A096774 Numbers k such that 9*10^k + 7 is prime.

1, 2, 3, 4, 5, 15, 19, 20, 46, 52, 53, 192, 380, 588, 776, 906, 1350, 1736, 2914, 7508, 15710, 16453, 17488, 18109, 21604, 25891, 26725, 34838, 67468

Offset: 1

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Aug 16 2004

Keywords

• more
• nonn

Comments

a(1) through a(12) have been certified prime. a(13) through a(19) are all Fermat and Lucas PRPs. No others less than 6300. - Jason Earls, Aug 18 2004

a(30) > 3*10^5. - Robert Price, Jul 10 2023

Examples

			k = 5; (9*10^5)+7 = 900007, which is prime.
		

Links

• Makoto Kamada, Prime numbers of the form 900...007.
• Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.
• Index entries for primes involving repunits.

Crossrefs

Cf. A100998.

Programs

Mathematica

Do[ If[ PrimeQ[9*10^n + 7], Print[n]], {n, 0, 10000}] (* Robert G. Wilson v, Jan 19 2005 *)

PARI

for(n=1, 1e5, if(isprime(9*10^n + 7), print1(n", "))) \\ Altug Alkan, Oct 16 2015

Formula

a(n) = A100998(n) + 1.

Extensions

More terms from Jason Earls, Aug 18 2004

a(20) from Robert G. Wilson v, Jan 19 2005

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(25)-a(29) from Kamada data by Robert Price, Dec 14 2010