A240680 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

(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