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Williams primes of the form 2•3ⁿ+1

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Current data

Base :	3
Count :	45
Max n :	1,175,200
Date :	2020-02-09

1, 2, 4, 5, 6, 9, 16, 17, 30, 54, 57, 60, 65, 132, 180, 320, 696, 782, 822, 897, 1252, 1454, 4217^[1], 5480, 6225^[2], 7842, 12096, 13782, 17720, 43956, 64822, 82780, 105106, 152529^[3], 165896, 191814, 529680, 1074726, 1086112, 1175232, 1277862, 1346542, 3123036, 3648969^[4], 5570081^[5]

Remarks :

The sequence A003306 in OEIS

Notes

↑ Divides Phi(3^4217,2)
↑ Divides Phi(3^6223,2)
↑ Divides Phi(3^152528,2)
↑ Divides Phi(3^3648964,2)
↑ Divides Phi(3^5570081,2)

History

2020-02-14: Found n = 5570081, Ryan Propper
2020-02-09: Found n = 3648969, Paul Vanderveen, Ryan Propper
2020-02-09: Found n = 3123036, Paul Vanderveen, Ryan Propper
2020-02-08: Found n = 1346542, Paul Vanderveen, Ryan Propper
2020-02-08: Found n = 1277862, Paul Vanderveen, Ryan Propper
2010-02-22: Found n = 1175232, David Broadhurst
2010-02-13: Found n = 1086112, David Broadhurst
2010-02-13: Found n = 1074726, David Broadhurst
2009-08-31: Found n = 529680, David Broadhurst
2004-01-15: Found n = 191814, Peter Benson
2003-05-07: Found n = 165896, Ingo Buechel, Wilfrid Keller
2000-05-13: Found n = 152529, Ingo Buechel, Wilfrid Keller
1999-05-28: Found n = 105106, Ingo Buechel, Wilfrid Keller
1999-03-03: Found n = 82780, Ingo Buechel, Wilfrid Keller
1999-01-19: Found n = 64822, Ingo Buechel, Wilfrid Keller
1998-10-29: Found n = 43956, Yves Gallot
1996-12-01: Found n = 17720, Chris Caldwell
1994: Found n = 13782, Chris Caldwell
1994: Found n = 12096, Chris Caldwell
1992-10: Found n = 7842, Chris Caldwell
1992: Found n = 6225, Chris Caldwell
1992: Found n = 5480, Chris Caldwell
1992: Found n = 4217, Chris Caldwell

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Williams prime MP