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-   -   Lucky 13 (M51 related) (https://www.mersenneforum.org/showthread.php?t=23877)

science_man_88 2018-12-09 19:39

[QUOTE=GP2;502193]I wonder if the exponent is congruent to 1 or to 3 (mod 4)?

There is a somewhat improbable imbalance in favor of the 1's.

[url]https://mersenneforum.org/showthread.php?p=502076[/url][/QUOTE]

even taking into account that all Sophie Germain primes that are 11 mod 12 are automatically not Mersenne prime exponents ?

a1call 2018-12-09 19:45

[U]Perhaps[/U] we are dancing around a cluster which happens to contain (by chance) primes rather than Mersenne-Numbers with relatively large factors. If so we should expect things to even out further down the road.

Prime95 2018-12-09 20:09

[QUOTE=ATH;502171]I am ready to test with CUDALucas, Mlucas etc.[/QUOTE]

I've sent you the exponent to begin official double-checking.

Prime95 2018-12-09 20:23

[QUOTE=GP2;502193]I wonder if the exponent is congruent to 1 or to 3 (mod 4)?[/QUOTE]

1 mod 4

ATH 2018-12-09 20:57

...and the exponent is 5 (mod 8).

ewmayer 2018-12-09 20:57

Congrats-in-advance to George and GIMPS!

This would of course have to happen just after George embarks on a 10-day preholiday ocean cruise ... George leaving town remains our best predictor of a new M-prime discovery. :)

Madpoo 2018-12-09 20:58

[QUOTE=GP2;502193]I wonder if the exponent is congruent to 1 or to 3 (mod 4)?

There is a somewhat improbable imbalance in favor of the 1's.

[url]https://mersenneforum.org/showthread.php?p=502076[/url][/QUOTE]

I don't think it's giving too much away (well, cutting the potential exponents in half is actually giving a lot away) to say we're chalking up another for (exponent mod 4) = 1

Batalov 2018-12-09 21:12

[QUOTE=Madpoo;502207]I don't think it's giving too much away (well, cutting the potential exponents in half is actually giving a lot away) to say we're chalking up another for (exponent mod 4) = 1[/QUOTE]
I must agree that this is indeed not giving away too much. :rolleyes:

[SPOILER]given posts number N-2 and N-3[/SPOILER]

Dr Sardonicus 2018-12-09 21:47

Congratulations to the lucky discoverer (assuming it checks out), and to GIMPS! Good grief, that's less than a year since the last one!
[QUOTE=Prime95;502200]1 mod 4[/QUOTE]
Ooooh! That's 50 odd exponents, with 31 of them congruent to 1 (mod 4) and 19 of them congruent to 3 (mod 4). And 19 and 31 are :drama: [i]consecutive Mersenne prime exponents![/i]

I don't know what it all means, but it [i]must[/i] mean [i]something[/i]... :cmd:

GP2 2018-12-09 22:25

[QUOTE=science_man_88;502194]even taking into account that all Sophie Germain primes that are 11 mod 12 are automatically not Mersenne prime exponents ?[/QUOTE]

There are just not that many Sophie Germain primes. The number of general primes goes as n/log n, whereas the number of Sophie Germain primes goes as n/(log n)^2

For example, [URL="https://en.wikipedia.org/wiki/Sophie_Germain_prime"]Wikipedia article[/URL] mentions that there are only 190 Sophie Germain primes less than 10[SUP]4[/SUP] and 56,032 Sophie Germain primes less than 10[SUP]7[/SUP], but there are 1,229 and 664,579 general primes respectively below those bounds.

So that can't account for the discrepancy.

ixfd64 2018-12-09 22:46

Silly question: now that new Mersenne primes are no longer marked as a "success" until they are verified, does this mean that there is no way to spot them early unless George tells us?


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