A062088 Primes with every digit a prime and the sum of the digits a prime.

2, 3, 5, 7, 23, 223, 227, 337, 353, 373, 557, 577, 733, 757, 773, 2333, 2357, 2377, 2557, 2753, 2777, 3253, 3257, 3323, 3527, 3727, 5233, 5237, 5273, 5323, 5527, 7237, 7253, 7523, 7723, 7727, 22573, 23327, 25237, 25253, 25523, 27253, 27527, 32233, 32237, 32257

Offset: 1

Author

Amarnath Murthy, Jun 16 2001

Keywords

• nonn
• base
• easy

Examples

			2357 is a prime, each digit is a prime and the sum of digits = 17 is also a prime, so 2357 is a term.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 718 terms from Marius A. Burtea)

Crossrefs

Intersection of A019546 and A046704.

Programs

MATLAB

prim=primes(1000000);
m=1;
for u=1:100;
    v=prim(u);
    nc=dec2base(v,10)-'0';
    s=sum(nc);
         if and(isprime(nc)==1,isprime(s)==1)
             sol(m)=v;
             m=m+1;
         end
end
sol; % Marius A. Burtea, Dec 08 2018

Mathematica

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 *)

PARI

isok(p) = isprime(p) && isprime(sumdigits(p)) && (#select(x->(! isprime(x)), digits(p)) == 0); \\ Michel Marcus, Dec 08 2018

Python

from sympy import isprime
from itertools import count, islice, product
def agen():
    yield from [2, 3, 5, 7]
    for d in count(2):
        for left in product("2357", repeat=d-1):
            for end in "37":
                ts = "".join(left) + end
                if isprime(sum(map(int, ts))):
                    t = int(ts)
                    if isprime(t): yield t
print(list(islice(agen(), 46))) # Michael S. Branicky, Sep 23 2022

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jun 21 2001