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A348699 Primes with a prime number of prime digits.

%I A348699 #24 Jun 26 2025 07:34:48
%S A348699 23,37,53,73,127,137,157,173,223,227,229,233,239,251,257,263,271,277,
%T A348699 283,293,307,313,317,331,337,347,353,359,367,373,379,383,397,433,457,
%U A348699 503,521,523,547,557,563,571,577,587,593,653,673,677,727,733,739,743,751,757,773,787,797
%N A348699 Primes with a prime number of prime digits.
%H A348699 Jens Ahlström, <a href="/A348699/b348699.txt">Table of n, a(n) for n = 1..5853</a> (all terms < 10^5)
%H A348699 Hackerearth, <a href="https://www.hackerearth.com/problem/algorithm/optimus-prime-2/">Optimus prime</a>
%t A348699 Select[Range[800], And @@ PrimeQ[{#, Count[IntegerDigits[#], _?PrimeQ]}] &] (* _Amiram Eldar_, Nov 04 2021 *)
%o A348699 (Python)
%o A348699 from sympy import isprime as i
%o A348699 from sympy import primerange as p
%o A348699 print([x for x in p(1, 800) if i(len([d for d in str(x) if i(int(d))]))])
%o A348699 (Python)
%o A348699 from sympy import isprime
%o A348699 def ok(n): return isprime(n) and isprime(sum(1 for d in str(n) if d in "2357"))
%o A348699 print([k for k in range(800) if ok(k)]) # _Michael S. Branicky_, Jun 26 2025
%Y A348699 Intersection of A000040 and A092619.
%Y A348699 Cf. A217090.
%K A348699 base,easy,nonn
%O A348699 1,1
%A A348699 _Jens Ahlström_, Oct 30 2021