## Re: [PrimeNumbers] Re: A PRP of the form 2*k*p +1

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• ... no need to use Mathematica for that: 2*7 = 14 ; + 1 = 15 . Indeed a quite improbable prime. ... This I cannot confirm, according to PARI, divisors
Message 1 of 9 , Sep 1, 2011
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>> 2*(10^100000 + 50617) + 1 as a probable prime of 100006 digits;

>
> Am I missing something, according to Mathematica:
>
>  2*(10^100000+50617) + 1 ends in a 5

no need to use Mathematica for that:

2*7 = 14 ; + 1 = 15 .

Indeed a quite improbable prime.

> 2*(10^100000*50617) + 1 is divisible by 967 & 23473

This I cannot confirm, according to PARI, divisors < 5e5 are:
5,36263 for 2*(10^100000+50617) + 1
3,7,17,19 for 2*(10^100000+50617) - 1
3,17,19,23473 for 2*(10^100000*50617) + 1
11,167 for 2*(10^100000*50617) - 1

But in fact the " * " versions don't make sense
(why the "2" would be outside and 50617 inside the (...) ?)

Maximilian
• ... Perhaps Peter meant to write something like 2*(10^100000+50617)*333019 + 1 David (looking at the title)
Message 2 of 9 , Sep 1, 2011
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"Alan R Powell" <AlanPowell@...> wrote:

> > 2*(10^100000 + 50617) + 1 as a probable prime of 100006 digits;
> 2*(10^100000+50617) + 1 ends in a 5
> 2*(10^100000*50617) + 1 is divisible by 967 & 23473

Perhaps Peter meant to write something like

2*(10^100000+50617)*333019 + 1

David (looking at the title)
• ... according to OpenPFGW (2*(10^100000+50617)+1)/(5*36263*376504523) has no small factor. David
Message 3 of 9 , Sep 1, 2011
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Maximilian Hasler <maximilian.hasler@...> wrote:

> according to PARI, divisors < 5e5 are:
> 5,36263 for 2*(10^100000+50617) + 1

according to OpenPFGW
(2*(10^100000+50617)+1)/(5*36263*376504523) has no small factor.

David
• ... It appears so: 2*(10^100000+50617)*333019+1 is 3-PRP! (1146.4749s+0.0010s) and hence may be Henrified. David
Message 4 of 9 , Sep 1, 2011
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> Perhaps Peter meant to write something like
> 2*(10^100000+50617)*333019 + 1

It appears so:

2*(10^100000+50617)*333019+1 is 3-PRP! (1146.4749s+0.0010s)

and hence may be Henrified.

David
• Really sorry for the clumsy mistake. I m indeed testing 2*k*p +1, and p=333019 is missing in the previous message. For interest s sake I found some two smaller
Message 5 of 9 , Sep 2, 2011
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Really sorry for the clumsy mistake. I'm indeed testing 2*k*p +1, and p=333019 is missing in the previous message. For interest's sake I found some two smaller PRPs before this one; i.e.

(1) 2*(10^10000+36107)*333019+1 is probable prime! (verification : a = 36761) (digits:10006)

(2) 2*(10^10000+49931)*333019+1 is probable prime! (verification : a = 36761) (digits:10006)

and then lately

(3) 2*(10^100000+50617)*333019+1 is probable prime! (verification : a = 42349) (digits:100006)

Thanks to David for the verification.

Peter.

----- Original Message -----
From: Peter Lesala
Sent: Thursday, September 01, 2011 12:22 PM
Subject: [PrimeNumbers] A PRP of the form 2*k*p +1

Keen to find prime factors of 2^333019 - 1, I went on to test 2*k*p + 1 for k = 10^100000. The test gives

2*(10^100000 + 50617) + 1 as a probable prime of 100006 digits; using Primeform.

Peter.

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• ... Might you tell us, please, Peter, why you chose to study this particular Mersenne exponent? ... Monna ya fetolang mmala ka nako le nako? Best regards David
Message 6 of 9 , Sep 2, 2011
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"Peter Lesala" <plesala@...> wrote:

> Keen to find prime factors of 2^333019 - 1

Might you tell us, please, Peter, why you chose
to study this particular Mersenne exponent?

> p=333019 is missing in the previous message

Monna ya fetolang mmala ka nako le nako?

Best regards

David
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