[quote]If I may go off on a fairly wild tangent here, I have a friend who tried sieving numbers of the form k*2^n+1, where 2^n+1 was a Fermat number. Sometimes he would find factors of 7 digits or more which would wipe out a huge chunk of the remaining equations in one fell swoop(as much as 1/3rd of the numbers in a sieve file). Maybe there are properties to the factors of the Mersenne numbers that we haven't discovered which could shed some light on why the last 8 Mersenne primes are so close together. Possibly even the sort of thing which could help find gigantic primes in general, since sieving is a major part of prime-finding.[/quote]I agree absolutely, but the solution will be mathematical not arithmetical.

[quote]If He exists outside of time, why did He wait until something was about to happen before "realizing" it and then changed things at almost the last moment?

I believe He extended His noodly appendage at the moment of creation to make sure everything worked out correctly.
[/quote]I recognize the humor, but you really have the beginnings of a proof
of his non-existence. In the religious intolerance thread, perhaps?

For M47: soon.

For M48: ~52,100,000 in 12/2011-2/2012.

For M49 (to jump the gun): sooner or later.

Here is a current summary of the current guesses.
[FONT="Fixedsys"]
Damian.........45,000,000
Storm5510......46,500,000....[COLOR="Red"][strike]09/15/2010[/strike][/COLOR]
Primeinator....47,300,000....[COLOR="Red"][strike]10/01/2009[/strike][/COLOR]
jasong.........48,200,000
ATH............49,000,000....[COLOR="Red"][strike]03/01/2010[/strike][/COLOR]
Raman..........50,000,000
MiniGeek.......50,000,000....[COLOR="Red"][strike]09/01/2009[/strike][/COLOR]
ixfd64.........50,000,000....[COLOR="Red"][strike]02/01/2010[/strike][/COLOR]
uigrad.........51,500,000....[COLOR="Red"][strike]08/01/2009[/strike][/COLOR]
davar55 .......52,100,000....12/31/2011
McDuck ........54,000,000....[COLOR="Red"][strike]06/24/2010[/strike][/COLOR]
firejuggler....57,500,000
10metreh.......59,278,411....06/30/2011
davieddy.......60,000,000....01/01/2012
joblack........60,500,000
Oddball........78,000,000....01/01/2013
MoooMoo........75,860,000....05/01/2013
XYYXF..........88,000,000....11/01/2011
nngs...........90,087,850
Terrance Law...98,000,000....05/01/2011
Uncwilly......332,192,831....02/12/2011
henryzz......................[COLOR="Red"][strike]08/31/2009[/strike][/COLOR]
ET_..........................12/20/2012
Yzzyx .......................01/19/2038[/FONT]


For the fun of it here are some calculations based upon data from the GIMPS era:
[CODE]Last discovery: 4/12/09
LD plus ave. gap 4/24/10
above
+1/2 standard deviation 9/7/10
+average dev 12/2/10
+1 std dev 1/20/11 <--already past
+1.5 std dev 6/5/11
LD + max gap 9/26/11[/CODE]
All exponents below 37,591,483 have been tested at least once.

My standing prediction (from another thread): [url]http://www.mersenneforum.org/showpost.php?p=86896&postcount=3[/url]

55,555,543

May 5, 2012 (2+0+1+2 = 5)

I have added those posted and went as far back as I could (older threads) and entered everything that was larger or later than the to-date status of 37591483 on 1/24/2011

[QUOTE=10metreh;176246]Well, we don't know "M47" is prime, but we have strong evidence for it, so it's time to have a guess at M48. My guess: about 59M, January 2011. :curtisc:

(Mods: Feel free to delete this thread if "M47" turns out not to be prime.)[/QUOTE]
Seems like it is prime.
OTOH it is now March 2011.
I have sussed a neat way of estimating the expected time
of discovery of the next Mersenne prime:

On the "Classic" GIMPs progress page the expected new primes
below 79.3M decreases by .001 in somewhat
over 2 days.

I'll wager you 50/50 that we'll find a new MP before 2015.

David

[QUOTE=davieddy;255109]On the "Classic" GIMPs progress page the expected new primes below 79.3M decreases by .001 in somewhat over 2 days.[/QUOTE]
Well the here is the recent history on that:
2010-10-25 1.34
2010-11-22 1.33
2010-12-25 1.31
2011-01-11 1.31
2011-02-05 1.30
2011-03-07 1.28

[QUOTE=Uncwilly;255110]Well the here is the recent history on that:
2010-10-25 1.34
2010-11-22 1.33
2010-12-25 1.31
2011-01-11 1.31
2011-02-05 1.30
2011-03-07 1.28[/QUOTE]

THX for this info.
But note that 0.01 = 10 x 0.001

David

[QUOTE=davieddy;255179]But note that 0.01 = 10 x 0.001[/QUOTE]
2008-10-25 1.747
2008-12-03 1.719
2009-10-25 1.528
2010-05-11 1.420
2010-10-25 1.342
2010-11-22 1.328
2010-12-25 1.314
2011-01-11 1.306
2011-02-05 1.295
2011-03-07 1.281

FWIW