A165508 Numbers k such that 10^k + 111 is prime.

2, 4, 184, 460, 784, 3248, 5194, 92386, 156428, 228208

Offset: 1

Author

Rick L. Shepherd, Sep 21 2009

Keywords

• nonn
• more

Comments

Terms must be congruent to 2 or 4 mod 6. Other than the first term, which produces 10^2 + 111 = 211, these terms produce primes whose decimal representation is 1 111 concatenated. These are only known to be highly probable primes for 184 and beyond. No more terms up to 15000.

a(8) > 55000. - Tyler NeSmith, Jul 10 2021

The corresponding primes have digit sum 4 (A062339). - Jeppe Stig Nielsen, Feb 10 2023

a(9) > 10^5. - Jeppe Stig Nielsen, Feb 11 2023

a(11) > 6.6*10^5. - Boyan Hu, Nov 14 2024

Examples

			As 10111 = 10^4 + 111 is a prime, 4 is a term.
		

Crossrefs

Cf. A096912, A157711, A062339, A020449, A036929, A161786.

Programs

Mathematica

Select[Range[5200], PrimeQ[10^# + 111] &] (* G. C. Greubel, Oct 21 2018 *)

PARI

is(k)=ispseudoprime(10^k+111) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(8) from Jeppe Stig Nielsen, Feb 10 2023

a(9)-a(10) from Boyan Hu, Oct 23 2024