A057171 Numbers n such that (5^n+1)/6 is a prime.
5, 67, 101, 103, 229, 347, 4013, 23297, 30133, 177337, 193939, 266863, 277183, 335429, 1856147
Offset: 1
Links
- Paul Bourdelais, A Generalized Repunit Conjecture
- J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
- H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
- H. Lifchitz, Mersenne and Fermat primes field
- Eric Weisstein's World of Mathematics, Repunit
- R. G. Wilson, v, Letter to N. J. A. Sloane, circa 1991.
Programs
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Mathematica
a={};Do[x=(5^n+1)/6;If[PrimeQ[x],AppendTo[a,n]],{n,0,12^2}];a (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *) Select[Range[40000],PrimeQ[(5^#+1)/6]&] (* The program generates the first 9 terms of the sequence. *) (* Harvey P. Dale, Dec 28 2024 *) -
PARI
isok(n) = (denominator(p=(5^n+1)/6) == 1) && isprime(p); \\ Michel Marcus, Oct 28 2017
Extensions
More terms from Kamil Duszenko (kdusz(AT)wp.pl), Jun 23 2003
30133 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008
a(10) discovered 10/29/08 is a probable prime based on trial factoring to 3.5e13 and Fermat testing base 2. - Paul Bourdelais, Nov 04 2008
a(11)=193939 from Paul Bourdelais discovered 12/24/08 is a probable prime based on trial factoring to 4e13 and Fermat primality testing base 2. - Paul Bourdelais, Dec 24 2008
a(12)=266863 is a probable prime discovered by Paul Bourdelais, Jul 09 2010
a(13)=277183 is a probable prime discovered by Paul Bourdelais, Jul 16 2010
a(14)=335429 is a probable prime discovered by Paul Bourdelais, Aug 23 2010
a(15)=1856147 corresponds to a probable prime discovered by Paul Bourdelais, Feb 26 2019
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