Mersenne Milestone
 

Recently, Alex Rodriguez (NY Yankee third baseman and slugger)
hit his lifetime home run #521, tying him with Ted Williams and
Willie McCovey on the all-time home run list.

A ho-mer-senne achievement !

(He has since passed that number, which I take as encouragement
that the next Mersenne prime M45 will soon be found.)

M521 is indeed a "Mersenne Milestone" albeit achieved 57 years ago.
The gap from M127 had lasted 75 years.
Notably Alan Turing would have discovered it first, were it not
for the fact that his memory was only 1024 bits.

As of this morning, A-Rod has 599 homers. When he hits the next one,
he'll be the seventh player to reach 600. Of course, this isn't the real
milestone -- we're counting up to #607. Barring a catastrophe, he
should get there in a few weeks. His chances of getting to the next
MP exponent (1279) are, however, rather slim.

Anyone want to check the Total Hits records for Mersenne-ality?

As of today, ARod has hit a total of six hundred five (that's 605) homers
in his major league career. According to extensive calculations, 605 is
not a prime number, so 2^605-1 is also composite. This means that
there is no Mersenneness in his total at the moment. If someone would
check 606 for exclusion of primality, we can jump ahead and anticipate
that 2 homers from now (which may come any day) he'll reach the MM
(Mersenne Milestone) of 607 dingers. No one has done better,
Mersenne-wise. At least in MLB. Number theorist Yankee fans wish
him the best.

Today, 9/17/2010, Alex Rodriguez of the New York Yankees,
batting against the Baltimore Orioles, hit the 607th home run
of his major league career.

2^607 - 1 is the 14th Mersenne Prime.

The long wait is over.

Footnote to previous post: in the same game, ARod hit a SECOND homer
in the ninth inning, a three-run blast that gave the Yankees the lead and
the win, which coupled with the Tampa Bay Rays' loss moments before
put the Yankees back into first place in their division. This was ARod's
608th homer.

2^608 - 1 is composite, not prime.

Unless he gets close to 1279 homers, this story is completed.

Will Mersenne's never cease?

I have a question. How can we designate our GIMPS milestones in advance?

We know that finding (i.e. locating) an MP is an identifiable milestone.
All of us eagerly wait for each such discovery.

Is proving an MP's sequence value a major or minor milestone?
Can we prioritize intermediate milestones in a measured way?

Just suggesting this would be useful for us to know.

[QUOTE=davar55;242597]I have a question. How can we designate our GIMPS milestones in advance?[/QUOTE]By following the Yankees, obviously. Or the Red Sox. :smile:

[QUOTE=cheesehead;242670]By following the Yankees, obviously. Or the Red Sox. [/QUOTE]

Well, the Red Sox are a good team,
but they don't have the same mersennality
as the new york yankees.

ARod ended the 2010 season with
(I think) 613 lifetime homers.

613 is prime, but 2^613-1 is composite.
What are its factors?

[QUOTE=davar55;243233]613 is prime, but 2^613-1 is composite.
What are its factors?[/QUOTE]
Isn't it just 333628015107245479, 474640860193534882628078580680807822523991, and 56272943145171606416041974272779967237377245135400982739236727888151415549771970573866251017208467153984404288129453336803370700223?

Or did I totally miss the point? :)

[QUOTE=KingKurly;243241]Isn't it just 333628015107245479, 474640860193534882628078580680807822523991, and 56272943145171606416041974272779967237377245135400982739236727888151415549771970573866251017208467153984404288129453336803370700223?

Or did I totally miss the point? :)[/QUOTE]

Actually, its [URL="http://factordb.com/index.php?query=2^613-1"]factors[/URL] are:[CODE]44599476833089207
332817722770314187794325446534549089
2290082526100134480992198124951512750039139339635155094272008280546850886939008711730865851616722892614369047154769105713048457413017[/CODE]But I don't get the point either. :unsure:

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?