A108052 Integers k such that 10^k+19 is a prime number.

1, 3, 5, 7, 10, 11, 17, 59, 81, 108, 574, 629, 1069, 1759, 2063, 2682, 9174, 40929, 42457, 66033

Offset: 1

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 01 2005

Keywords

• more
• nonn
• hard

Comments

Verified terms through 9174. - Robert Price, May 24 2010

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10019".

No other terms <= 100,000. - Robert Price, Mar 03 2011

Examples

			n = 7 we have 10^7+19 = 10000000+19 = 10000019, which is prime.
		

Links

• Makoto Kamada, List of near-repdigit-related prime numbers.
• Index entries for primes involving repunits.

Crossrefs

Cf. A049054, A088274, A088275, A095688.

Programs

Mathematica

Select[Range[2*10^3],PrimeQ[10^#+19]&] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

PARI

is(n)=ispseudoprime(10^n+19) \\ Charles R Greathouse IV, Apr 28 2015

Extensions

a(17)=9174 from Ryan Propper, Jan 02 2008

Edited by Ray Chandler, Dec 23 2010

a(18)=40929 and a(19)=42457 from Robert Price, Dec 27 2010

a(20)=66033 from Robert Price, Jan 09 2011