## the factorization of 2^3780-1

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• Will Edgington reports in http://www.garlic.com/~wedgingt/factoredM.txt that this number is fully factored and lists the following factors of Phi(3780,2): 7561
Message 1 of 2 , Apr 18, 2010
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Will Edgington reports in http://www.garlic.com/~wedgingt/factoredM.txt that this number is fully factored and lists the following factors of Phi(3780,2):

7561
457381
2143261
43887888187572165151544641
53557082595126165043094157045628806518641
596526861195233662750200340726624395569101

But the 137-digit cofactor

11835608140763071524303999533711842540641126211504770258957518988760449701201552155974559825090452912710060535156149229064438721828906941

is still composite.

Maybe I misunderstand something there..?

Thanks,

Andrey

[Non-text portions of this message have been removed]
• ... Yes, Andrey: you failed to understand that Will expects you to do the remaining Aurifeuillian factorization for yourself. Here, I ask Pari-GP to do it for
Message 2 of 2 , Apr 18, 2010
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Andrey Kulsha <Andrey_601@...> wrote:

> Will Edgington reports in
> http://www.garlic.com/~wedgingt/factoredM.txt
> that this number is fully factored

> Maybe I misunderstand something there..?

Yes, Andrey: you failed to understand that Will expects
you to do the remaining Aurifeuillian factorization
for yourself.

Here, I ask Pari-GP to do it for you:

{wills=[7561,457381,2143261,43887888187572165151544641,
53557082595126165043094157045628806518641,
596526861195233662750200340726624395569101];}

N=subst(polcyclo(3780),x,2);
will=N/prod(k=1,#wills,wills[k]);

\\ http://homes.cerias.purdue.edu/~ssw/cun/pmain1209
\\ 2^2h+1=L.M, L=2^h-2^k+1, M=2^h+2^k+1, h=2k-1.

k=473; h=2*k-1; L=2^h-2^k+1; M=2^h+2^k+1;

print(gcd(will,[L,M]))

[2670383929348266924341948931151336592642126516143095249535829086413119821,
4432174718656154579820150556638898270574244648997765405952796721]

David
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