20041126, 19:45  #1 
Sep 2002
106_{16} Posts 
Suggestion to P1 procedure
if I do some p1 on 2^2622611
with b1=10000 and b2=262261 supposing b2 is the largest factor of p1 and b1 is larger than the second largest factor of p1 and one comes after with a test of b1=20000 and b2=100000 it will remove my entry from the list but that work as checked nothing no factor can be found since 262261 is larger than 20000 and 100000. could a warning to the user be put in if b2 is smaller than m best regards Joss 
20041126, 22:15  #2 
Aug 2002
Termonfeckin, IE
5·7·79 Posts 
There isno need to put such a warning. You may remember that any factor n of a Mersenne number 2^p1 is such that n = 2kp+1. So for all factors n, n1 has p as a factor. Therefore George's P1 code automatically takes p into account. So your bounds of B1=20000 and B2=100000 are valid since this will find factors such that the secondlargest factor of p1 is less than 100000 (as the largest is obviously 262221) and all other factors are less than 20000.

20041128, 07:32  #3 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
1) Extending garo's reply:
Since any factor is of the form 2kp+1, George's P1 code takes both the 2 and p into account, and the specified bounds b1,b2 are bounds on k, not on the factor itself. (This [b1 and b2 are bounds on k, not the factor] ought to be included in any explanation of P1 implementation, to avoid confusion.) 2) BTW, the smallest potential factor of 2^2622611 is 2*1*262261 + 1 = 524523. Last fiddled with by cheesehead on 20041128 at 07:42 
20041128, 12:41  #4  
"Richard B. Woods"
Aug 2002
Wisconsin USA
1E0C_{16} Posts 
Oops. Need to correct something ...
Quote:
Example: P1 on 2^26296671 with b1 = b2 = 75000 found factor 773961743231142391. 773961743231142391  1 = 2kp = 2 × 3^4 × 5 × 5273 × 68909 × 2629667. k = 147159648585 = 3^4 × 5 × 5273 × 68909 If I still didn't get it right, someone please correct me. Thanks. Last fiddled with by cheesehead on 20041128 at 12:52 

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