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-   -   InterimResidues -prime 95 (https://www.mersenneforum.org/showthread.php?t=22931)

 pepi37 2018-01-15 21:21

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.

 ATH 2018-01-16 00:35

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.

 pacionet 2018-01-16 09:30

Do some math analysis exist on the residues of composite Mersenne candidates? Can the residue values suggest something of next Mersenne?

 pepi37 2018-01-16 11:43

[QUOTE=ATH;477637]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.[/QUOTE]
So my recollection is false :(

 science_man_88 2018-01-16 12:59

[QUOTE=pacionet;477652]Do some math analysis exist on the residues of composite Mersenne candidates? Can the residue values suggest something of next Mersenne?[/QUOTE]

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 non-zero 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.

 GP2 2018-01-16 16:38

[QUOTE=pacionet;477652]Do some math analysis exist on the residues of composite Mersenne candidates? Can the residue values suggest something of next Mersenne?[/QUOTE]

In nearly all cases, all we retain are the final 64 hexadecimal bits of each residue.

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.

 science_man_88 2018-01-16 17:16

[QUOTE=GP2;477668]I don't think that Mersenne primes create some kind of numerological distortion field that leaves clues in the residues of nearby Mersenne exponents.[/QUOTE]

I can tell you outright , that the residue of the even exponent mersenne after a mersenne prime exponent gives you
(-(2r+1))^2-2 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.

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