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A355856
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Primes, with at least one prime digit, that remain primes when all of their prime digits are removed.
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1
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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
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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q[n_] := (r = FromDigits[Select[IntegerDigits[n], ! PrimeQ[#] &]]) != n && PrimeQ[r]; Select[Prime[Range[250]], q] (* Amiram Eldar, Jul 19 2022 *)
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PROG
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(MATLAB)
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
(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)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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