(n^2) + (m^2 ± 2m)n + [41m^2 ± (m ± 1)]": This Formula Generates The Quadratic Prime-Generating Polynomials Related To Euler Quadratic Polynomial, P(n) = n^2 + n + 41
P(m) = m^2(n^2) + (m^2 - 2m)n + [41m^2 - (m - 1)] P(m) = m^2(n^2) + (m^2 + 2m)n + [41m^2 + (m + 1)]
m m^2 41m^2 - (m - 1) 41m^2 - (m - 1) m^2(n^2) + (m^2 - 2m)n + [41m^2 - (m - 1)] m m^2 41m^2 + (m + 1) 41m^2 + (m + 1) m^2(n^2) + (m^2 + 2m)n + [41m^2 + (m + 1)]
0 0 41 x 0 - -1 1 P(n) = 0n^2 + 0n + 1 0n -1 1 41 x 1 + 0 41 P(n) = n^2 - n + 41 -1n
1 1
1 1 41 x 1 - 0 41 P(n) = n^2 - n + 41 -1n 0 0 41 x 0 + 1 1 P(n) = 0n^2 + 0n + 1 0n
1 3
2 4 41 x 4 - 1 163 P(n) = 4n^2 + 0n + 163 0n 1 1 41 x 1 + 2 43 P(n) = n^2 + 3n + 43 3n
3 5
3 9 41 x 9 - 2 367 P(n) = 9n^2 + 3n + 367 3n 2 4 41 x 4 + 3 167 P(n) = 4n^2 + 8n + 167 8n
5 7
4 16 41 x 16 - 3 653 P(n) = 16n^2 + 8n + 653 8n 3 9 41 x 9 + 4 373 P(n) = 9n^2 + 15n + 373 15n
7 9
5 25 41 x 25 - 4 1021 P(n) = 25n^2 + 15n + 1021 15n 4 16 41 x 16 + 5 661 P(n) = 16n^2 + 24n + 661 24n
9 11
6 36 41 x 36 - 5 1471 P(n) = 36n^2 + 24n + 1471 24n 5 25 41 x 25 + 6 1031 P(n) = 25n^2 + 35n + 1031 35n
11 13
7 49 41 x 49 - 6 2003 P(n) = 49n^2 + 35n + 2003 35n 6 36 41 x 36 + 7 1483 P(n) = 36n^2 + 48n + 1483 48n
13 15
8 64 41 x 64 - 7 2617 P(n) = 64n^2 + 48n + 2617 48n 7 49 41 x 49 + 8 2017 P(n) = 49n^2 + 63n + 2017 63n
15 17
9 81 41 x 81 - 8 3313 P(n) = 81n^2 + 63n + 3313 63n 8 64 41 x 64 + 9 2633 P(n) = 64n^2 + 80n + 2633 80n
17 19
10 100 41 x 100 - 9 4091 P(n) = 100n^2 + 80n + 4091 80n 9 81 41 x 81 + 10 3331 P(n) = 81n^2 + 99n + 3331 99n
19 21
11 121 41 x 121 - 10 4951 P(n) = 121n^2 + 99n + 4951 99n 10 100 41 x 100 + 11 4111 P(n) = 100n^2 + 120n + 4111 120n
21 23
12 144 41 x 144 - 11 5893 71 x 83 P(n) = 144n^2 + 120n + 5893 120n 11 121 41 x 121 + 12 4973 P(n) = 121n^2 + 143n + 4973 143n
23 25
13 169 41 x 169 - 12 6917 P(n) = 169n^2 + 143n + 6917 143n 12 144 41 x 144 + 13 5917 61 x 97 P(n) = 144n^2 + 168n + 5917 168n
25 27
14 196 41 x 196 - 13 8023 71 x 113 P(n) = 196n^2 + 168n + 8023 168n 13 169 41 x 169 + 14 6943 53 x 131 P(n) = 169n^2 + 195n + 6943 195n
27 29
15 225 41 x 225 - 14 9211 61 x 151 P(n) = 225n^2 + 195n + 9211 195n 14 196 41 x 196 +15 8051 83 x 97 P(n) = 196n^2 + 224n + 8051 224n
29 31
16 256 41 x 256 - 15 10481 47 x 223 P(n) = 256n^2 + 224n + 10481 224n 15 225 41 x 225 + 16 9241 P(n) = 225n^2 + 255n + 9241 255n
31 33
17 289 41 x 289 - 16 11833 P(n) = 289n^2 + 255n + 11833 255n 16 256 41 x 256 + 17 10513 P(n) = 256n^2 + 288n + 10513 288n
33 35
18 324 41 x 324 - 17 13267 P(n) = 324n^2 + 288n + 13267 288n 17 289 41 x 289 + 18 11867 P(n) = 289n^2 + 323n + 11867 323n
35 37
19 361 41 x 361 - 18 14783 P(n) = 361n^2 + 323n + 14783 323n 18 324 41 x 324 + 19 13303 53 x 251 P(n) = 324n^2 + 360n + 13303 360n
37 39
20 400 41 x 400 - 19 16381 P(n) = 400n^2 + 360n + 16381 360n 19 361 41 x 361 + 20 14821 P(n) = 361n^2 + 399n + 14821 399n
39 41
21 441 41 x 441 - 20 18061 P(n) = 441n^2 + 399n + 18061 399n 20 400 41 x 400 + 21 16421 P(n) = 400n^2 + 440n + 16421 440n
41 43
22 484 41 x 484 - 21 19823 43 x 461 P(n) = 484n^2 + 440n + 19823 440n 21 441 41 x 441 + 22 18103 43 x 421 P(n) = 441n^2 + 483n + 18103 483n
43 45
23 529 41 x 529 - 22 21667 47 x 461 P(n) = 529n^2 + 483n + 21667 483n 22 484 41 x 484 + 23 19867 P(n) = 484n^2 + 528n + 19867 528n
45 47
24 576 41 x 576 - 23 23593 P(n) = 576n^2 + 528n + 23593 528n 23 529 41 x 529 + 24 21713 P(n) = 529n^2 + 575n + 21713 575n
47 49
25 625 41 x 625 - 24 25601 P(n) = 625n^2 + 575n + 25601 575n 24 576 41 x 576 + 25 23641 47 x 503 P(n) = 576n^2 + 624n + 23641 624n
49 51
26 676 41 x 676 - 25 27691 P(n) = 676n^2 + 624n + 27691 624n 25 625 41 x 625 + 26 25651 113 x 227 P(n) = 625n^2 + 675n + 25651 675n
51 53
27 729 41 x 729 - 26 29863 P(n) = 729n^2 + 675n + 29863 675n 26 676 41 x 676 + 27 27743 P(n) = 676n^2 + 728n + 27743 728n
53 55
28 784 41 x 784 - 27 32117 P(n) = 784n^2 + 728n + 32117 728n 27 729 41 x 729 + 28 29917 P(n) = 729n^2 + 783n + 29917 783n
55 57
29 841 41 x 841 - 28 34453 131 x 263 P(n) = 841n^2 + 783n + 34453 783n 28 784 41 x 784 + 29 32173 P(n) = 784n^2 + 840n + 32173 840n
57 59
30 900 41 x 900 - 29 36871 P(n) = 900n^2 + 840n + 36871 840n 29 841 41 x 841 + 30 34511 P(n) = 841n^2 + 899n + 34511 899n
59 61
31 961 41 x 31^2 - 30 39371 P(n) = 961n^2 + 899n + 39371 899n 30 900 41 x 900 + 31 36931 P(n) = 900n^2 + 960n + 36931 960n
61 63
32 1024 41 x 32^2 - 31 41953 P(n) = 1024n^2 + 960n + 41953 960n 31 961 41 x 31^2 + 32 39433 47 x 839 P(n) = 961n^2 + 1023n + 39433 1023n
63 65
33 1089 41 x 33^2 - 32 44617 P(n) = 1089n^2 + 1023n + 44617 1023n 32 1024 41 x 32^2 + 33 42017 P(n) = 1024n^2 + 1088n + 42017 1088n
65 67
34 1156 41 x 34^2 - 33 47363 P(n) = 1156n^2 + 1088n + 47363 1088n 33 1089 41 x 33^2 + 34 44683 P(n) = 1089n^2 + 1155n + 44683 1155n
67 69
35 1225 41 x 35^2 - 34 50191 53 x 947 P(n) = 1225n^2 + 1155n + 50191 1155n 34 1156 41 x 34^2 + 35 47431 P(n) = 1156n^2 + 1224n + 47431 1224n
69 71
36 1296 41 x 36^2 - 35 53101 P(n) = 1296n^2 + 1224n + 53101 1224n 35 1225 41 x 35^2 + 36 50261 P(n) = 1225n^2 + 1295n + 50261 1295n
71 73
37 1369 41 x 37^2 - 36 56093 P(n) = 1369n^2 + 1295n + 56093 1295n 36 1296 41 x 36^2 + 37 53173 P(n) = 1296n^2 + 1368n + 53173 1368n
73 75
38 1444 41 x 38^2 - 37 59167 P(n) = 1444n^2 + 1368n + 59167 1368n 37 1369 41 x 37^2 + 38 56167 P(n) = 1369n^2 + 1443n + 56167 1443n
75 77
39 1521 41 x 39^2 - 38 62323 P(n) = 1521n^2 + 1443n + 62323 1443n 38 1444 41 x 38^2 + 39 59243 P(n) = 1444n^2 + 1520n + 59243 1520n
77 79
40 1600 41 x 40^2 - 39 65561 53 x 1237 P(n) = 1600n^2 + 1520n + 65561 1520n 39 1521 41 x 39^2 + 40 62401 P(n) = 1521n^2 + 1599n + 62401 1599n
79 81
41 1681 41 x 41^2 - 40 68881 P(n) = 1681n^2 + 1599n + 68881 1599n 40 1600 41 x 40^2 + 41 65641 41 x 1601 P(n) = 1600n^2 + 1680n + 65641 1680n
81 83
42 1764 41 x 42^2 - 41 72283 41 x 41 x 43 P(n) = 1764n^2 + 1680n + 72283 1680n 41 1681 41 x 41^2 + 42 68963 P(n) = 1681n^2 + 1763n + 68963 1763n
83 85
43 1849 41 x 43^2 - 42 75767 P(n) = 1849n^2 + 1763n + 75767 1763n 42 1764 41 x 42^2 + 43 72367 P(n) = 1764n^2 + 1848n + 72367 1848n
85 87
44 1936 41 x 44^2 - 43 79333 P(n) = 1936n^2 + 1848n + 79333 1848n 43 1849 41 x 43^2 + 44 75853 P(n) = 1849n^2 + 1935n + 75853 1935n
87 89
45 2025 41 x 45^2 - 44 82981 P(n) = 2025n^2 + 1935n + 82981 1935n 44 1936 41 x 44^2 + 45 79421 43 x 1847 P(n) = 1936n^2 + 2024n + 79421 2024n
89 91
46 2116 41 x 46^2 - 45 86711 P(n) = 2116n^2 + 2024n + 86711 2024n 45 2025 41 x 45^2 + 46 83071 P(n) = 2025n^2 + 2115n + 83071 2115n
91 93
47 2209 41 x 47^2 - 46 90523 P(n) = 2209n^2 + 2115n + 90523 2115n 46 2116 41 x 46^2 + 47 86803 61 x 1423 P(n) = 2116n^2 + 2208n + 86803 2208n
93 95
48 2304 41 x 48^2 - 47 94417 263 x 359 P(n) = 2304n^2 + 2208n + 94417 2208n 47 2209 41 x 47^2 + 48 90617 P(n) = 2209n^2 + 2303n + 90617 2303n
95 97
49 2401 41 x 49^2 - 48 98393 61 x 1613 P(n) = 2401n^2 + 2303n + 98393 2303n 48 2304 41 x 48^2 + 49 94513 P(n) = 2304n^2 + 2400n + 94513 2400n
97 99
50 2500 41 x 50^2 - 49 102451 P(n) = 2500n^2 + 2400n + 102451 2400n 49 2401 41 x 49^2 + 50 98491 P(n) = 2401n^2 + 2499n + 98491 2499n
99 101
51 2601 41 x 51^2 - 50 106591 P(n) = 2601n^2 + 2499n + 106591 2499n 50 2500 41 x 50^2 + 51 102551 P(n) = 2500n^2 + 2600n + 102551 2600n
101 103
52 2704 41 x 52^2 - 51 110813 P(n) = 2704n^2 + 2600n + 110813 2600n 51 2601 41 x 51^2 + 52 106693 P(n) = 2601n^2 + 2703n + 106693 2703n
103 105
53 2809 41 x 53^2 - 52 115117 P(n) = 2809n^2 + 2703n + 115117 2703n 52 2704 41 x 52^2 + 53 110917 P(n) = 2704n^2 + 2808n + 110917 2808n
105 107
54 2916 41 x 54^2 - 53 119503 P(n) = 2916n^2 +2808n + 119503 2808n 53 2809 41 x 53^2 + 54 115223 P(n) = 2809n^2 + 2915n + 115223 2915n
107 109
55 3025 41 x 55^2 - 54 123971 151 x 821 P(n) = 3025n^2 + 2915n + 123971 2915n 54 2916 41 x 54^2 + 55 119611 P(n) = 2916n^2 + 3024n + 119611 3024n
109 111
56 3136 41 x 56^2 - 55 128521 P(n) = 3136n^2 + 3024n + 128521 3024n 55 3025 41 x 55^2 + 56 124081 167 x 743 P(n) = 3025n^2 + 3135n + 124081 3135n
111 113
57 3249 41 x 57^2 - 56 133153 P(n) = 3249n^2 + 3135n + 133153 3135n 56 3136 41 x 56^2 + 57 128633 307 x 419 P(n) = 3136n^2 + 3248n + 128633 3248n
113 115
58 3364 41 x 58^2 - 57 137867 P(n) = 3364n^2 + 3248n + 137867 3248n 57 3249 41 x 57^2 + 58 133267 71 x 1877 P(n) = 3249n^2 + 3363n + 133267 3363n
115 117
59 3481 41 x 59^2 - 58 142663 179 x 797 P(n) = 3481n^2 + 3363n + 142663 3363n 58 3364 41 x 58^2 + 59 137983 P(n) = 3364n^2 + 3480n + 137983 3480n
117 119
60 3600 41 x 60^2 - 59 147541 P(n) = 3600n^2 + 3480n + 147541 3480n 59 3481 41 x 59^2 + 60 142781 71 x 2011 P(n) = 3481n^2 + 3599n + 142781 3599n
119 121
61 3721 41 x 61^2 - 60 152501 P(n) = 3721n^2 + 3599n + 152501 3599n 60 3600 41 x 60^2 + 61 147661 P(n) = 3600n^2 + 3720n + 147661 3720n
121 123
62 3844 41 x 62^2 - 61 157543 P(n) = 3844n^2 + 3720n + 157543 3720n 61 3721 41 x 61^2 + 62 152623 P(n) = 3721n^2 + 3843n + 152623 3843n
123 125
63 3969 41 x 63^2 - 62 162667 47 x 3461 P(n) = 3969n^2 + 3843n + 162667 3843n 62 3844 41 x 62^2 + 63 157667 P(n) = 3844n^2 + 3968n + 157667 3968n
125 127
64 4096 41 x 64^2 - 63 167873 P(n) = 4096n^2 + 3968n + 167873 3968n 63 3969 41 x 63^2 + 64 162793 173 x 941 P(n) = 3969n^2 + 4095n + 162793 4095n
127 129
65 4225 41 x 65^2 - 64 173161 43 x 4027 P(n) = 4225n^2 + 4095n + 173161 4095n 64 4096 41 x 64^2 + 65 168001 43 x 3907 P(n) = 4096n^2 + 4224n + 168001 4224n
129 131
66 4356 41 x 66^2 - 65 178531 P(n) = 4356n^2 + 4224n + 178531 4224n 65 4225 41 x 65^2 + 66 173291 P(n) = 4225n^2 + 4355n + 173291 4355n
131 133
67 4489 41 x 67^2 - 66 183983 251 x 733 P(n) = 4489n^2 + 4355n + 183983 4355n 66 4356 41 x 66^2 + 67 178663 53 x 3371 P(n) = 4356n^2 + 4488n + 178663 4488n
133 135
68 4624 41 x 68^2 - 67 189517 P(n) = 4624n^2 + 4488n + 189517 4488n 67 4489 41 x 67^2 + 68 184117 P(n) = 4489n^2 + 4623n + 184117 4623n
135 137
69 4761 41 x 69^2 - 68 195133 83 x 2351 P(n) = 4761n^2 + 4623n + 195133 4623n 68 4624 41 x 68^2 + 69 189653 P(n) = 4624n^2 + 4760n + 189653 4760n
137 139
70 4900 41 x 70^2 - 69 200831 47 x 4273 P(n) = 4900n^2 + 4760n + 200831 4760n 69 4761 41 x 69^2 + 70 195271 P(n) = 4761n^2 + 4899n + 195271 4899n
139 141
71 5041 41 x 71^2 - 70 206611 307 x 673 P(n) = 5041n^2 + 4899n + 206611 4899n 70 4900 41 x 70^2 + 71 200971 P(n) = 4900n^2 + 5040n + 200971 5040n
141 143
72 5184 41 x 72^2 - 71 212473 179 x 1187 P(n) = 5184n^2 + 5040n + 212473 5040n 71 5041 41 x 71^2 + 72 206753 47 x 53 x 83 P(n) = 5041n^2 + 5183n + 206753 5183n
143 145
73 5329 41 x 73^2 - 72 218417 P(n) = 5329n^2 + 5183n + 218417 5183n 72 5184 41 x 72^2 + 73 212617 173 x 1229 P(n) = 5184n^2 + 5328n + 212617 5328n
145 147
74 5476 41 x 74^2 - 73 224443 P(n) = 5476n^2 + 5328n + 224443 5328n 73 5329 41 x 73^2 + 74 218563 61 x 3583 P(n) = 5329n^2 + 5475n + 218563 5475n
147 149
75 5625 41 x 75^2 - 74 230551 P(n) = 5625n^2 + 5475n + 230551 5475n 74 5476 41 x 74^2 + 75 224591 P(n) = 5476n^2 + 5624n + 224591 5624n
149 151
76 5776 41 x 76^2 - 75 236741 61 x 3881 P(n) = 5776n^2 + 5624n + 236741 5624n 75 5625 41 x 75^2 + 76 230701 281 x 821 P(n) = 5625n^2 + 5775n + 230701 5775n
151 153
77 5929 41 x 77^2 - 76 243013 487 x 499 P(n) = 5929n^2 + 5775n + 243013 5775n 76 5776 41 x 76^2 + 77 236893 P(n) = 5776n^2 + 5928n + 236893 5928n
153 155
78 6084 41 x 78^2 - 77 249367 P(n) = 6084n^2 + 5928n + 249367 5928n 77 5929 41 x 77^2 + 78 243167 P(n) = 5929n^2 + 6083n + 243167 6083n
155 157
79 6241 41 x 79^2 - 78 255803 P(n) = 6241n^2 + 6083n + 255803 6083n 78 6084 41 x 78^2 + 79 249523 47 x 5309 P(n) = 6084n^2 + 6240n + 249523 6240n
157 159
80 6400 41 x 80^2 - 79 262321 P(n) = 6400n^2 + 6240n + 262321 6240n 79 6241 41 x 79^2 + 80 255961 P(n) = 6241n^2 + 6399n + 255961 6399n
159 161
81 6561 41 x 81^2 - 80 268921 P(n) = 6561n^2 + 6399n + 268921 6399n 80 6400 41 x 80^2 + 81 262481 199 x 1319 P(n) = 6400n^2 + 6560n + 262481 6560n
161 163
82 6724 41 x 82^2 - 81 275603 197 x 1399 P(n) = 6724n^2 + 6560n + 275603 6560n 81 6561 41 x 81^2 + 82 269083 41 x 6563 P(n) = 6561n^2 + 6723n + 269083 6723n
163 165
83 6889 41 x 83^2 - 82 282367 41 x 71 x 97 P(n) = 6889n^2 + 6723n + 282367 6723n 82 6724 41 x 82^2 + 83 275767 P(n) = 6724n^2 + 6888n + 275767 6888n
165 167
84 7056 41 x 84^2 - 83 289213 P(n) = 7056n^2 + 6888n + 289213 6888n 83 6889 41 x 83^2 + 84 282533 359 x 787 P(n) = 6889n^2 + 7055n + 282533 7055n
167 169
85 7225 41 x 85^2 - 84 296141 43 x 71 x 97 P(n) = 7225n^2 + 7055n + 296141 7055n 84 7056 41 x 84^2 + 85 289381 P(n) = 7056n^2 + 7224n + 289381 7224n
169 171
86 7396 41 x 86^2 - 85 303151 P(n) = 7396n^2 + 7224n + 303151 7224n 85 7225 41 x 85^2 + 86 296311 199 x 1489 P(n) = 7225n^2 + 7395n + 296311 7395n
171 173
87 7569 41 x 87^2 - 86 310243 P(n) = 7569n^2 + 7395n + 310243 7395n 86 7396 41 x 86^2 + 87 303323 P(n) = 7396n^2 + 7568n + 303323 7568n
173 175
88 7744 41 x 88^2 - 87 317417 53 x 53 x 113 P(n) = 7744n^2 + 7568n + 317417 7568n 87 7569 41 x 87^2 + 88 310417 43 x 7219 P(n) = 7569n^2 + 7743n + 310417 7743n
175 177
89 7921 41 x 89^2 - 88 324673 P(n) = 7921n^2 + 7743n + 324673 7743n 88 7744 41 x 88^2 + 89 317593 P(n) = 7744n^2 + 7920n + 317593 7920n
177 179
90 8100 41 x 90^2 - 89 332011 P(n) = 8100n^2 + 7920n + 332011 7920n 89 7921 41 x 89^2 + 90 324851 563 x 577 P(n) = 7921n^2 + 8099n + 324851 8099n
179 181
91 8281 41 x 91^2 - 90 339431 197 x 1723 P(n) = 8281n^2 + 8099n + 339431 8099n 90 8100 41 x 90^2 + 91 332191 P(n) = 8100n^2 + 8280n + 332191 8280n
181 183
92 8464 41 x 92^2 - 91 346933 P(n) = 8464n^2 + 8280n + 346933 8280n 91 8281 41 x 91^2 + 92 339613 P(n) = 8281n^2 + 8463n + 339613 8463n
183 185
93 8649 41 x 93^2 - 92 354517 53 x 6689 P(n) = 8649n^2 + 8463n + 354517 8463n 92 8464 41 x 92^2 + 93 347117 313 x 1109 P(n) = 8464n^2 + 8648n + 347117 8648n
185 187
94 8836 41 x 94^2 - 93 362183 373 x 971 P(n) = 8836n^2 + 8648n + 362183 8648n 93 8649 41 x 93^2 + 94 354703 P(n) = 8649n^2 + 8835n + 354703 8835n
187 189
95 9025 41 x 95^2 - 94 369931 83 x 4457 P(n) = 9025n^2 + 8835n + 369931 8835n 94 8836 41 x 94^2 + 95 362371 P(n) = 8836n^2 + 9024n + 362371 9024n
189 191
96 9216 41 x 96^2 - 95 377761 P(n) = 9216n^2 + 9024n + 377761 9024n 95 9025 41 x 95^2 + 96 370121 P(n) = 9025n^2 + 9215n + 370121 9215n
191 193
97 9409 41 x 97^2 - 96 385673 227 x 1699 P(n) = 9409n^2 + 9215n + 385673 9215n 96 9216 41 x 96^2 + 97 377953 151 x 2503 P(n) = 9216n^2 + 9408n + 377953 9408n
193 195
98 9604 41 x 98^2 - 97 393667 P(n) = 9604n^2 + 9408n + 393667 9408n 97 9409 41 x 97^2 + 98 385867 83 x 4649 P(n) = 9409n^2 + 9603n + 385867 9603n
195 197
99 9801 41 x 99^2 - 98 401743 P(n) = 9801n^2 + 9603n + 401743 9603n 98 9604 41 x 98^2 + 99 393863 P(n) = 9604n^2 + 9800n + 393863 9800n
197 199
100 10000 41 x 100^2 - 99 409901 P(n) = 10000n^2 + 9800n + 409901 9800n 99 9801 41 x 99^2 + 100 401941 113 x 3557 P(n) = 9801n^2 + 9999n + 401941 9999n
201
100 10000 41 x 100^2 + 101 410101 397 x 1033 P(n) = 1000n^2 + 10200n + 410101 10200n
69 Prime Numbers 32 Composite Numbers 67 Prime Numbers 34 Composite Numbers

Formula "P(m) = m^2(n^2) + (m^2 ± 2m)n + [41m^2 ± (m ± 1)]": This Formula Generates The QuadraAc Prime-GeneraAng Polynomials Related To Euler QuadraAc Polynomial, P(n) = n^2 + n + 41
P(m) = m^2(n^2) + (m^2 - 2m)n + [41m^2 - (m - 1)]
P(m) = m^2(n^2) + (m^2 - 2m)n + [41m^2 - (m - 1)] generates 19 (m1 - m19) consecuAve polynomials that produce a prime number for n = 4.
m n = 0 n = 1 n = -1 n = 2 n = -2 n = 3 n = -3 n = 4 n = -4 n = 5 n = 6 n = 7 n = 8 n = 9 n = 10 n = 11 n = 16
0 P(n) = 0n^2 + 0n + 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 P(n) = n^2 - n + 41 41 41 43 43 47 47 53 53 61 61 71 83 97 113 131 151 281
2 P(n) = 4n^2 + 163 163 167 167 179 179 199 199 227 227 263 307 359 419 487 563 647 1187
3 P(n) = 9n^2 + 3n + 367 367 379 373 409 397 457 439 523 499 607 709 829 967 1123 1297 1489 2719
4 P(n) = 16n^2 + 8n + 653 653 677 661 733 701 821 773 941 877 1093 1277 1493 1741 2021 43 x47 2333 2677 4877
5 P(n) = 25n^2 + 15n + 1021 1021 1061 1031 1151 1091 1291 1201 1481 1361 1721 2011 2351 2741 3181 3671 4211 7661 47 x 163
6 P(n) = 36n^2 + 24n + 1471 1471 1531 1483 1663 1567 1867 1723 2143 1951 2491 47 x 53 2911 41 x 71 3403 41 x 83 3967 4603 5311 47 x 113 6091 11071
7 P(n) = 49n^2 + 35n + 2003 2003 2087 2017 2269 2129 2549 2339 2927 2647 3403 41 x 83 3977 41 x 97 4649 5419 6287 7253 8317 15107
8 P(n) = 64n^2 + 48n + 2617 2617 2729 2633 2969 2777 3337 47 x 71 3049 3833 3449 4457 5209 6089 7097 47 x 151 8233 9497 10889 19769 53 x 373
9 P(n) = 81n^2 + 63n + 3313 3313 3457 3331 3763 53 x 71 3511 4231 3853 4861 4357 5653 6607 7723 9001 10441 53 x 197 12043 13807 25057
10 P(n) = 100n^2 + 80n + 4091 4091 4271 4111 4651 4331 61 x 71 5231 4751 6011 5371 41 x 131 6991 8171 9551 11131 12911 14891 17071 43 x 397 30971
11 P(n) = 121n^2 + 99n + 4951 4951 5171 4973 5633 43 x 131 5237 6337 5743 7283 6491 8471 43 x 197 9901 11573 71 x 163 13487 15643 18041 20681 37511
12 P(n) = 144n^2 + 120n + 5893 5893 71 x 83 6157 47 x 131 5917 61 x 97 6709 6229 7549 6829 8677 7717 10093 11797 47 x 251 13789 16069 18637 21493 24637 71 x 347 44677 43 x 1039
13 P(n) = 169n^2 + 143n + 6917 6917 7229 6943 53 x 131 7879 7307 8867 8009 10193 9049 11857 71 x 167 13859 16199 97 x 167 18877 43 x 439 21893 25247 28939 43 x 673 52469 71 x 739
14 P(n) = 196n^2 + 168n + 8023 8023 71 x 113 8387 8051 83 x 97 9143 41 x 223 8471 43 x 197 10291 41 x 251 9283 11831 10487 13763 16087 18803 21911 25411 29303 33587 60887
15 P(n) = 225n^2 + 195n + 9211 9211 61 x 151 9631 9241 10501 9721 11821 10651 13591 12031 53 x 227 15811 97 x 163 18481 21601 25171 29191 33661 41 x 821 38581 41 x 941 69931
16 P(n) = 256n^2 + 224n + 10481 10481 47 x 223 10961 97 x 113 10513 11953 11057 13457 12113 15473 13681 18001 47 x 383 21041 53 x 397 24593 28657 33233 167 x 199 38321 43921 167 x 263 79601
17 P(n) = 289n^2 + 255n + 11833 11833 12377 11867 13499 12479 15199 13669 17477 15437 43 x 359 20333 23767 27779 32369 37537 43283 49607 113 x 439 89897
18 P(n) = 324n^2 + 288n + 13267 13267 13879 13303 53 x 251 15139 13987 71 x 197 17047 15319 19603 17299 22807 26659 53 x 503 31159 36307 42103 71 x 593 48547 43 x 1129 55639 100819 41 x 2459
19 P(n) = 361n^2 + 323n + 14783 14783 15467 14821 16873 47 x 359 15581 19001 17063 113 x 151 21851 19267 25423 29717 34733 47 x 739 40471 46931 71 x 661 54113 53 x 1021 62017 112367 313 x 359
20 P(n) = 400n^2 + 360n + 16381 16381 17141 61 x 281 16421 18701 17261 41 x 421 21061 18901 41 x 461 24221 53 x 457 21341 28181 32941 38501 44861 113 x 397 52021 59981 68741 53 x 1297 124541
21 P(n) = 441n^2 + 399n + 18061 18061 18901 41 x 461 18103 43 x 421 20623 41 x 503 19027 53 x 359 23227 20833 83 x 251 26713 23521 43 x 547 31081 36331 47 x 773 42463 49477 57373 66151 83 x 797 75811 47 x 1613 137341
22 P(n) = 484n^2 + 440n + 19823 19823 43 x 461 20747 19867 22639 20879 25499 43 x 593 22859 29327 25807 131 x 197 34123 39887 46619 54319 62987 72623 83227 150767
23 P(n) = 529n^2 + 483n + 21667 21667 47 x 461 22679 21713 24749 22817 27877 61 x 457 24979 32063 28199 163 x 173 37307 43609 50969 59387 68863 79397 90989 164819 43 x 3833
24 P(n) = 576n^2 + 528n + 23593 23593 24697 23641 47 x 503 26953 24841 30361 97 x 313 27193 71 x 383 34921 47 x 743 30697 40633 179 x 227 47497 55513 43 x 1291 64681 71 x 911 75001 179 x 419 86473 43 x 2011 99097 41 x 2417 179497
25 P(n) = 625n^2 + 575n + 25601 25601 26801 25651 113 x 227 29251 26951 32951 83 x 397 29501 37901 151 x 251 33301 44101 51551 60251 70201 81401 93851 107551 131 x 821 194801 83 x 2347
26 P(n) = 676n^2 + 624n + 27691 27691 28991 53 x 547 27743 31643 29147 35647 43 x 829 31903 61 x 523 41003 131 x 313 36011 47711 55771 43 x 1297 65183 75947 173 x 439 88063 83 x 1061 101531 116351 210731
27 P(n) = 729n^2 + 675n + 29863 29863 31267 29917 34129 31429 53 x 593 38449 34399 41 x 839 44227 47 x 941 38827 41 x 947 51463 53 x 971 60157 43 x 1399 70309 81919 94987 43 x 47 x 47 109513 97 x 1129 125497 227287 167 x 1361
28 P(n) = 784n^2 + 728n + 32117 32117 33629 32173 36709 33797 41357 36989 47 x 787 47573 113 x 421 41749 83 x 503 55357 197 x 281 64709 75629 88117 102173 83 x 1231 117797 134989 244469 151 x 1619
29 P(n) = 841n^2 + 783n + 34453 34453 131 x 263 36077 43 x 839 34511 39383 36251 44371 39673 97 x 409 51041 43 x 1187 44777 59393 69427 81143 53 x 1531 94541 109621 126383 47 x 2689 144827 251 x 577 262277 41 x 6397
30 P(n) = 900n^2 + 840n + 36871 36871 38611 36931 42151 61 x 691 38791 47491 42451 54631 47911 63571 151 x 421 74311 86851 101191 47 x 2153 117331 135271 155011 379 x 409 280711
31 P(n) = 961n^2 + 899n + 39371 39371 41231 39433 47 x 839 45013 41417 83 x 499 50717 41 x 1237 45323 61 x 743 58343 41 x 1423 51151 67891 79361 61 x 1301 92753 108067 53 x 2039 125303 144461 165541 299771
32 P(n) = 1024n^2 + 960n + 41953 41953 43937 53 x 829 42017 47969 44129 54049 48289 43 x 1123 62177 97 x 641 54497 72353 84577 83 x 1019 98849 115169 41 x 53 x 53 133537 41 x 3257 153953 176417 319457 61 x 5237
33 P(n) = 1089n^2 + 1023n + 44617 44617 46729 83 x 563 44683 51019 163 x 313 46927 167 x 281 57487 51349 66133 41 x 1613 57949 167 x 347 76957 41 x 1877 89959 105139 47 x 2237 122497 142033 173 x 821 163747 373 x 439 187639 339769
34 P(n) = 1156n^2 + 1088n + 47363 47363 49607 113 x 439 47431 54163 49811 61031 54503 70211 61 x 1151 61507 81703 95507 111623 130051 150791 173843 263 x 661 199207 360707 197 x 1831
35 P(n) = 1225n^2 + 1155n + 50191 50191 53 x 947 52571 50261 57401 61 x 941 52781 47 x 1123 64681 71 x 911 57751 74411 65171 86591 131 x 661 101221 118301 281 x 421 137831 159811 184241 211121 61 x 3461 382271
36 P(n) = 1296n^2 + 1224n + 53101 53101 55621 53173 60733 55837 68437 61093 199 x 307 78733 43 x 1831 68941 71 x 971 91621 107101 125173 41 x 43 x 71 145837 41 x 3557 169093 194941 151 x 1291 223381 404461
37 P(n) = 1369n^2 + 1295n + 56093 56093 58757 56167 64159 83 x 773 58979 72299 197 x 367 64529 173 x 373 83177 72817 96793 43 x 2251 113147 132239 223 x 593 154069 43 x 3583 178637 41 x 4357 205943 41 x 5023 235987 47 x 5021 427277 47 x 9091
38 P(n) = 1444n^2 + 1368n + 59167 59167 61979 59243 67679 62207 76267 53 x 1439 68059 87743 76799 61 x 1259 102107 119359 139499 199 x 701 162527 188443 217247 53 x 4099 248939 113 x 2203 450719
39 P(n) = 1521n^2 + 1443n + 62323 62323 65287 62401 71293 65521 80341 71683 97 x 739 92431 80887 47 x 1721 107563 125737 146953 171211 313 x 547 198511 179 x 1109 228853 262237 474787
40 P(n) = 1600n^2 + 1520n + 65561 65561 53 x 1237 68681 173 x 397 65641 41 x 1601 75001 179 x 419 68921 41 x 41 x 41 84521 75401 97241 85081 113161 132281 179 x 739 154601 53 x 2917 180121 281 x 641 208841 97 x 2153 240761 71 x 3391 275881 499481
41 P(n) = 1681n^2 + 1599n + 68881 68881 72161 68963 78803 72407 61 x 1187 88807 79213 113 x 701 102173 83 x 1231 89381 118901 138991 131 x 1061 162443 61 x 2663 189257 219433 252971 289871 524801
42 P(n) = 1764n^2 + 1680n + 72283 72283 41 x 41 x 43 75727 41 x 1847 72367 82699 75979 93199 83119 43 x 1933 107227 93787 124783 145867 199 x 733 170479 151 x 1129 198619 83 x 2393 230287 421 x 547 265483 304207 61 x 4987 550747 71 x 7757
43 P(n) = 1849n^2 + 1763n + 75767 75767 79379 75853 86689 79637 97 x 821 97697 151 x 647 87119 112403 98299 130807 152909 178709 173 x 1033 208207 241403 163 x 1481 278297 397 x 701 318889 577319 167 x 3457
44 P(n) = 1936n^2 + 1848n + 79333 79333 83117 79421 43 x 1847 90773 43 x 2111 83381 199 x 419 102301 91213 53 x 1721 117701 102917 97 x 1061 136973 160117 187133 218021 252781 113 x 2237 291413 83 x 3511 333917 227 x 1471 604517
45 P(n) = 2025n^2 + 1935n + 82981 82981 86941 227 x 383 83071 94951 87211 107011 113 x 947 95401 123121 107641 143281 167491 195751 228061 264421 281 x 941 304831 349291 632341 367 x 1723
46 P(n) = 2116n^2 + 2024n + 86711 86711 90851 47 x 1933 86803 61 x 1423 99223 91127 111827 99683 83 x 1201 128663 112471 47 x 2393 149731 175031 383 x 457 204563 238327 61 x 3907 276323 318551 461 x 691 365011 53 x 71 x 97 660791
47 P(n) = 2209n^2 + 2115n + 90523 90523 94847 90617 103589 71 x 1459 95129 251 x 379 116749 313 x 373 104059 134327 117407 113 x 1039 156323 223 x 701 182737 41 x 4457 213569 41 x 5209 248819 61 x 4079 288487 43 x 6709 332573 381077 689867
48 P(n) = 2304n^2 + 2208n + 94417 94417 263 x 359 98929 94513 108049 167 x 647 99217 47 x 2111 121777 47 x 2591 108529 140113 167 x 839 122449 163057 41 x 41 x 97 190609 41 x 4649 222769 367 x 607 259537 300913 61 x 4933 346897 263 x 1319 397489 719569
49 P(n) = 2401n^2 + 2303n + 98393 98393 61 x 1613 103097 131 x 787 98491 112603 103391 126911 179 x 709 113093 146021 127597 169933 198647 232163 179 x 1297 270481 197 x 1373 313601 53 x 61 x 97 361523 414247 379 x 1093 749897 53 x 14149
50 P(n) = 2500n^2 + 2400n + 102451 102451 107351 102551 117251 107651 83 x 1297 132151 117751 152051 383 x 397 132851 176951 206851 61 x 3391 241751 151 x 1601 281651 326551 251 x 1301 376451 487 x 773 431351 83 x 5197 780851
51 P(n) = 2601n^2 + 2499n + 106591 106591 111691 61 x 1831 106693 121993 111997 137497 359 x 383 122503 158203 281 x 563 138211 41 x 3371 184111 215221 373 x 577 251533 293047 131 x 2237 339763 47 x 7229 391681 61 x 6421 448801 812431
52 P(n) = 2704n^2 + 2600n + 110813 110813 116117 83 x 1399 110917 126829 53 x 2393 116429 173 x 673 142949 127349 347 x 367 164477 143677 191413 223757 261509 304669 199 x 1531 353237 407213 313 x 1301 466597 457 x 1021 844637 47 x 17971
53 P(n) = 2809n^2 + 2703n + 115117 115117 120629 71 x 1699 115223 131759 120947 148507 97 x 1531 132289 263 x 503 170873 149249 198857 47 x 4231 232459 271679 263 x 1033 316517 307 x 1031 366973 423047 47 x 9001 484739 43 x 11273 877469
54 P(n) = 2916n^2 +2808n + 119503 119503 125227 97 x 1291 119611 136783 43 x 3181 125551 154171 151 x 1021 137323 53 x 2591 177391 53 x 3347 154927 206443 43 x 4801 241327 282043 131 x 2153 328591 380971 439183 503227 910927 97 x 9391
55 P(n) = 3025n^2 + 2915n + 123971 123971 151 x 821 129911 163 x 797 124081 167 x 743 141901 41 x 3461 130241 159941 41 x 47 x 83 142451 167 x 853 184031 160711 214171 61 x 3511 250361 292601 340891 47 x 7253 395231 455621 673 x 677 522061 945011 43 x 21977
56 P(n) = 3136n^2 + 3024n + 128521 128521 134681 128633 307 x 419 147113 131 x 1123 135017 165817 147673 190793 166601 222041 259561 113 x 2297 303353 61 x 4973 353417 43 x 8219 409753 472361 41 x 41 x 281 541241 41 x 43 x 307 979721 61 x 16061
57 P(n) = 3249n^2 + 3135n + 133153 133153 139537 133267 71 x 1877 152419 139879 43 x 3253 171799 152989 197677 172597 230053 379 x 607 268927 314299 366169 424537 489403 61 x 71 x 113 560767 1015057
58 P(n) = 3364n^2 + 3248n + 137867 137867 144479 137983 157819 97 x 1627 144827 251 x 577 177887 158399 151 x 1049 204683 197 x 1039 178699 83 x 2153 238207 278459 325439 379147 439583 506747 313 x 1619 580639 1051019
59 P(n) = 3481n^2 + 3363n + 142663 142663 179 x 797 149507 47 x 3181 142781 71 x 2011 163313 197 x 829 149861 184081 163903 251 x 653 211811 184907 179 x 1033 246503 53 x 4651 288157 47 x 6131 336773 392351 454891 524393 131 x 4003 600857 1087607 41 x 41 x 647
60 P(n) = 3600n^2 + 3480n + 147541 147541 154621 147661 168901 154981 190381 61 x 3121 169501 219061 439 x 499 191221 43 x 4447 254941 298021 348301 379 x 919 405781 470461 542341 197 x 2753 621421 83 x 7487 1124821 1031 x 1091
61 P(n) = 3721n^2 + 3599n + 152501 152501 159821 71 x 2251 152623 174583 160187 41 x 3907 196787 307 x 641 175193 41 x 4273 226433 197641 263521 308051 360023 419437 607 x 691 486293 560591 43 x 13037 642331 503 x 1277 1162661 53 x 21937
62 P(n) = 3844n^2 + 3720n + 157543 157543 165107 41 x 4027 157667 180359 41 x 53 x 83 165479 203299 263 x 773 180979 71 x 2549 233927 223 x 1049 204167 61 x 3347 272243 61 x 4463 318247 371939 433319 502387 53 x 9479 579143 347 x 1669 663587 1201127 971 x 1237
63 P(n) = 3969n^2 + 3843n + 162667 162667 47 x 3461 170479 151 x 1129 162793 173 x 941 186229 170857 209917 186859 241543 210799 71 x 2969 281107 47 x 5981 328609 347 x 947 384049 447427 518743 597997 685189 367 x 1867 1240219
64 P(n) = 4096n^2 + 3968n + 167873 167873 175937 168001 43 x 3907 192193 176321 216641 192833 249281 71 x 3511 217537 43 x 5059 290113 339137 396353 461761 409 x 1129 535361 617153 707137 829 x 853 1279937
65 P(n) = 4225n^2 + 4095n + 173161 173161 43 x 4027 181481 347 x 523 173291 198251 181871 223471 43 x 5197 198901 257141 224381 173 x 1297 299261 349831 408851 131 x 3121 476321 373 x 1277 552241 636611 97 x 6563 729431 41 x 17791 1320281 83 x 15907
66 P(n) = 4356n^2 + 4224n + 178531 178531 187111 178663 53 x 3371 204403 47 x 4349 187507 230407 113 x 2039 205063 265123 231331 308551 360691 373 x 967 421543 47 x 8969 491107 71 x 6917 569383 439 x 1297 656371 752071 131 x 5741 1361251 43 x 31657
67 P(n) = 4489n^2 + 4355n + 183983 183983 251 x 733 192827 151 x 1277 184117 210649 313 x 673 193229 199 x 971 237449 367 x 647 211319 273227 199 x 1373 238387 223 x 1069 317983 371717 503 x 739 434429 43 x 10103 506119 586787 676433 43 x 15731 775057 1402847
68 P(n) = 4624n^2 + 4488n + 189517 189517 198629 307 x 647 189653 216989 97 x 2237 199037 244597 217669 41 x 5309 281453 83 x 3391 245549 41 x 53 x 113 327557 382909 47 x 8147 447509 521357 604453 151 x 4003 696797 419 x 1663 798389 47 x 16987 1445069 173 x 8353
69 P(n) = 4761n^2 + 4623n + 195133 195133 83 x 2351 204517 195271 223423 204931 251851 43 x 5857 224113 289801 179 x 1619 252817 337273 367 x 919 394267 43 x 53 x 173 460783 197 x 2339 536821 179 x 2999 622381 131 x 4751 717463 822067 1487917
70 P(n) = 4900n^2 + 4760n + 200831 200831 47 x 4273 210491 200971 229951 227 x 1013 210911 259211 230651 263 x 877 298271 71 x 4201 260191 347131 405791 43 x 9437 474251 647 x 733 552511 640571 43 x 14897 738431 227 x 3253 846091 281 x 3011 1531391 41 x 41 x 911
71 P(n) = 5041n^2 + 4899n + 206611 206611 307 x 673 216551 206753 47 x 53 x 83 236573 216977 61 x 3557 266677 237283 306863 47 x 6529 267671 357131 417481 53 x 7877 487913 397 x 1229 568427 223 x 2549 659023 759701 870461 1575491 853 x 1847
72 P(n) = 5184n^2 + 5040n + 212473 212473 179 x 1187 222697 43 x 5179 212617 173 x 1229 243289 113 x 2153 223129 274249 41 x 6689 244009 315577 41 x 43 x 179 275257 409 x 673 367273 429337 71 x 6047 501769 584569 83 x 7043 677737 781273 53 x 14741 895177 701 x 1277 1620217
73 P(n) = 5329n^2 + 5183n + 218417 218417 228929 218563 61 x 3583 250099 383 x 653 229367 347 x 661 281927 250829 324413 53 x 6121 282949 97 x 2917 377557 441359 515819 379 x 1361 600937 41 x 14657 696713 41 x 16993 803147 773 x 1039 920239 53 x 97 x 179 1665569
74 P(n) = 5476n^2 + 5328n + 224443 224443 235247 367 x 641 224591 257003 235691 53 x 4447 289711 281 x 1031 257743 373 x 691 333371 41 x 47 x 173 290747 167 x 1741 387983 41 x 9463 453547 647 x 701 530063 617531 715951 47 x 15233 825323 223 x 3701 945647 1711547
75 P(n) = 5625n^2 + 5475n + 230551 230551 241651 230701 281 x 821 264001 227 x 1163 242101 297601 264751 43 x 47 x 131 342451 298651 398551 113 x 3527 465901 544501 634351 151 x 4201 735451 847801 499 x 1699 971401 1758151 131 x 13421
76 P(n) = 5776n^2 + 5624n + 236741 236741 61 x 3881 248141 236893 271093 419 x 647 248597 305597 271853 351653 306661 409261 478421 559133 651397 755213 870581 47 x 18523 997501 499 x 1999 1805381
77 P(n) = 5929n^2 + 5775n + 243013 243013 487 x 499 254717 179 x 1423 243167 278279 255179 313699 279049 173 x 1613 360977 314777 420113 179 x 2347 491107 71 x 6917 573959 41 x 13999 668669 41 x 47 x 347 775237 893663 877 x 1019 1023947 1853237 419 x 4423
78 P(n) = 6084n^2 + 5928n + 249367 249367 261379 249523 47 x 5309 285559 261847 321907 487 x 661 286339 281 x 1019 370423 322999 431107 503959 588979 421 x 1399 686167 263 x 2609 795523 41 x 19403 917047 41 x 22367 1050739 1901719
79 P(n) = 6241n^2 + 6083n + 255803 255803 268127 53 x 5059 255961 292933 268601 113 x 2377 330221 71 x 4651 293723 379991 43 x 8837 331327 421 x 787 442243 516977 604193 43 x 14051 703891 593 x 1187 816071 691 x 1181 940733 1077877 307 x 3511 1950827
80 P(n) = 6400n^2 + 6240n + 262321 262321 274961 262481 199 x 1319 300401 71 x 4231 275441 53 x 5197 338641 397 x 853 301201 359 x 839 389681 347 x 1123 339761 453521 43 x 53 x 199 530161 151 x 3511 619601 47 x 13183 721841 43 x 16787 836881 964721 1105361 359 x 3079 2000561 641 x 3121
81 P(n) = 6561n^2 + 6399n + 268921 268921 281881 61 x 4621 269083 41 x 6563 307963 223 x 1381 282367 41 x 71 x 97 347167 308773 399493 348301 379 x 919 464941 543511 421 x 1291 635203 740017 499 x 1483 857953 989011 1133191 2050921 251 x 8171
82 P(n) = 6724n^2 + 6560n + 275603 275603 197 x 1399 288887 307 x 941 275767 315619 547 x 577 289379 47 x 47 x 131 355799 316439 409427 383 x 1069 356947 476503 83 x 5741 557027 650999 53 x 71 x 173 758419 281 x 2699 879287 1013603 1161367 967 x 1201 2101907
83 P(n) = 6889n^2 + 6723n + 282367 282367 41 x 71 x 97 295979 41 x 7219 282533 359 x 787 323369 296477 364537 324199 419483 365699 488207 570709 197 x 2897 666989 777047 647 x 1201 900883 379 x 2377 1038497 1189889 71 x 16759 2153519
84 P(n) = 7056n^2 + 6888n + 289213 289213 303157 289381 331213 303661 151 x 2011 373381 61 x 6121 332053 429661 374557 500053 71 x 7043 584557 683173 83 x 8231 795901 53 x 15017 922741 1063693 1218757 47 x 25931 2205757 47 x 71 x 661
85 P(n) = 7225n^2 + 7055n + 296141 296141 43 x 71 x 97 310421 53 x 5857 296311 199 x 1489 339151 310931 382331 340001 43 x 7907 439961 383521 512041 151 x 3391 598571 699551 223 x 3137 814981 53 x 15377 944861 383 x 2467 1089191 1247971 877 x 1423 2258621
86 P(n) = 7396n^2 + 7224n + 303151 303151 317771 303323 347183 318287 391387 348043 450383 392591 47 x 8353 524171 612751 716123 834287 967243 173 x 5591 1114991 179 x 6229 1277531 419 x 3049 2312111 1019 x 2269
87 P(n) = 7569n^2 + 7395n + 310243 310243 325207 313 x 1039 310417 43 x 7219 355309 43 x 8263 325729 400549 263 x 1523 356179 61 x 5839 460927 113 x 4079 401767 383 x 1049 536443 627097 131 x 4787 732889 853819 989887 1141093 1307437 2366227
88 P(n) = 7744n^2 + 7568n + 317417 317417 53 x 53 x 113 332729 317593 363529 333257 151 x 2207 409817 364409 307 x 1187 471593 411049 548857 457 x 1201 641609 41 x 15649 749849 41 x 18289 873577 167 x 5231 1012793 307 x 3299 1167497 167 x 6991 1337689 2420969
89 P(n) = 7921n^2 + 7743n + 324673 324673 340337 324851 563 x 577 371843 340871 71 x 4801 419191 372733 482381 97 x 4973 420437 593 x 709 561413 41 x 13693 656287 41 x 16007 767003 83 x 9241 893561 223 x 4007 1035961 71 x 14591 1194203 1368287 2476337
90 P(n) = 8100n^2 + 7920n + 332011 332011 348031 332191 380251 348571 428671 381151 563 x 677 493291 429931 574111 83 x 6917 671131 784351 913771 1059391 43 x 71 x 347 1221211 1061 x 1151 1399231 2532331
91 P(n) = 8281n^2 + 8099n + 339431 339431 197 x 1723 355811 339613 388753 61 x 6373 356357 367 x 971 438257 53 x 8269 389663 504323 439531 419 x 1049 586951 686141 801893 499 x 1607 934207 97 x 9631 1083083 1248521 53 x 23557 1430521 2588951 547 x 4733
92 P(n) = 8464n^2 + 8280n + 346933 346933 363677 347117 313 x 1109 397349 197 x 2017 364229 457 x 797 447949 199 x 2251 398269 61 x 6529 515477 449237 41 x 10957 599933 701317 61 x 11497 819629 954869 1107037 199 x 5563 1276133 1462157 2646197 499 x 5303
93 P(n) = 8649n^2 + 8463n + 354517 354517 53 x 6689 371629 47 x 7907 354703 406039 151 x 2689 372187 223 x 1669 457747 167 x 2741 406969 526753 199 x 2647 459049 47 x 9767 613057 167 x 3671 716659 837559 53 x 15803 975757 839 x 1163 1131253 1304047 199 x 6553 1494139 677 x 2207 2704069 61 x 97 x 457
94 P(n) = 8836n^2 + 8648n + 362183 362183 373 x 971 379667 362371 414823 113 x 3671 380231 467651 415763 379 x 1097 538151 468967 626323 732167 251 x 2917 855683 996871 1155731 577 x 2003 1332263 227 x 5869 1526467 2762567
95 P(n) = 9025n^2 + 8835n + 369931 369931 83 x 4457 387791 370121 423701 641 x 661 388361 47 x 8263 477661 47 x 10163 424651 71 x 5981 549671 61 x 9011 478991 639731 747841 874001 1018211 71 x 14341 1180471 439 x 2689 1360781 1559141 773 x 2017 2821691 409 x 6899
96 P(n) = 9216n^2 + 9024n + 377761 377761 396001 377953 151 x 2503 432673 41 x 61 x 173 396577 487777 41 x 11897 433633 561313 489121 461 x 1061 653281 763681 97 x 7873 892513 1039777 163 x 6379 1205473 1389601 691 x 2011 1592161 43 x 61 x 607 2881441
97 P(n) = 9409n^2 + 9215n + 385673 385673 227 x 1699 404297 461 x 877 385867 83 x 4649 441739 43 x 10273 404879 113 x 3583 497999 442709 53 x 8353 573077 263 x 2179 499357 151 x 3307 666973 43 x 15511 779687 487 x 1601 911219 1061569 1230737 223 x 5519 1418723 41 x 34603 1625527 41 x 41 x 967 2941817 199 x 14783
98 P(n) = 9604n^2 + 9408n + 393667 393667 412679 563 x 733 393863 450899 413267 508327 451879 584963 509699 680807 131 x 5197 795859 113 x 7043 930119 1083587 97 x 11171 1256263 47 x 26729 1448147 197 x 7351 1659239 3002819 43 x 69833
99 P(n) = 9801n^2 + 9603n + 401743 401743 421147 401941 113 x 3557 460153 421 x 1093 421741 518761 461143 596971 223 x 2677 520147 61 x 8527 694783 812197 379 x 2143 949213 1105831 43 x 25717 1282051 1477873 347 x 4259 1693297 43 x 53 x 743 3064447 47 x 113 x 577
100 P(n) = 10000n^2 + 9800n + 409901 409901 429701 410101 397 x 1033 469501 430301 43 x 10007 529301 470501 609101 530701 708901 47 x 15083 828701 968501 1128301 1308101 1039 x 1259 1507901 47 x 32083 1727701 3126701 41 x 76261
68 PN 32 CN 62 PN 38 CN 66 PN 34 CN 60 PN 40 CN 63 PN 37 CN 61 PN 39 CN 60 PN 40 CN 62 PN 38 CN 61 PN 39 CN 63 PN 37 CN 58 PN 42 CN 59 PN 41 CN 53 PN 47 CN 56 PN 44 CN 48 PN 52 CN 54 PN 46 CN 55 PN 45 CN
PN = Prime Numbers CN = Composite Numbers P(m) = m^2(n^2) + (m^2 - 2m)n + [41m^2 - (m - 1)] generates 18 (m1 - m18) consecuAve polynomials that produce a prime number for n = -3.

Just Numbers (14 March 2022).pdf

Just Numbers (14 March 2022).pdf

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