A020458 Primes that contain digits 2 and 3 only.

2, 3, 23, 223, 233, 2333, 3323, 23333, 32233, 32323, 33223, 222323, 232333, 233323, 323233, 323333, 333233, 333323, 2222333, 2223233, 2232323, 2233223, 2332333, 2333323, 3222223, 3223223, 3223333, 3233323, 3233333, 3332233, 3333233, 22222223, 22223323, 22232233

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)

Crossrefs

Cf. A139067, A139069, A032810, A020463.

Programs

Mathematica

Flatten[Table[Select[FromDigits/@Tuples[{2,3},n],PrimeQ],{n,7}]] (* Harvey P. Dale, Jul 13 2012 *)

PARI

go(n)=my(v=List([2]),x,t); for(d=1,n, x=10^d\9*2; forstep(i=1,2^d-1,2, if(ispseudoprime(t=x+fromdigits(binary(i))), listput(v,t)))); Vec(v) \\ Charles R Greathouse IV, Sep 14 2015

Python

from sympy import isprime
from itertools import count, islice, product
def agen(): # generator of terms
    yield from [2, 3]
    for d in count(2):
        for first in product("23", repeat=d-1):
            t = int("".join(first) + "3")
            if isprime(t): yield t
print(list(islice(agen(), 34))) # Michael S. Branicky, Jun 08 2022

Extensions

Edited by N. J. A. Sloane, Jul 27 2008 at the suggestion of Dmitry Kamenetsky.

Edited by Charles R Greathouse IV, Mar 17 2010