It is now Sep 27th here in Denmark, and we may have a new sad record. The biggest prime gap since GIMPS started: 898 days (since April 12th 2009).

I say [B][I]may[/I][/B] since there is a very small chance (0.01% according to George, since [B]a lot[/B] of error codes on it) that we found a prime on Sep 21st: [URL="http://www.mersenneforum.org/showthread.php?t=16074"]http://www.mersenneforum.org/showthread.php?t=16074[/URL]


[QUOTE]GIMPS found 13 primes so there are 12 gaps. Maximum gap is 897 days, minimum gap 14 days.

M(1398269) Nov 13 1996
M(2976221) Aug 24 1997 +284 days
M(3021377) Jan 27 1998 +156 days
M(6972593) Jun 1 1999 +490 days
M(13466917) Nov 14 2001 +897 days
M(20996011) Nov 17 2003 +733 days
M(24036583) May 15 2004 +180 days
M(25964951) Feb 18 2005 +279 days
M(30402457) Dec 15 2005 +300 days
M(32582657) Sep 4 2006 +263 days
M(43112609) Aug 23 2008 +719 days
M(37156667) Sep 6 2008 +14 days
M(42643801) Apr 12 2009 +218 days
[/QUOTE]

Lol I was reading the guesses at the beginning of this thread, and given the excellent perception of my hindsight, I laughed :)
But... 49.6M<M48<50.1M, in May of 2012. If you'll excuse my rather ambiguous notation. (Woe that is Indo-European languages! Woe that is Mersenne, that his last initial is the same as Million!)

[QUOTE=ATH;272811]It is now Sep 27th here in Denmark, and we may have a new sad record. The biggest prime gap since GIMPS started: 898 days (since April 12th 2009).

I say [B][I]may[/I][/B] since there is a very small chance (0.01% according to George, since [B]a lot[/B] of error codes on it) that we found a prime on Sep 21st: [URL]http://www.mersenneforum.org/showthread.php?t=16074[/URL][/QUOTE]

You'll also notice that we have never seen a gap including two full primeless calendar years (i.e. if you look at the sequence of years in which we found primes, you never skip over more than a single year). If neither of the two "M48" candidates are really prime, we have but 96 days until the end of 2011 and the first time in GIMPS history that the sequence of prime-discovery years will skip two slots.

Well, the wavefront is about 10M+ in front of the last prime, so either there's a HUGE gap, or we're in for a large group coming in close succession (though probably not two weeks like last time).

Gaps
 

[QUOTE=ATH;272811]It is now Sep 27th here in Denmark, and we may have a new sad record. The biggest prime gap since GIMPS started: 898 days (since April 12th 2009).

GIMPS found 13 primes so there are 12 [B][COLOR=#ff0000]gaps[/COLOR][/B]. Maximum gap is 897 days, minimum gap 14 days.

M(1398269) Nov 13 1996
M(2976221) Aug 24 1997 +284 days
M(3021377) Jan 27 1998 +156 days
M(6972593) Jun 1 1999 +490 days
M(13466917) Nov 14 2001 +897 days
M(20996011) Nov 17 2003 +733 days
M(24036583) May 15 2004 +180 days
M(25964951) Feb 18 2005 +279 days
M(30402457) Dec 15 2005 +300 days
M(32582657) Sep 4 2006 +263 days
M(43112609) Aug 23 2008 +719 days
M(37156667) Sep 6 2008 +14 days
M(42643801) Apr 12 2009 +218 days

[/QUOTE]

You might add (if you want):

Jan 4 ([FONT=Times New Roman][FONT=Verdana][SIZE=2]±3 days) 1996 Beginning of GIMPS[/SIZE][/FONT][/FONT]
[FONT=Times New Roman][FONT=Verdana][SIZE=2]M(1398269) Nov 13 1996 +314 ([FONT=Times New Roman]±[FONT=Verdana][SIZE=2]3) days[/SIZE][/FONT][/FONT][/SIZE][/FONT][/FONT]

[FONT=Times New Roman][FONT=Times New Roman][FONT=Verdana][SIZE=2]or if you prefer:[/SIZE][/FONT][/FONT][/FONT]

[FONT=Times New Roman][FONT=Times New Roman][FONT=Verdana][SIZE=2]Jan 4 ([FONT=Times New Roman]±[FONT=Verdana][SIZE=2]3 days) 1996 Beginning of GIMPS[/SIZE][/FONT][/FONT][/SIZE][/FONT]
[FONT=Times New Roman][FONT=Verdana][SIZE=2]M(1257787) Sep 3 1996 +243 ([FONT=Times New Roman]±[FONT=Verdana][SIZE=2]3) days[/SIZE][/FONT][/FONT] [David Slowinski & Paul Gage][/SIZE][/FONT][/FONT]
[FONT=Times New Roman][FONT=Times New Roman][FONT=Verdana][SIZE=2]M(1398269) Nov 13 1996 +71 days[/SIZE][/FONT][/FONT][/FONT]

[/FONT][FONT=Verdana][SIZE=2]And the gap from Apr 12 2009 is today 903 days (or if you prefer Jun 4 2009 as the date of discovery of [FONT=Times New Roman][SIZE=3][FONT=Verdana][SIZE=2]M(42643801)[/SIZE][/FONT] [/SIZE][/FONT]850 days).[/SIZE][/FONT]

[FONT=Verdana][SIZE=2]So I suppose there is 12, 13, 14 or 15 gaps depending on your perspective.[/SIZE][/FONT]

[/FONT]

I have a side bet...M48 (here meaning the 48th Mersenne to be found, since there's a nonzero chance that M(43112609) is actually M48) has already had an LL check performed on it, but the residue was erroneously returned nonzero.

[QUOTE=Christenson;273249]I have a side bet...M48 (here meaning the 48th Mersenne to be found, since there's a nonzero chance that M(43112609) is actually M48) has already had an LL check performed on it, but the residue was erroneously returned nonzero.[/QUOTE]

I too believe that this is bound to happen (if not with M48, then at some point in the near future) as the tests get larger, admitting more chance for fatal errors (whether the usual hardware variety or cosmic ray type), and also as the sheer number of tests performed increases to the point where the quoted 1.5% error rate even for "good" first time LLs becomes significant. If you perform one million LLs, and expect 1.5% of them to have a blank-but-incorrect error code, that is 15,000 potential candidates to be found prime on a double check!

[QUOTE=Christenson;273249]I have a side bet...M48 (here meaning the 48th Mersenne to be found, since there's a nonzero chance that M(43112609) is actually M48) has already had an LL check performed on it, but the residue was erroneously returned nonzero.[/QUOTE]
You're on!
If you mean 50/50 I'll bet my shirt for yours:smile:

David

PS I would offer to eat my hat if I still owned one.

Another shirt in prospect
 

[QUOTE=NBtarheel_33;273254]I too believe that this is bound to happen (if not with M48, then at some point in the near future) as the tests get larger, admitting more chance for fatal errors (whether the usual hardware variety or cosmic ray type), and also as the sheer number of tests performed increases to the point where the quoted 1.5% error rate even for "good" first time LLs becomes significant. If you perform one million LLs, and expect 1.5% of them to have a blank-but-incorrect error code, that is 15,000 potential candidates to be found prime on a double check![/QUOTE]

Suffering from disbelief in PNT?

David

[QUOTE=Christenson;273249]I have a side bet...M48 (here meaning the 48th Mersenne to be found, since there's a nonzero chance that M(43112609) is actually M48) has already had an LL check performed on it, but the residue was erroneously returned nonzero.[/QUOTE]
This had also occurred to me after my previous post... and is very good motivation for speeding up the DC's. Otherwise we'll never find it!!

[QUOTE=davieddy;273257]Suffering from disbelief in PNT?

David[/QUOTE]

Not really; it's not like I'm making a claim about the distribution of primes. Just saying that one day, we might miss one on the first go-around, and that we'll catch it on the double-check. If hardware errors can cause a non-zero residue to be corrupted to zeroes, I'm sure the other way around could very easily happen, as well.