## Naive question on 2^1896-1

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• I m trying to factor the last part of 2^1896-1 or: 72009645598802661741572237135153453757864421072572019369424603012486080
Message 1 of 6 , Jun 11, 2007
I'm trying to factor the last part of 2^1896-1 or:

72009645598802661741572237135153453757864421072572019369424603012486080
97428061518078682794754267412326389601722982929011560986986540564455161
820809601187482593072913719887735073

Now I am pretty sure that this divides:

2^538068484267451755443320936669773737369137536084905561829471950020466
0377974294835542217932123668240-1

Would this conceivably help me to finish factoring 2^1896-1, assuming
the factoring of
53806848426745175544332093666977373736913753608490556182947195002046603
77974294835542217932123668240 is the simpler of the two tasks?

Kevin.
• Sorry, Forget that, I hadn t checked for divisibility by 1896 before I posted. Which is what comes of too much haste and not enough speed. Kevin. ... I m
Message 2 of 6 , Jun 11, 2007
Sorry,

Forget that, I hadn't checked for divisibility by 1896 before I posted.
Which is what comes of too much haste and not enough speed.

Kevin.

-----Original Message-----

I'm trying to factor the last part of 2^1896-1 or:
[...]
• ... Do you just want the factors, or do you want to learn how to find the factors? If you just want the factors, you can use Alpertron at
Message 3 of 6 , Jun 12, 2007
--- In primenumbers@yahoogroups.com, "Kevin" <research@...> wrote:
>
> I'm trying to factor the last part of 2^1896-1 or:
>
> 72009645598802661741572237135153453757864421072572019369424603012486080
> 97428061518078682794754267412326389601722982929011560986986540564455161
> 820809601187482593072913719887735073

Do you just want the factors, or do you want to learn how to find the
factors?

If you just want the factors, you can use Alpertron at

http://www.alpertron.com.ar/ECM.HTM

known factors for numbers of this form. If you want to know how to
find the factors, you need to learn about algebraic factors and the
various factor lists. There is a discussion of Algebraic Factors in
the Cunningham Book, available online, and in the ElevenSmooth FAQ.
The needed factors are in Will Edgington's Mersenne factors lists
(2^n-1) and also Richard Brent's factor lists (a^n +/- 1 for a<10000
n<10000).
• ... From: elevensmooth [mailto:elevensmooth@yahoo.com] Sent: 12 June 2007 22:57 To: primenumbers@yahoogroups.com Subject: [PrimeNumbers] Re: Naive question on
Message 4 of 6 , Jun 12, 2007
-----Original Message-----
From: elevensmooth [mailto:elevensmooth@...]
Sent: 12 June 2007 22:57
Subject: [PrimeNumbers] Re: Naive question on 2^1896-1

--- In primenumbers@yahoogroups.com, "Kevin" <research@...> wrote:
>
> I'm trying to factor the last part of 2^1896-1 or:
>
> 72009645598802661741572237135153453757864421072572019369424603012486080
> 97428061518078682794754267412326389601722982929011560986986540564455161
> 820809601187482593072913719887735073

> Do you just want the factors, or do you want to learn how to find the
> factors?

Hi,

The question arises from the results of a program I have that diverged from
the Wieferich search.

Basically it finds composite Mersenne numbers and a large composite or prime
(if you're lucky) that divides it.

A better example than the previous one is where the program output shows:

2869070461631637574244868351418889546260799144254581951743734382009219393441
76261145611475682317574468979232833614978133229351

divides 2^19071324012257094604424955-1

Which isn't much of a find since the above number actually divides 2^795-1.

So basically an hours running throws up a lot of large primes, it's just
unfortunate that nearly all already exist in lowM.txt or are trivially found
on Alpertron.

The premise is that it's very easy to produce thousands of large primes or
composites that divide a range of Mersenne numbers. What isn't easy is to
find a prime that isn't already known. Rather than attempt to factor a
specific number it produces a number that it knows will factor some Mersenne
number.

Still, I'll spend a while tuning the program and see if anything new pops
up.

Kevin.
• Hello, I have found in few seconds with my program: 2^1896 have prime factor 201487636602438195784363 I don t know, this factor are known ? regards
Message 5 of 6 , Jun 13, 2007
Hello,
I have found in few seconds with my program:

2^1896 have prime factor 201487636602438195784363

I don't know, this factor are known ?

regards

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• ... All factors of 2^1896-1 are known. The simplest way to check that is to use the Alpertron Java factoring applet at http://www.alpertron.com.ar/ECM.HTM
Message 6 of 6 , Jun 13, 2007
--- In primenumbers@yahoogroups.com, "N.L." <nluhn@...> wrote:

> 2^1896 have prime factor 201487636602438195784363
>
> I don't know, this factor are known ?

All factors of 2^1896-1 are known. The simplest way to check that is
to use the Alpertron Java factoring applet at
http://www.alpertron.com.ar/ECM.HTM

William
Poohbah of OddPerfect.org
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