New Random Number Generator, Modified Mid-Sqaure Method

2. Starting with an n digit number, squaring it
and taking the n digit in the middle as the
next number, which is then squared to
obtain the next number.
E.g.: Seed= 5673, Square= 32182929.
1829² = 3345241…

3. Converge on a constant.
• Seed= 2500, Square= 6250000,
2500, 2500…
• Seed= 2504, Square= 6270016,
2700²= 7290000, 2900²=
8410000…

4. Starting with an n digit number, squaring it
and taking the n digit in the middle as the
random number.
For the next seed, add the removing higher
order and lower order digits to the middle n
digit number (random number), which is
then squared to obtain the next number.

5. Seed, X0= 5673.
5673²= 32182929. X1= 1829+3+2+2+9= 1845.
1845²= 3404025. X2= 4040+3+2+5= 4050.
4050²= 16402500. X3= 4025+ 1+6= 4032.
Random Numbers= 1829, 4040, 4025, 2570…

6. Seed, X0= 5673
MID-SQUARE Modified MOD-SQUARE
 KS Test, D= 0.2536  KS Test, D= 0.3282
 Chi-Square, X²0= 5.29  Chi-Square, X²0= 5.31
 Runs Up & Down, Z= -  Runs Up & Down, Z=
0.366 0.188
 Runs above & Below  Runs above & Below
mean, Z=0.844 mean, Z= -0.161