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 2005-07-31, 10:52 #1 amcfarlane     Nov 2004 UK 2×19 Posts 3*2^n+1 I'm curious, has anyone made any inroads into this form of number or am I missing something obvious?
 2005-07-31, 14:36 #2 axn     Jun 2003 10101000000012 Posts Check out prothsearch
 2005-07-31, 23:55 #3 wfgarnett3     "William Garnett III" Oct 2002 Langhorne, PA 1268 Posts John Cosgrave has. http://www.spd.dcu.ie/johnbcos/
 2005-08-01, 16:23 #4 paulunderwood     Sep 2002 Database er0rr 2×5×421 Posts John's Univerisity have found the biggest 3*2^n+1, but I have noticed some smaller submissions to UTM recently of this form. Here is what I got from UTM's records: ----- -------------------------------- ------- ---- ---- -------------- rank description digits who year comment ----- -------------------------------- ------- ---- ---- -------------- 16 3*2^2478785+1 746190 g245 2003 Divides Fermat F(2478782), GF(2478782,3), GF(2478776,6), GF(2478782,12) 18 3*2^2145353+1 645817 g245 2003 Divides Fermat F(2145351), GF(2145351,3), GF(2145352,5), GF(2145348,6), GF(2145352,10), GF(2145351,12) 101 3*2^916773+1 275977 g245 2001 Divides GF(916771,3), GF(916772,10) 149 3*2^709968+1 213723 g372 2005 Divides GF(709962,3), GF(709963,5) 729 3*2^382449+1 115130 g132 1999 Divides Fermat F(382447), GF(382447,3), GF(382447,12), GF(382443,6) 793 3*2^362765+1 109204 g245 2002 Divides GF(362763,12), GF(362764,10) 1656 3*2^303093+1 91241 Y 1998 Divides Fermat F(303088); GF(303088,3), GF(303086,6), GF(303092,10), GF(303088,12), GF(303092,5) [g0] 3770 3*2^213321+1 64217 Y 1997 Divides Fermat F(213319); GF(213316,6), GF(213319,12) [g0] 9664 3*2^157169+1 47314 Y 1995 Divides Fermat F(157167); GF(157167,3), GF(157168,5), GF(157163,6), GF(157168,10), GF(157167,12) [g0]; GF(157168,5) [g0] 18847 3*2^80190+1 24141 Y 1995 Divides GF(80187,3) [BR], arithmetic progression (1,d=(39*2^27588-3)*2^80190) [x12] ----- -------------------------------- ------- ---- ---- -------------- Last fiddled with by paulunderwood on 2005-08-01 at 19:57
 2005-09-02, 10:02 #5 paulunderwood     Sep 2002 Database er0rr 2×5×421 Posts Add to the above list the recent find: 3*2^801978+1. The gap between John Cosgrove's search and Adney's must be almost nil.
2005-09-02, 12:40   #6
rogue

"Mark"
Apr 2003
Between here and the

61·109 Posts

Quote:
 Originally Posted by paulunderwood Add to the above list the recent find: 3*2^801978+1. The gap between John Cosgrove's search and Adney's must be almost nil.
Keith has a way to go. John went up to 2,600,000 and had many PCs working on it. I don't know how many PCs Keith has, but there are almost twice as many even exponents are there are odd exponents. There are a few years of PRP testing left to get the even exponents up to 2,600,000. As long as Keith finds primes (and I'm surprised he has found two), he will probably continue. If anyone wants to assist, they are welcome to take a range.

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