3*2^n+1

[amcfarlane]

I'm curious, has anyone made any inroads into this form of number or am I missing something obvious?

[axn]

Check out prothsearch

[wfgarnett3]

John Cosgrave has.

http://www.spd.dcu.ie/johnbcos/

[paulunderwood]

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]
----- -------------------------------- ------- ---- ---- --------------

[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.

[rogue]

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.