mersenneforum.org > Data How close have you been to finding a Mersenne prime?
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 2013-05-30, 21:09 #1 NBtarheel_33     "Nathan" Jul 2008 Maryland, USA 5×223 Posts How close have you been to finding a Mersenne prime? Define "close" in the following manner: a residue of 000000000001 is the closest possible residue to a Mersenne prime, while FFFFFFFFFFFF is the farthest possible residue from a Mersenne prime. Given this definition, what is the closest/farthest you have personally been from discovering a new Mersenne prime? How about GIMPS as a whole?
 2013-05-30, 21:52 #2 firejuggler     Apr 2010 Over the rainbow 22×641 Posts pretty bad for me 06738331905537__
2013-05-30, 22:22   #3
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

2×4,783 Posts

Quote:
 Originally Posted by NBtarheel_33 while FFFFFFFFFFFF is the farthest possible residue from a Mersenne prime.
Would that not be 1 off, just like 0001?
Would not 8888888888888888 be furtherest from 000....000?

 2013-05-30, 22:25 #4 Mini-Geek Account Deleted     "Tim Sorbera" Aug 2006 San Antonio, TX USA 426710 Posts Excluding known-bad residues, my "closest" in the last 365 days is 054A974FAF0241__ (the sorting at http://www.mersenne.org/results/ makes this easy to find). I think the definition should be such that 000000000001 and FFFFFFFFFFFF are equally close - they're each just 1 apart from showing all zeroes in the 64-bit residue. In other words: the "closest" residue is the one that is closest to 0 mod 2^64. If we drop the "Mersenne" restriction and I look at my PRPnet log files, my closest is: 0000083778FDEA40 on 507292*40^20317+1. I've run enough tests on even smaller numbers that I might have closer ones out there, but not in log files that are at hand (or exist at all).
 2013-05-30, 22:33 #5 firejuggler     Apr 2010 Over the rainbow 256410 Posts I Could see Chuck Curtis smugly posting 3 "000000000000" residue
 2013-05-30, 23:00 #6 kar_bon     Mar 2006 Germany 33×107 Posts 1881*2^774126-1 is not prime. Res64: 00000F12ABCED83E 1745*2^872506-1 is not prime. Res64: 00000E6B7FE01929 797*2^1088860-1 is not prime. Res64: 00000C48959C0818 1471*2^944575-1 is not prime. Res64: 000008C5C489296D 333*2^1194794-1 is not prime. Res64: 0000085458B0E7B9 3645*2^21+1 is not prime. Proth RES64: 000000015B5CADFD 108045*2^18+1 is not prime. Proth RES64: 00000004206C33F6 651358155*2^13+1 is not prime. RES64: 0000000000081BF1 607815*2^17+1 is not prime. RES64: 00000000000002D9 and many other examples like these.
 2013-05-30, 23:40 #7 CRGreathouse     Aug 2006 176116 Posts So many ways to measure distance! Linearly, from 000...0 to FFF...F? Circularly, with FFF...F being just as near as 000...1? Digit-wise, so 100...0 and 000...1 are equally far? By digits but circularly? Etc.
 2013-05-30, 23:52 #8 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2·3·1,571 Posts Code: # pfgw -f0 -b2 -q"2^65536+2^32768+1" 2^65536+2^32768+1 is composite: RES64: [0000000000000000]
2013-05-31, 00:04   #9
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT/BST)

10110111011102 Posts

Quote:
 Originally Posted by kar_bon 607815*2^17+1 is not prime. RES64: 00000000000002D9
0x2D9=729=3^6
This implies I believe(assuming that the residue being 2D9 wasn't a fluke)(607815*2^17+1)/(6+1) is 3-PRP(In reality it is prime).

There are probably more similar examples in your list. It would be nice if we could harness this to find prps.

 2013-05-31, 00:12 #10 chalsall If I May     "Chris Halsall" Sep 2002 Barbados 2·4,787 Posts Code: mysql> select Exponent.Exponent,Users.DisplayName,Assigned.FactFrom,Assigned.FactTo from Assigned,Exponent,Users where Assigned.Exponent=Exponent.Exponent and Exponent.Status=1 and Assigned.User=Users.User; +----------+---------------+----------+--------+ | Exponent | DisplayName | FactFrom | FactTo | +----------+---------------+----------+--------+ | 57885161 | Jerry Hallett | 72 | 73 | +----------+---------------+----------+--------+ 1 row in set (0.00 sec)
 2013-05-31, 00:37 #11 chalsall If I May     "Chris Halsall" Sep 2002 Barbados 2×4,787 Posts But, to be fair, it was close... Code: mysql> select Exponent.Exponent,Users.DisplayName,Assigned.FactFrom,Assigned.FactTo from Assigned,Exponent,Users where Assigned.Exponent=Exponent.Exponent and Exponent.Exponent>=57884571 and Exponent.Exponent<=57885257 and Assigned.User=Users.User and Assigned.WorkType=1; +----------+---------------+----------+--------+ | Exponent | DisplayName | FactFrom | FactTo | +----------+---------------+----------+--------+ | 57884647 | KyleAskine | 72 | 73 | | 57884747 | Bdot | 72 | 73 | | 57884891 | Jerry Hallett | 72 | 73 | | 57885143 | Bdot | 72 | 73 | | 57885161 | Jerry Hallett | 72 | 73 | | 57885167 | Bdot | 72 | 73 | | 57885209 | KyleAskine | 72 | 73 | | 57885211 | KyleAskine | 72 | 73 | | 57885257 | KyleAskine | 72 | 73 | +----------+---------------+----------+--------+ 9 rows in set (0.01 sec)

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