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

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

Offset

1,1

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 <n-3 0's> 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

Links

Table of n, a(n) for n=1..8.

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A012369 A009609 A012367 * A018633 A307556 A018637

Adjacent sequences: A165505 A165506 A165507 * A165509 A165510 A165511

Keyword

nonn,more

Author

Rick L. Shepherd, Sep 21 2009

Extensions

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

Status

approved