A180561 Primes that cannot become a different prime under any mapping of some single decimal digit <=> with some other single decimal digit.

11, 11779, 22669, 23333, 33533, 55333, 74279, 77999, 78857, 80603, 84871, 88177, 88747, 97039, 103091, 112181, 119701, 125813, 128147, 131143, 133499, 141587, 158771, 159979, 164341, 166063, 173933, 175781, 219613, 220279, 222601, 227387, 229727, 231317, 238829

Offset: 1

Author

Zak Seidov and Robert G. Wilson v, Sep 09 2010

Keywords

• base
• nonn

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000
• Index to Primes, Primes that become a different prime under some mapping.

Crossrefs

Cf. A175791, A180517 thru A180559, A175789, A180560.

Programs

Mathematica

fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, s[[1]]] || MemberQ[id, s[[2]]]) && PrimeQ[ FromDigits[id /. {s[[1]] -> s[[2]], s[[2]] -> s[[1]] }] ]]; t = Union@ Flatten@ Table[s = {j, k}; Select[ Prime@ Range@ 25000, fQ], {j, 0, 8}, {k, j + 1, 9}]; Complement[ Prime@ Range@ 25000, t]

Python

from sympy import isprime
def m(s):
    return [s.translate({ord(c):ord(d), ord(d):ord(c)}) for c in set(s) for d in "0123456789" if d != c]
def ok(n):
    return isprime(n) and not any(isprime(int(t)) for t in m(str(n)))
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Oct 31 2023

Formula

Complement of all the primes with the union of the sequences A175791, A175789, A180517 thru A180559.

Extensions

a(33) and beyond from Michael S. Branicky, Oct 31 2023