Hi all,
I wrote a little program to show the distribution of factors among
congruence classes, especially (mod 8) and (mod 120) (all others were
as uninteresting as you would expect). What surprised me was that the
distribution is not smooth at all, some congruence classes contain a
lot more factors than others. Is there a nice mathematical explanation
for this?
Maybe in the factoring code of Prime95, the sixteen congruence classes
(mod 120) should be arranged so that the luckier classes get tested first,
because if a factor is found, the following classes need to be
checked only up to that factor to find a smaller factor. Finding the factor
early will save a little time.
The factors were from lowM.txt, but only from prime exponent mersennes.
Ciao,
Alex.
P.S. I have no idea what the factor 55 (mod 120) is doing there. I'll add
something to my program to print out offending factors when I have time.
1 7
8 : 16517 21290
1 7 17 23 31 41 47 49 55 71
73 79 89 97 103 113 119
120 : 16752627234030092015192830341985*1 2387
2049258122271996267423172962
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