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-   -   Announcing a new Wagstaff PRP (https://www.mersenneforum.org/showthread.php?t=26961)

ryanp 2021-06-28 20:14

Announcing a new Wagstaff PRP
 
[B](2^15135397+1)/3 is a Fermat Probable prime! (4556209 decimal digits)
[/B]

Also submitted to PRPTop.

I am searching the range n=13M .. 17M currently, and nearly done. No other discoveries as of yet.

paulunderwood 2021-06-28 21:19

[QUOTE=ryanp;582170][B](2^15135397+1)/3 is a Fermat Probable prime! (4556209 decimal digits)
[/B]

Also submitted to PRPTop.

I am searching the range n=13M .. 17M currently, and nearly done. No other discoveries as of yet.[/QUOTE]

Congrats

:party:

diep 2021-06-28 23:38

That's a very lucky find! Congrats on that one!

Had you asked me i would've guessed next one might've lurked at 30M earliest and 70M latest.

Dr Sardonicus 2021-06-29 11:29

[QUOTE=ryanp;582170][B](2^15135397+1)/3 is a Fermat Probable prime! (4556209 decimal digits)
[/B]

Also submitted to PRPTop.[/QUOTE]:beer2: :beer2: :beer2: :beer2: :beer2: :beer2:

:party:

Congratulations! What base did you use for the PRP test? Three, perhaps?

ryanp 2021-06-29 13:24

[QUOTE=Dr Sardonicus;582206]Congratulations! What base did you use for the PRP test? Three, perhaps?[/QUOTE]

I've run the Fermat PRP test with sllr64 using b=3, b=5, b=7 and b=11.

Dr Sardonicus 2021-06-29 15:32

[QUOTE=ryanp;582213]I've run the Fermat PRP test with sllr64 using b=3, b=5, b=7 and b=11.[/QUOTE]Thanks!

Silly me, I failed to consider that you had tested multiple bases. :blush:

Of course, these numbers automatically "pass" the test to base 2. Paper and pencil suffices for this one.

If p > 3 is prime, N = (2^p + 1)/3, then (N-1)/2 = (2^(p-1) - 1)/3 is odd and divisible by p, so

N = (2^p + 1)/3 divides 2^p + 1, and 2^p + 1 divides 2^((N-1)/2) + 1, so N divides 2^((N-1)/2) + 1.

Now 2^((N-1)/2) + 1 divides 2^(N-1) - 1, so N divides 2^(N-1) -1, but does not divide 2^((N-1)/2) - 1.

sweety439 2021-06-29 16:59

[QUOTE=ryanp;582170][B](2^15135397+1)/3 is a Fermat Probable prime! (4556209 decimal digits)
[/B]

Also submitted to PRPTop.

I am searching the range n=13M .. 17M currently, and nearly done. No other discoveries as of yet.[/QUOTE]

Can you test all Wagstaff exponents below it? Currently only the Wagstaff exponents below 10 million are tested, see [URL="https://mersenneforum.org/showthread.php?t=24185"]https://mersenneforum.org/showthread.php?t=24185[/URL]

sweety439 2021-06-29 17:02

[QUOTE=ryanp;582213]I've run the Fermat PRP test with sllr64 using b=3, b=5, b=7 and b=11.[/QUOTE]

Only run Fermat test is dangerous, as there are many Carmichael numbers, see [URL="https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test#The%20danger%20of%20relying%20only%20on%20Fermat%20tests"]https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test#The%20danger%20of%20relying%20only%20on%20Fermat%20tests[/URL], you should run either Miller-Rabin test or Baillie–PSW test.

mathwiz 2021-06-29 20:23

[QUOTE=sweety439;582230]Only run Fermat test is dangerous, as there are many Carmichael numbers, see [URL="https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test#The%20danger%20of%20relying%20only%20on%20Fermat%20tests"]https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test#The%20danger%20of%20relying%20only%20on%20Fermat%20tests[/URL], you should run either Miller-Rabin test or Baillie–PSW test.[/QUOTE]

As has been asked in numerous other threads: Is it that you lack the understanding, or the software/hardware, to do this yourself?

Maybe a mod can ban this guy until he stops flooding the forum with requests for other people to do things.

paulunderwood 2021-06-29 20:37

[QUOTE=sweety439;582230]Only run Fermat test is dangerous, as there are many Carmichael numbers, see [URL="https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test#The%20danger%20of%20relying%20only%20on%20Fermat%20tests"]https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test#The%20danger%20of%20relying%20only%20on%20Fermat%20tests[/URL], you should run either Miller-Rabin test or Baillie–PSW test.[/QUOTE]

The instructions on how to run sllr with switches to do a lucas test and a bpsw test are given in [URL="https://mersenneforum.org/showpost.php?p=578120&postcount=50"]this post[/URL]. If Ryan nor someone else does not step up to the plate in the meantime, I'll do it at the weekend.

VBCurtis 2021-06-29 21:33

[QUOTE=mathwiz;582247]Maybe a mod can ban this guy until he stops flooding the forum with requests for other people to do things.[/QUOTE]

We gave him some time off to consider his behavior, and it hasn't changed much. I suppose your suggestion and this reply might be considered yet another warning to Sweety before the banhammer falls again.


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