Mersenne: Distribution of factors among congruence classes

[Alex Kruppa]

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




Unsubscribe  list info -- http://www.scruz.net/~luke/signup.htm

Re: Mersenne: Distribution of factors among congruence classes

[Will Edgington]

Alex Kruppa wrote:

   Now I know how the 55 (mod 120) got there, it's:

   M( 310169 )C: 3486114749130405725455

   and the problem is that that's not a factor. Not remotely.

   3486114749130405725455 = 2*3*11*69720503*757595229073 +1

   so doesn't seem to be a factor of another Mersenne we've tested,
   either. Must have snuck in there by mistake, or maybe a typo.

You're using an old copy of my data; that particular false factor
took me several updates to eradicate for some reason, but it's
not in my data presently.

Will

Unsubscribe  list info -- http://www.scruz.net/~luke/signup.htm