20191004, 09:09  #1508 
Romulan Interpreter
Jun 2011
Thailand
31·271 Posts 
yeah, that's what we said... ye only made it (too) technical... hehe

20191004, 14:41  #1509 
Nov 2018
Poland
2·7 Posts 
One more newbie question. Why TF on bigger exponents is faster than on smaller ones? It seems counterintuitive
Last fiddled with by Maciej Kmieciak on 20191004 at 14:45 
20191004, 15:30  #1510  
"Dylan"
Mar 2017
2^{2}×113 Posts 
Quote:
Case in point: for M22040009 you need to test to k = 26782920567714 to get to 2^70 whereas for M220400143 you have to test to k = 2678291412717 to get to the same point. 

20191004, 15:31  #1511  
"James Heinrich"
May 2004
exNorthern Ontario
2×3^{2}×157 Posts 
Quote:
The smallest possible factor for any Mersenne number is where k=1. Take for example M83, which does indeed have such a factor: (2 * 1 * 83) + 1 = 167 (roughly 7.4 bits) and 167 is a factor of M83. But if we take a larger exponent, say M830,000,063, then the smallest possible factor is: (2 * 1 * 830000063) + 1 = 1660000127 (roughly 30.6 bits) So you can see the larger the exponent, by necessity the factors are also bigger. TF software doesn't work by bitlevel directly (that's just a convenient measure of progress) but by checking all the valid k values between the two bit levels. Due to the relationship between exponent and k and bitsize, you have fewer possible k values at a given bitlevel for larger exponents. To illustrate, consider three exponent ranges, that you want to TF from 2^{40}2^{41}: for M10,000 k is between 54975581 and 109951162, giving 54,975,581 candidates to test for M10,000,000 k is between 54975 and 109951, giving 54,975 candidates to test for M1,000,000,000 k is between 549 and 1099, giving 549 candidates to test So even though the bitsize of the factors that might be found is constant, as the exponents get larger there are fewer possible candidates that need to be checked. Does that make sense? Last fiddled with by James Heinrich on 20191004 at 15:32 

20191004, 17:00  #1512  
Nov 2018
Poland
2·7 Posts 
Quote:
Quote:


20191004, 17:56  #1513 
"James Heinrich"
May 2004
exNorthern Ontario
2×3^{2}×157 Posts 

20191012, 16:21  #1514 
Oct 2018
Slovakia
2^{4}·3 Posts 
P1 found a factor in stage #2, B1=915000, B2=21045000, E=12.
UID: js2010/SATURN, M97388611 has a factor: 107653599012618660746761 (B1=915000, B2=21045000) 
20191012, 16:50  #1515 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
14C5_{16} Posts 

20191012, 16:53  #1516 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
10AE_{16} Posts 

20191012, 17:29  #1517 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5317_{10} Posts 

20191012, 17:46  #1518  
P90 years forever!
Aug 2002
Yeehaw, FL
1101001100100_{2} Posts 
Quote:


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