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 : 1675 2627 2340 3009 2015 1928 3034 1985 *1 2387
2049 2581 2227 1996 2674 2317 2962
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
