A049054 Numbers k such that 10^k + 3 is prime.

1, 2, 5, 6, 11, 17, 18, 39, 56, 101, 105, 107, 123, 413, 426, 2607, 7668, 10470, 11021, 17753, 26927, 60776, 98288, 300476, 509546

Offset: 1

Author

G. L. Honaker, Jr.

Keywords

• hard
• more
• nonn

Comments

A102006 is another version of the same sequence. - N. J. A. Sloane, Jan 28 2010

Verified existing 21 terms. If another term exists, it is > 39456. - Robert Price, Aug 16 2010

Examples

			5 is a term since 10^5 + 3 = 100003 is a prime.
6 is a term since 10^6 + 3 = 1000003 is a prime.
		

Links

• Makoto Kamada, Prime numbers of the form 100...003.
• Henri & Renaud Lifchitz, PRP Records.
• Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Crossrefs

Cf. A102006, A159352.

Programs

Mathematica

Do[ If[ PrimeQ[ 10^n + 3], Print[n]], {n, 0, 18000}] (* Robert G. Wilson v Jun 15 2002 *)

PARI

is(n)=isprime(10^n + 3) \\ Charles R Greathouse IV, Apr 28 2015

Formula

a(n) = A102006(n) + 1.

Extensions

More terms from Robert G. Wilson v, Jun 15 2002

a(16) from Ray Chandler, Oct 09 2003

a(17)-a(20) from Robert G. Wilson v, Jan 18 2005

a(21) from Jason Earls, Jan 01 2008

a(22) from Robert Price, Jan 09 2011

a(23) from Robert Price, Mar 03 2011

a(24) from Edward A. Trice, Oct 21 2012

a(25) from Paul Bourdelais, Jan 28 2021