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Old 2018-12-09, 19:39   #12
science_man_88
 
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Quote:
Originally Posted by GP2 View Post
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.

https://mersenneforum.org/showthread.php?p=502076
even taking into account that all Sophie Germain primes that are 11 mod 12 are automatically not Mersenne prime exponents ?
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Old 2018-12-09, 19:45   #13
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Perhaps 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.

Last fiddled with by a1call on 2018-12-09 at 19:46
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Old 2018-12-09, 20:09   #14
Prime95
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Quote:
Originally Posted by ATH View Post
I am ready to test with CUDALucas, Mlucas etc.
I've sent you the exponent to begin official double-checking.
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Old 2018-12-09, 20:23   #15
Prime95
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Quote:
Originally Posted by GP2 View Post
I wonder if the exponent is congruent to 1 or to 3 (mod 4)?
1 mod 4
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Old 2018-12-09, 20:57   #16
ATH
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...and the exponent is 5 (mod 8).
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Old 2018-12-09, 20:57   #17
ewmayer
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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. :)
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Old 2018-12-09, 20:58   #18
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Quote:
Originally Posted by GP2 View Post
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.

https://mersenneforum.org/showthread.php?p=502076
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
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Old 2018-12-09, 21:12   #19
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Quote:
Originally Posted by Madpoo View Post
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
I must agree that this is indeed not giving away too much.

given posts number N-2 and N-3
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Old 2018-12-09, 21:47   #20
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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:
Originally Posted by Prime95 View Post
1 mod 4
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 consecutive Mersenne prime exponents!

I don't know what it all means, but it must mean something...
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Old 2018-12-09, 22:25   #21
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Quote:
Originally Posted by science_man_88 View Post
even taking into account that all Sophie Germain primes that are 11 mod 12 are automatically not Mersenne prime exponents ?
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, Wikipedia article mentions that there are only 190 Sophie Germain primes less than 104 and 56,032 Sophie Germain primes less than 107, but there are 1,229 and 664,579 general primes respectively below those bounds.

So that can't account for the discrepancy.
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Old 2018-12-09, 22:46   #22
ixfd64
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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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