A351925 Squares which are the concatenation of two primes.

25, 289, 361, 529, 729, 2401, 2601, 2809, 4761, 5329, 5929, 7569, 11449, 11881, 15129, 19881, 21609, 22801, 23409, 24649, 25281, 26569, 29241, 29929, 31329, 34969, 36481, 39601, 47961, 52441, 53361, 54289, 57121, 58081, 59049, 71289, 77841, 83521, 89401

Offset: 1

Author

Max Z. Scialabba, Feb 25 2022

Keywords

• nonn
• base

Comments

The first term that is the concatenation of two primes in more than one way is a(11) = 5929 = 5 | 929 = 59 | 29. - Robert Israel, Oct 01 2023

Examples

			25 is the concatenation of 2 and 5, both primes.
4761 is the concatenation of 47 and 61, both primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290 (squares), A039686, A106582, inverse of A167535.

Cf. A038692, A225135.

Programs

Maple

L:= NULL: count:=0:
for x from 1 by 2 while count < 100 do
  xs:= x^2;
  for i from 1 to ilog10(xs) do
    a:= xs mod 10^i;
    if a > 10^(i-1) and isprime(a) then
      b:= (xs-a)/10^i;
      if isprime(b) then
        L:= L, xs; count:= count+1; break
      fi fi
od od:
L; # Robert Israel, Oct 01 2023

PARI

isb(n)={my(d=10); while(dAndrew Howroyd, Feb 26 2022

Python

from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    for k in count(1):
        s = str(k*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*k
print(list(islice(agen(), 39))) # Michael S. Branicky, Feb 26 2022

Formula

Intersection of A106582 and A000290.