A124888 Primes with prime number of only prime digits (i.e., 2, 3, 5, 7).

23, 37, 53, 73, 223, 227, 233, 257, 277, 337, 353, 373, 523, 557, 577, 727, 733, 757, 773, 22273, 22277, 22573, 22727, 22777, 23227, 23327, 23333, 23357, 23537, 23557, 23753, 23773, 25237, 25253, 25357, 25373, 25523, 25537, 25577, 25733, 27253, 27277

Offset: 1

Author

Lekraj Beedassy, Nov 12 2006

Keywords

• nonn
• base

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000
• József Bölcsföldi, György Birkás, and Miklós Ferenczi, Bölcsföldi-Birkás-Ferenczi prime numbers (Full prime numbers), International Journal of Mathematics and Statistics Invention (IJMSI), Volume 5, Issue 2, February 2017, pp. 4-7.

Crossrefs

Cf. A019546, A120533.

Programs

Mathematica

Select[Prime[Range[3000]],ContainsOnly[IntegerDigits[#],{2,3,5,7}]&&PrimeQ[Length[IntegerDigits[#]]]&] (* James C. McMahon, Dec 14 2024 *)

PARI

isok(p) = isprime(p) && (d=digits(p)) && isprime(#d) && vecmin(vector(#d, k, isprime(d[k]))); \\ Michel Marcus, Sep 21 2017

Python

from sympy import isprime, prime
from itertools import count, islice, product
def agen(): yield from filter(isprime, (int("".join(s)+e) for i in count(1) for s in product("2357", repeat=prime(i)-1) for e in "37"))
print(list(islice(agen(), 42))) # Michael S. Branicky, Jun 23 2022

Extensions

Terms 773, 23753 inserted by Georg Fischer, Jun 23 2022