Hi, I've got a weird problem here. I'm trying to implement the Pollard P-1 algorithm in Mathematica, which my textbook states is guaranteed to work for $\displaystyle B = \sqrt{n}$, but in this particular example, if B gets too large, say, equal to 500, which is about the square root of the number in consideration, the algorithm actually stops working. My instructor and I looked at it for a long time and decided it's correct rendering of Douglas Stinson's pseudo-code fromCryptography: Theory and Practice... so what's going on? I've found it works for B ranging from 14 to 251, but no larger.

n = 262063;

B = 251; (* Largest B that works *)

a = 2;

For[i = 2, i < B, i++,

a = PowerMod[a, i, n];

]

d1 = GCD[a - 1, n];

If[

1 < d1 && d1 < n,

Print["d is " <> ToString[d1] <> " and n/d is " <> ToString[n/d1]],

Print["Fail"]

]