Thread: 3*2^n+1
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Old 2005-08-01, 16:23   #4
paulunderwood
 
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Sep 2002
Database er0rr

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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:
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rank description digits who year comment
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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]
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Last fiddled with by paulunderwood on 2005-08-01 at 19:57
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