Since you had ready access to that factorization of 2^613-1,
I now could double-check both my assertion that it was not
prime as well as the correct functioning of my self-built integer
arbitrary precision calculator, which is currently in mothballs
since I'm on a different computer now. Thanks for the factors.

As a result of not having to actually factor 2^613-1 on my own,
I was able to relocate my YJ-Conjecture,

It starts at post#11 of thread [URL="http://www.mersenneforum.org/showthread.php?t=2475"]41st Known Mersenne Prime Reported!![/URL] in the Lounge.

This connects to a (possible) proof of the Infinitude of the Mersenne Primes,
currently in progress. That would be the automatic corollary.

I'll have to check what I put into the wiki and wikipedia first ...

Can't get in, forgot account names and passwords. Later.

[QUOTE=Mini-Geek;243280]Actually, its [URL="http://factordb.com/index.php?query=2%5E613-1"]factors[/URL] are:[CODE]44599476833089207
332817722770314187794325446534549089
2290082526100134480992198124951512750039139339635155094272008280546850886939008711730865851616722892614369047154769105713048457413017[/CODE]But I don't get the point either. :unsure:[/QUOTE]
Ooooooooops. I did M631, not M613 as requested. I was wondering how I was so far off the mark. :loco:

My calculator confirms the correct products producing M613 and M631.

Thanks.

As of April 22, 2011 A.D., Alex Rodriquez,
popularly known as ARod (by way of some
mathematically based name reduction known
as nicknaming) is on the verge of hitting
his 618th lifetime homer. This puts him
squarely among the top HR sluggers of
all time. Since 618 is not prime, the
Mersenne number value of 2^618-1 is
factorable. ARod's slow approach to
the next Mersenne exponent, namely 1279,
will undoubtedly take a while. In the
meantime, Yankee fans can hopefully look
forward eventually to homers 650 (maybe
this season) and if he stays healthy 700
and maybe higher.

As of today, New York Yankee shortstop Derek Jeter has
pounded out 3012 career hits with the Yankees. This is
within reach of the Mersenne exponent 3217, but not
this season. We look forward to Derek's prime accomplishment.

Derek has, as of today, gotten 3215 lifetime hits.
Barring injury to the Yankee star, he should reach
the Mersenne milestone of 3217 hits very soon.

BTW of course 2^3217 - 1 is prime, and is
the 18th Mersenne prime.

The next Mersenne prime exponent is 4253, which
may take a while for him to reach. The record number
of lifetime hits is 4256.

I missed it.

In the last few days, Derek Jeter smacked his 3217th hit,
and none of us was even there to witness it.

What's next, not finding M48 in 2012?