MM61

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• Hi How can i perform this expression: (2^(2^61-1)-1) mod 223 with GMP library? What s the C function sequence? Thank you Giovanni
Message 1 of 13 , Oct 2, 2009
Hi
How can i perform this expression:

(2^(2^61-1)-1) mod 223

with GMP library?
What's the C function sequence?
Thank you
Giovanni
• ... in PARI, use Mod(2,223)^(2^61 % eulerphi(223) -1) - 1 %146 = Mod(14, 223) i.e. MM61 = 14 (mod 223) Since 223 is prime, the exponent can be reduced mod
Message 2 of 13 , Oct 2, 2009
--- In primenumbers@yahoogroups.com, "Di Maria Giovanni" <calimero22@...> wrote:
>
> Hi
> How can i perform this expression:
>
> (2^(2^61-1)-1) mod 223
>
> with GMP library?
> What's the C function sequence?

in PARI, use

Mod(2,223)^(2^61 % eulerphi(223) -1) - 1
%146 = Mod(14, 223)

i.e. MM61 = 14 (mod 223)

Since 223 is prime, the exponent can be reduced mod phi(223).
Here I did it using %, but it would be better to do it via Mod(),
to avoid computation of the big number:

Mod(2,223)^lift(Mod(2,eulerphi(223))^61-1) - 1

Maximilian
• ... According to Landon Curt Noll and Tony Forbes, MM61 is not divisible by any prime less than 43180130614086110782608760243
Message 3 of 13 , Oct 2, 2009
"maximilian_hasler" <maximilian.hasler@...> wrote:

> i.e. MM61 = 14 (mod 223)

According to Landon Curt Noll and Tony Forbes,
MM61 is not divisible by any prime less than
43180130614086110782608760243

http://www.garlic.com/~wedgingt/MMPstats.txt

David
• More also here: http://anthony.d.forbes.googlepages.com/mm61prog.htm Norman
Message 4 of 13 , Oct 2, 2009
• ... Geoff Reynolds and I wrote a program that is faster than Tony s, but he has not responded to our inquiries to see if he is interested in our code. --Mark
Message 5 of 13 , Oct 2, 2009
---- Norman Luhn <nluhn@...> wrote:
> More also here:
>

Geoff Reynolds and I wrote a program that is faster than Tony's, but he has not responded to our inquiries to see if he is interested in our code.

--Mark
• Hi, BTW, does someone here know if there s (still) an active project to find a factor of MM127 (i.e. C5); and if so, what s the current status for this number?
Message 6 of 13 , Oct 5, 2009
Hi,

BTW, does someone here know if there's (still) an active project to find a factor of MM127 (i.e. C5); and if so, what's the current status for this number?

http://www.garlic.com/~wedgingt/MMPstats.txt page seems a bit outdated.

Jean-Louis

>
>
> ---- Norman Luhn <nluhn@...> wrote:
> > More also here:
> >
>
> Geoff Reynolds and I wrote a program that is faster than Tony's, but he has not responded to our inquiries to see if he is interested in our code.
>
> --Mark
>
• Andrew Steward maintains an amazing list of all known legal generalized repunit primes at http://www.primes.viner-steward.org/andy/titans.html . In Chris
Message 7 of 13 , Oct 5, 2009
Andrew Steward maintains an amazing list of all known legal generalized
repunit primes at http://www.primes.viner-steward.org/andy/titans.html .

In Chris Caldwell's sense, a legal generalized repunit prime is a prime
number of the form (b^p-1)/(b-1) such that 3<=b<=5p, b<>10, p prime.

Unfortunately, as far as I know, a list of pseudoprimes to fill the gaps
in Andy's list is not available, so I started collecting them to help
Andrew's site grow.

You can find the list at phi.redgolpe.com .

Bernardo Boncompagni

________________________________________________

"When the missionaries arrived, the Africans had
the land and the missionaries had the bible.
They taught how to pray with our eyes closed.
When we opened them, they had the land and we
Jomo Kenyatta

VisualTaxa - Taxonomy in a visual way
http://visualtaxa.redgolpe.com
________________________________________________
• ... If you mean Caldwell-legal probable GRU primes, then Andy has no gaps below 16679 digits: http://www.primes.viner-steward.org/andy/titans.html ... Those
Message 8 of 13 , Oct 5, 2009
Bernardo Boncompagni <RedGolpe@...> wrote:

> a list of pseudoprimes to fill the gaps

If you mean Caldwell-legal probable GRU primes,
then Andy has no gaps below 16679 digits:

http://www.primes.viner-steward.org/andy/titans.html
> All legal examples with fewer than 16679 digits
> have been found. 3452 await proof.

Those PRPs sit in his private files, while ECM tries
to factorize cyclotomic cofactors of N-1, for a proof.

David
• ... I know. Since his files are private I m just trying to speed up the process of primality proving by publishing at least a small portion of those PRP s. A
Message 9 of 13 , Oct 5, 2009

> If you mean Caldwell-legal probable GRU primes,
> then Andy has no gaps below 16679 digits:

> Those PRPs sit in his private files

I know. Since his files are private I'm just trying to speed up the
process of primality proving by publishing at least a small portion of
those PRP's. A quantity of them are below 3,500 digits and could be
easily proven with PRIMO without terrible efforts. And tbh, I don't like
the idea of "private files" in the first place.

Bernardo Boncompagni

________________________________________________

"When the missionaries arrived, the Africans had
the land and the missionaries had the bible.
They taught how to pray with our eyes closed.
When we opened them, they had the land and we
Jomo Kenyatta

VisualTaxa - Taxonomy in a visual way
http://visualtaxa.redgolpe.com
________________________________________________
• ... Here s a PRP for your collection: http://www.primenumbers.net/prptop/searchform.php?form=%3F180181%3F ... Solution:
Message 10 of 13 , Oct 6, 2009
Bernardo Boncompagni <RedGolpe@...> wrote:

> Since his files are private I'm just trying to speed up the
> process of primality proving by publishing at least a small
> portion of those PRP's.

Here's a PRP for your collection:

Incidentally, Andy's site provides what is neeed here:

> Puzzle 89: For a base with 89 > b > 2, find a gigantic
> base-b superpseudoprime with precisely 26 composite divisors.

Solution: 206007889*425389507*662130751*2517984907*(15^8741-1)/14
is a gigantic base-15 pseudoprime with precisely
26 composite divisors, all of which are 15-PRP.

David
• ... Added :) I was aware of Henry Lifchitz s site but didn t think about checking it for generalized repunits. Unfortunately now that I did I couldn t find any
Message 11 of 13 , Oct 7, 2009

> Here's a PRP for your collection:

Added :) I was aware of Henry Lifchitz's site but didn't think about
checking it for generalized repunits. Unfortunately now that I did I
couldn't find any more than the one you mentioned.

Bernardo Boncompagni

________________________________________________

"When the missionaries arrived, the Africans had
the land and the missionaries had the bible.
They taught how to pray with our eyes closed.
When we opened them, they had the land and we
Jomo Kenyatta

VisualTaxa - Taxonomy in a visual way
http://visualtaxa.redgolpe.com
________________________________________________
• ... http://www.primenumbers.net/prptop/searchform.php?form=%28b^n-1%29%2Fa&action=Search That will catch some Mersenne cofactors as well, but will turn up no
Message 12 of 13 , Oct 7, 2009
--- In primenumbers@yahoogroups.com, Bernardo Boncompagni <RedGolpe@...> wrote:
>
>
> > Here's a PRP for your collection:
>
> Added :) I was aware of Henry Lifchitz's site but didn't think about
> checking it for generalized repunits. Unfortunately now that I did I
> couldn't find any more than the one you mentioned.

That will catch some Mersenne cofactors as well, but will turn up no shortage of PrP GRUs.

Tom
• ... Nice one. I actually searched only for ?Phi? . Bernardo Boncompagni ________________________________________________ When the missionaries arrived, the
Message 13 of 13 , Oct 8, 2009
tjw99 dice:

> That will catch some Mersenne cofactors as well, but will turn up no
> shortage of PrP GRUs.

Nice one. I actually searched only for "?Phi?".

Bernardo Boncompagni

________________________________________________

"When the missionaries arrived, the Africans had
the land and the missionaries had the bible.
They taught how to pray with our eyes closed.
When we opened them, they had the land and we