A376030 Primes which can be turned into a different prime by exchanging two digits. (Leading zeros are not allowed.)

13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 131, 137, 139, 149, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 239, 241, 251, 277, 281, 283, 293, 311, 313, 317, 331, 337, 347, 349, 359, 373, 379, 389, 397, 419, 421, 439, 457, 461, 463, 467, 491, 521, 547, 563

Offset: 1

Author

James S. DeArmon, Sep 06 2024

Keywords

• base
• nonn

Examples

			13 is the first term, since 31 is also prime.  113 is a term, since 131 is prime. 101 is not allowed as a term: 011 is prime, but has a leading zero.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A225035.

Cf. A375965.

Programs

Python

from sympy import isprime
from itertools import combinations
def ok(n):
    if not isprime(n): return False
    s = list(str(n))
    for i, j in combinations(range(len(s)), 2):
        sij = s[:]
        sij[i], sij[j] = sij[j], sij[i]
        if sij[0] != "0" and sij != s and isprime(int("".join(sij))):
            return True
    return False
print([k for k in range(565) if ok(k)]) # Michael S. Branicky, Sep 07 2024

Extensions

Corrected and more terms from Michael S. Branicky, Sep 07 2024