A081677 Numbers n such that 2*10^n + 3 is prime.

0, 1, 3, 5, 6, 7, 12, 16, 17, 22, 24, 35, 115, 120, 358, 1488, 1819, 4679, 9821, 27217, 27693, 194413

Offset: 1

Author

Robert G. Wilson v, Mar 26 2003

Keywords

• more
• nonn

Comments

a(22) > 10^5. - Robert Price, Nov 16 2014

a(23) > 2*10^5. - Robert Price, Jul 11 2015

Examples

			2+3 is prime, so are 23, 2003, 200003, 2000003, 20000003,2000000000003, etc. which are all of the form 2*10^n +3.
		

References

• Mark A. Herkommer, Number Theory, A Programmer's Guide, McGraw-Hill, New York, 1999, page 51.

Links

• Makoto Kamada, Prime numbers of the form 200...003.
• Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Crossrefs

Cf. A101951.

Programs

Magma

[n: n in [0..500] | IsPrime(2*10^n+3)]; // Vincenzo Librandi, Nov 17 2014

Mathematica

Do[ If[ PrimeQ[2*10^n + 3], Print[n]], {n, 0, 10000}]
Select[Range[0, 1000], PrimeQ[(2 10^# + 3)] &] (* Vincenzo Librandi, Nov 17 2014 *)

PARI

is(n)=isprime(2*10^n+3) \\ Charles R Greathouse IV, Feb 17 2017

Formula

a(n) = A101951(n-1) + 1.

Extensions

More terms from Robert G. Wilson v, Jan 18 2005

a(20)-a(21) from Kamada data by Robert Price, Dec 09 2010

a(22) from Robert Price, Jul 11 2015