A240680 Primes p such that p*10+k is prime for exactly three values of the digit k.

7, 13, 31, 43, 61, 103, 109, 199, 271, 367, 409, 421, 523, 541, 547, 787, 823, 829, 883, 1009, 1033, 1117, 1237, 1291, 1669, 1999, 2131, 2161, 2203, 2269, 2437, 2503, 2593, 2671, 2857, 3049, 3253, 3271, 3361, 3559, 3583, 3769, 3823, 4003, 4201, 4339, 4357

Offset: 1

Author

Colin Barker, Apr 10 2014

Keywords

• nonn
• base

Examples

			7 is in the sequence because 71, 73 and 79 are prime, but 77 is not prime.
		

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A067267, A119289, A240678, A240679, A240689.

Programs

Magma

[p: p in PrimesUpTo(10^4) | {k: k in [1,3,7,9] | IsPrime(p*10+k)} in Subsets({1,3,7,9},3)]; // Bruno Berselli, Apr 10 2014

Mathematica

Select[Prime[Range[600]],Total[Boole[PrimeQ[10#+{1,3,7,9}]]]==3&] (* Harvey P. Dale, Apr 07 2023 *)

PARI

forprime(p=2, 10000, t=0; forstep(k=1, 9, 2, if(isprime(p*10+k), t++)); if(t==3, print1(p, ", ")))