A165701 Numbers n such that 5^n-6 is prime.

2, 4, 5, 6, 10, 53, 76, 82, 88, 242, 247, 473, 586, 966, 1015, 1297, 1825, 2413, 2599, 2833, 5850, 5965, 6052, 27199, 49704, 79000

Offset: 1

Author

M. F. Hasler and Farideh Firoozbakht, Oct 30 2009

Keywords

• more
• nonn

Comments

Numbers corresponding to the a(n) for n>11 are probable prime.

If Q is a 4-perfect number and gcd(Q, 5*(5^a(n)-6))=1 then m=5^(a(n)-1)

(5^a(n)-6)*Q is a solution of the equation sigma(x)=5(x+Q)(see comment lines of the sequence A058959). 142990848 is the smallest 4-perfect number m such that 5 doesn't divide m.

a(27) > 10^5. - Robert Price, Feb 03 2014

Links

• F. Firoozbakht, M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1
• H. Lifchitz, R. Lifchitz: PRP Top Records Search for 5^n-6.

Crossrefs

Cf. A007691, A054030, A058959.

Programs

Mathematica

Do[If[PrimeQ[5^n-6],Print[n]],{n,8888}]

PARI

is(n)=ispseudoprime(5^n-6) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(24)-a(26) from Robert Price, Feb 03 2014