A244282 Consider a prime number p with m decimal digits. The sequence lists the primes p such that the prefix of length m-1 and the suffix of length m-1 are both prime numbers.

23, 37, 53, 73, 113, 131, 137, 173, 179, 197, 311, 313, 317, 373, 379, 419, 431, 479, 613, 617, 619, 673, 719, 797, 971, 1013, 1019, 1031, 1097, 1277, 1373, 1499, 1571, 1733, 1811, 1997, 2113, 2239, 2293, 2719, 3079, 3137, 3313, 3373, 3491, 3499, 3593, 3673, 3677, 3733

Offset: 1

Author

Michel Lagneau, Jun 25 2014

Keywords

• nonn
• base

Comments

Let x(0)x(1)... x(q-1)x(q) denote the decimal expansion of a prime p. The sequence lists the primes p such that the prefix x(0)x(1)... x(q-1) and the suffix x(1)... x(q-1)x(q) are primes.

Superset of A051362; a(n) first differs from A051362 when n=12.

Examples

			The prime number 179 is in the sequence because 17 and 79 are primes.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A051362, A244283.

Programs

Maple

with(numtheory):
for m from 1 to 200 do:
      n:=ithprime(m):x:=convert(n, base, 10):n1:=nops(x):
      s1:=sum('x[i]*10^(i-1) ', 'i'=1..n1-1):
      s2:=(n-irem(n,10))/10:
      if type(s1,prime)=true and type(s2,prime)=true
      then
        printf(`%d, `, n):
        else
      fi:
od:

Mathematica

Select[Prime[Range[1000]], (id = IntegerDigits[#]; PrimeQ[FromDigits[Take[id, {1, -2}]]] && PrimeQ[FromDigits[Take[id, {2, -1}]]]) &] (* César Eliud Lozada, Mar 31 2024 *)
Select[Prime[Range[600]],With[{idp=IntegerDigits[#]},AllTrue[FromDigits/@{Rest[idp],Most[idp]},PrimeQ]]&] (* Harvey P. Dale, Feb 06 2025 *)

Extensions

Inserted missing term a(49) and corrected a(50) by Paolo P. Lava, Dec 04 2017