A383813 Primes which satisfy the requirements of A380943 in exactly four ways.

257931013, 1394821313, 2699357347, 3122419127, 3132143093, 3647381953, 3736320359, 3799933727, 6130099337, 7622281937, 7943701397, 7991407367

Offset: 1

Author

James C. McMahon and Robert G. Wilson v, May 23 2025

Keywords

• nonn
• base
• more

Comments

The requirements of A380943 are that primes, p_n, written in decimal representation by the concatenation of primes p and q such that the concatenation of q and p also forms a prime.

The number of terms <= 10^k beginning with k=1: 0, 0, 0, 0, 0, 0, 0, 1, 12, ..., .

Crossrefs

Cf. A000040, A238500, A380943, A383810, A383811, A383812, A383814, A383815, A383816.

Programs

Mathematica

f[n_] := Block[{cnt = 0, id = IntegerDigits@ n, k = 1, len, p, q, qp}, len = Length@ id; While[k < len, p = Take[id, k]; q = Take[id, -len + k]; qp = FromDigits[ Join[q, p]]; If[ PrimeQ[FromDigits[p]] && PrimeQ[FromDigits[q]] && PrimeQ[qp] && IntegerLength[qp] == len, cnt++]; k++]; cnt];Select[ Prime@ Range@ 10000000, f@# == 4 &]