## RE: [PrimeNumbers] RE: Anyone like to prove primality of a Mersenne cofactor?

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• How s the factorization of 2^(2^n)-1 coming along? Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/
Message 1 of 7 , Mar 31, 2003
How's the factorization of 2^(2^n)-1 coming along?

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths/
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• Voodoo De Ja!!! Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP
Message 2 of 7 , Mar 31, 2003
• Will Edgington and I try to keep our tables of Mersenne factorizations up to date by synchronizng every week or so. The latest indicated that another
Message 3 of 7 , Apr 1, 2003
Will Edgington and I try to keep our tables of Mersenne factorizations up to date by synchronizng every week or so. The latest indicated that another Mersenne number had been completely factored. Neither Will nor I have the resources at the moment to prove the 2193-digit cofactor of M(7417) is prime. It's certainly a strong pseudoprime.

If anyone would care to complete the proof, please let Will and me know the result. The known prime factors of M(7417) are 118673, 16269026327 and 3888241452787718190543521.

Apologies for not crediting the person who found the largest of the three factors given above. I don't know who he or she is.

Paul
• Hi, Well I would do, but Primo doesn t seem to like wine. Has anyone had any success with that, or does anyone know of a Linux ECPP tool with comparable
Message 4 of 7 , Apr 1, 2003
Hi,

Well I would do, but Primo doesn't seem to like wine. Has anyone had any
success with that, or does anyone know of a Linux ECPP tool with comparable
speed?

Mike.

Paul Leyland wrote:
> Will Edgington and I try to keep our tables of Mersenne factorizations
> up to date by synchronizng every week or so. The latest indicated that
> another Mersenne number had been completely factored. Neither Will nor
> I have the resources at the moment to prove the 2193-digit cofactor of
> M(7417) is prime. It's certainly a strong pseudoprime.
>
> If anyone would care to complete the proof, please let Will and me know
> the result. The known prime factors of M(7417) are 118673, 16269026327
> and 3888241452787718190543521.
>
> Apologies for not crediting the person who found the largest of the
> three factors given above. I don't know who he or she is.
>
> Paul
>
>
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
>
>
> <http://docs.yahoo.com/info/terms/>.
• (2^7417-1)/(1930694161304071*3888241452787718190543521) 2193 c8 2002 Mersenne cofactor, ECPP
Message 5 of 7 , Apr 1, 2003
(2^7417-1)/(1930694161304071*3888241452787718190543521) 2193 c8 2002
Mersenne cofactor, ECPP
• These are the 6 smallest unproven probably prime Mersenne cofactors known to me: (2^14561-1)/8074991336582835391 (2^17029-1)/418879343
Message 6 of 7 , Apr 1, 2003
These are the 6 smallest unproven probably prime
Mersenne cofactors known to me:

(2^14561-1)/8074991336582835391

(2^17029-1)/418879343

(2^20887-1)/(694257144641*3156563122511*28533972487913*\
1893804442513836092687)

(2^28759-1)/226160777

(2^28771-1)/104726441

(2^32531-1)/(65063*25225122959)

• ... About as well as the factorization of 2^(2^n)+1 (the Fermat numbers). ... 2^(2^n)-1 == prod(i=0,n-1,2^(2^i)+1) So, completely factored up to 2^(2^12)-1.
Message 7 of 7 , Apr 1, 2003
--- In primenumbers@yahoogroups.com, "Jon Perry" <perry@g...> wrote:
> How's the factorization of 2^(2^n)-1 coming along?

About as well as the factorization of 2^(2^n)+1 (the Fermat numbers).

:)

2^(2^n)-1 == prod(i=0,n-1,2^(2^i)+1)

So, completely factored up to 2^(2^12)-1.

2^(2^13)-1, not yet factored.
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