A375965 -id:A375965 - cp's OEIS frontend

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

James S. DeArmon, Sep 06 2024

			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.

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

Subsequence of A225035.

Cf. A375965.

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

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

A376213 Prime numbers wherein a triple exchange of 3 of the digits creates two prime numbers, neither of which has a leading zero digit.

Original entry on oeis.org

113, 131, 197, 199, 311, 337, 373, 719, 733, 919, 971, 991, 1013, 1019, 1031, 1091, 1123, 1163, 1181, 1193, 1213, 1231, 1237, 1279, 1297, 1307, 1319, 1321, 1327, 1399, 1439, 1487, 1499, 1543, 1549, 1571, 1613, 1621, 1637, 1733, 1747, 1759, 1777, 1811, 1831, 1913

Offset: 1

James S. DeArmon, Sep 15 2024

A triple exchange is a permutation of 3 elements in which all 3 three items change position. (For the triple "ABC", that would be "BCA" and "CAB".)

			The first term is the prime 113, since 131 and 311 are also prime. Another term is 1013, since 1103 and 1301 are prime.

Subsequence of A225035. Cf. A375965.

from sympy import isprime
from itertools import combinations, permutations
def ok(n):
    if n < 100 or not isprime(n): return False
    s = list(str(n))
    for i, j, k in combinations(range(len(s)), 3):
        pset, w, x = {n}, s[:], s[:]
        w[i], w[j], w[k] = w[j], w[k], w[i]
        x[i], x[j], x[k] = x[k], x[i], x[j]
        if w[0] != "0" and isprime(t:=int("".join(w))): pset.add(t)
        if x[0] != "0" and isprime(t:=int("".join(x))): pset.add(t)
        if len(pset) == 3: return True
    return False
print([k for k in range(1920) if ok(k)]) # Michael S. Branicky, Sep 17 2024

Terms corrected by Michael S. Branicky, Sep 17 2024

cp's OEIS Frontend

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

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