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%I #25 Sep 23 2022 16:39:09
%S 2,3,5,7,23,223,227,337,353,373,557,577,733,757,773,2333,2357,2377,
%T 2557,2753,2777,3253,3257,3323,3527,3727,5233,5237,5273,5323,5527,
%U 7237,7253,7523,7723,7727,22573,23327,25237,25253,25523,27253,27527,32233,32237,32257
%N Primes with every digit a prime and the sum of the digits a prime.
%H Alois P. Heinz, <a href="/A062088/b062088.txt">Table of n, a(n) for n = 1..10000</a> (first 718 terms from Marius A. Burtea)
%e 2357 is a prime, each digit is a prime and the sum of digits = 17 is also a prime, so 2357 is a term.
%t aQ[p_] := PrimeQ[p] && Module[{d = IntegerDigits[p]}, PrimeQ[Total[d]] && LengthWhile[d, PrimeQ[#] &] == Length[d]]; Select[Range[33000], aQ] (* _Amiram Eldar_, Dec 08 2018 *)
%o (PARI) isok(p) = isprime(p) && isprime(sumdigits(p)) && (#select(x->(! isprime(x)), digits(p)) == 0); \\ _Michel Marcus_, Dec 08 2018
%o (MATLAB)
%o prim=primes(1000000);
%o m=1;
%o for u=1:100;
%o v=prim(u);
%o nc=dec2base(v,10)-'0';
%o s=sum(nc);
%o if and(isprime(nc)==1,isprime(s)==1)
%o sol(m)=v;
%o m=m+1;
%o end
%o end
%o sol; % _Marius A. Burtea_, Dec 08 2018
%o (Python)
%o from sympy import isprime
%o from itertools import count, islice, product
%o def agen():
%o yield from [2, 3, 5, 7]
%o for d in count(2):
%o for left in product("2357", repeat=d-1):
%o for end in "37":
%o ts = "".join(left) + end
%o if isprime(sum(map(int, ts))):
%o t = int(ts)
%o if isprime(t): yield t
%o print(list(islice(agen(), 46))) # _Michael S. Branicky_, Sep 23 2022
%Y Intersection of A019546 and A046704.
%K nonn,base,easy
%O 1,1
%A _Amarnath Murthy_, Jun 16 2001
%E Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jun 21 2001
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