A106582 Numbers which are the concatenation of two primes.

22, 23, 25, 27, 32, 33, 35, 37, 52, 53, 55, 57, 72, 73, 75, 77, 112, 113, 115, 117, 132, 133, 135, 137, 172, 173, 175, 177, 192, 193, 195, 197, 211, 213, 217, 219, 223, 229, 231, 232, 233, 235, 237, 241, 243, 247, 253, 259, 261, 267, 271, 273, 279, 283, 289

Offset: 1

Author

Eric Angelini and Robert G. Wilson v, May 09 2005

Keywords

• base
• nonn

Comments

A105184 and A121609 are subsequences.

Examples

			133 is in the sequence because 133 = 13*10+3 = A000040(6)*10+A000040(2).
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 17257

Crossrefs

Cf. A001358, A105184, A121609.

Programs

Mathematica

nn=500; t=Union[Reap[Do[n=FromDigits[Join[IntegerDigits[Prime[i]], IntegerDigits[Prime[j]]]]; If[n<=nn, Sow[n]], {i,PrimePi[nn/10]}, {j,PrimePi[nn/IntegerDigits[nn][[1]]]}]][[2,1]]] (* T. D. Noe, Mar 11 2011 *)
Take[FromDigits[Flatten[IntegerDigits/@#]]&/@Tuples[Prime[Range[30]],2]//Union,60] (* Harvey P. Dale, May 28 2025 *)

Python

from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    for k in count(1):
        s = str(k)
        if any(s[i] != '0' and isprime(int(s[:i])) and isprime(int(s[i:])) for i in range(1, len(s))):
            yield k
print(list(islice(agen(), 55))) # Michael S. Branicky, Feb 26 2022

Extensions

Corrected by Arkadiusz Wesolowski, Mar 11 2011