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Old 2004-11-26, 19:45   #1
jocelynl
 
Sep 2002

10616 Posts
Default Suggestion to P-1 procedure

if I do some p-1 on 2^262261-1
with b1=10000 and b2=262261
supposing b2 is the largest factor of p-1 and b1 is larger than the second largest factor of p-1

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
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Old 2004-11-26, 22:15   #2
garo
 
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There isno need to put such a warning. You may remember that any factor n of a Mersenne number 2^p-1 is such that n = 2kp+1. So for all factors n, n-1 has p as a factor. Therefore George's P-1 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 second-largest factor of p-1 is less than 100000 (as the largest is obviously 262221) and all other factors are less than 20000.
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Old 2004-11-28, 07:32   #3
cheesehead
 
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"Richard B. Woods"
Aug 2002
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1) Extending garo's reply:

Since any factor is of the form 2kp+1, George's P-1 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 P-1 implementation, to avoid confusion.)

2) BTW, the smallest potential factor of 2^262261-1 is 2*1*262261 + 1 = 524523.

Last fiddled with by cheesehead on 2004-11-28 at 07:42
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Old 2004-11-28, 12:41   #4
cheesehead
 
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"Richard B. Woods"
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Oops. Need to correct something ...

Quote:
Originally Posted by cheesehead
... 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] ...
should have been "... the specified bounds b1,b2 are bounds on factors of k, not on factors of (the Mersenne number minus 1). (This [b1 and b2 are bounds on factors of k] ..."

Example: P-1 on 2^2629667-1 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 2004-11-28 at 12:52
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