A355856 Primes, with at least one prime digit, that remain primes when all of their prime digits are removed.

113, 131, 139, 151, 179, 193, 197, 211, 241, 311, 389, 421, 431, 541, 613, 617, 631, 719, 761, 829, 839, 859, 1013, 1021, 1031, 1039, 1051, 1093, 1097, 1123, 1153, 1201, 1213, 1217, 1229, 1231, 1249, 1259, 1279, 1291, 1297, 1301, 1321, 1381, 1399, 1429, 1439, 1459, 1493, 1531, 1549

Offset: 1

Author

Tamas Sandor Nagy, Jul 19 2022

Keywords

• nonn
• base

Comments

Terms of A034844 that only have nonprime digits are not terms here. - Michel Marcus, Jul 19 2022

Examples

			The prime 179 is a term because when its prime digit 7 is removed, it remains 19, which is still a prime.
The prime 136457911 is a term because when all of its prime digits, 3, 5, and 7 are removed, it remains 164911, which is still a prime.
		

Links

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

Crossrefs

Cf. A000040, A034844, A019546.

Programs

MATLAB

function a = A355856( max_prime )
    a = []; p = primes( max_prime );
    for n = 1:length(p)
        s = num2str(p(n));
        s = strrep(s,'2',''); s = strrep(s,'3','');
        s = strrep(s,'5',''); s = strrep(s,'7','');
        m = str2double(s);
        if m > 1
            if isprime(m) && m ~= p(n)
                a = [a p(n)];
            end
        end
    end
end % Thomas Scheuerle, Jul 19 2022

Mathematica

q[n_] := (r = FromDigits[Select[IntegerDigits[n], ! PrimeQ[#] &]]) != n && PrimeQ[r]; Select[Prime[Range[250]], q] (* Amiram Eldar, Jul 19 2022 *)

PARI

isok(p) = if (isprime(p), my(d=digits(p), v=select(x->(!isprime(x)), d)); (#v != #d) && isprime(fromdigits(v));) \\ Michel Marcus, Jul 19 2022

Python

from sympy import isprime
def ok(n):
    s = str(n)
    if n < 10 or set(s) & set("2357") == set(): return False
    sd = s.translate({ord(c): None for c in "2357"})
    return len(sd) and isprime(int(sd)) and isprime(n)
print([k for k in range(2000) if ok(k)]) # Michael S. Branicky, Jul 23 2022