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Old 2021-06-28, 20:14   #1
ryanp
 
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Default Announcing a new Wagstaff PRP

(2^15135397+1)/3 is a Fermat Probable prime! (4556209 decimal digits)


Also submitted to PRPTop.

I am searching the range n=13M .. 17M currently, and nearly done. No other discoveries as of yet.
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Old 2021-06-28, 21:19   #2
paulunderwood
 
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Quote:
Originally Posted by ryanp View Post
(2^15135397+1)/3 is a Fermat Probable prime! (4556209 decimal digits)


Also submitted to PRPTop.

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

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Old 2021-06-28, 23:38   #3
diep
 
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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.
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Old 2021-06-29, 11:29   #4
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Quote:
Originally Posted by ryanp View Post
(2^15135397+1)/3 is a Fermat Probable prime! (4556209 decimal digits)


Also submitted to PRPTop.




Congratulations! What base did you use for the PRP test? Three, perhaps?
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Old 2021-06-29, 13:24   #5
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Quote:
Originally Posted by Dr Sardonicus View Post
Congratulations! What base did you use for the PRP test? Three, perhaps?
I've run the Fermat PRP test with sllr64 using b=3, b=5, b=7 and b=11.
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Old 2021-06-29, 15:32   #6
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Quote:
Originally Posted by ryanp View Post
I've run the Fermat PRP test with sllr64 using b=3, b=5, b=7 and b=11.
Thanks!

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

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.
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Old 2021-06-29, 16:59   #7
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Quote:
Originally Posted by ryanp View Post
(2^15135397+1)/3 is a Fermat Probable prime! (4556209 decimal digits)


Also submitted to PRPTop.

I am searching the range n=13M .. 17M currently, and nearly done. No other discoveries as of yet.
Can you test all Wagstaff exponents below it? Currently only the Wagstaff exponents below 10 million are tested, see https://mersenneforum.org/showthread.php?t=24185
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Old 2021-06-29, 17:02   #8
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Quote:
Originally Posted by ryanp View Post
I've run the Fermat PRP test with sllr64 using b=3, b=5, b=7 and b=11.
Only run Fermat test is dangerous, as there are many Carmichael numbers, see https://en.wikipedia.org/wiki/Bailli...Fermat%20tests, you should run either Miller-Rabin test or Baillie–PSW test.

Last fiddled with by sweety439 on 2021-06-29 at 17:02
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Old 2021-06-29, 20:23   #9
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Quote:
Originally Posted by sweety439 View Post
Only run Fermat test is dangerous, as there are many Carmichael numbers, see https://en.wikipedia.org/wiki/Bailli...Fermat%20tests, you should run either Miller-Rabin test or Baillie–PSW test.
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.
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Old 2021-06-29, 20:37   #10
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Quote:
Originally Posted by sweety439 View Post
Only run Fermat test is dangerous, as there are many Carmichael numbers, see https://en.wikipedia.org/wiki/Bailli...Fermat%20tests, you should run either Miller-Rabin test or Baillie–PSW test.
The instructions on how to run sllr with switches to do a lucas test and a bpsw test are given in this post. If Ryan nor someone else does not step up to the plate in the meantime, I'll do it at the weekend.

Last fiddled with by paulunderwood on 2021-06-29 at 20:38
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Old 2021-06-29, 21:33   #11
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Quote:
Originally Posted by mathwiz View Post
Maybe a mod can ban this guy until he stops flooding the forum with requests for other people to do things.
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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