20180115, 21:21  #1 
Dec 2011
After milion nines:)
2×7×103 Posts 
InterimResidues prime 95
Since many of you use Prime95 for LL checking , I will ask one thing
If I remember correctly ( and there is possibility that my recollection is false) that was option in Prime95 ( or in other program that can make LL test) that show some kind of residue every xxx iterations. And if program is PRP or prime that residue drops to 0000000000. Most similar that i found is InterimResidues and it looks similar , but it doesnot drop to 0000000000 when I test prime. So am I missed something , or there is no such option. Thanks for reply 
20180116, 00:35  #2 
Einyen
Dec 2003
Denmark
2×1,571 Posts 
For example
InterimResidues=1000000 in prime.txt will output the residues every 1M iterations to screen and to results.txt. Actually in results.txt it will output 3 consecutive residues lines each times: n*1M, n*1M+1 and n*1M+2, and it is the n*1M+2 line that will match the n*1M residue from CUDALucas / Mlucas since they number iterations differently. It is only the very final residue that will be 0000000000000000 for the known primes, not the Interrim Residues. 
20180116, 09:30  #3 
Oct 2005
Italy
153_{16} Posts 
Do some math analysis exist on the residues of composite Mersenne candidates? Can the residue values suggest something of next Mersenne?

20180116, 11:43  #4  
Dec 2011
After milion nines:)
2×7×103 Posts 
Quote:
Thanks for answer ATH 

20180116, 12:59  #5 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
Theoretically, if we could store the other divisor of S_n we could start a test at the nearest mersenne prime exponent. It gets a bit harder with nonzero residues though. There are properties a residue has to have if the number is composite, these are at best useful for checking factors slower than trial factoring currently though.

20180116, 16:38  #6  
Sep 2003
2584_{10} Posts 
Quote:
You could check to make sure that the frequency of each hexadecimal digit is roughly equal. I think I did that at one point and found nothing out of the ordinary. I don't think that Mersenne primes create some kind of numerological distortion field that leaves clues in the residues of nearby Mersenne exponents. 

20180116, 17:16  #7  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
Quote:
((2r+1))^22 mod the even exponent mersenne, where 2(2r+1)*adjacent mersenne prime = previous S_n. 14=2*7 tells you the next value mod 15 is 14 (aka 1). That being said I can't extend the math usefully to help.okay not quite right but close. Last fiddled with by science_man_88 on 20180116 at 18:15 

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