A225193 Composite numbers such that every non-identity permutation gives a prime.

14, 16, 20, 30, 32, 34, 35, 38, 50, 70, 74, 76, 91, 92, 95, 98, 110, 118, 119, 133, 772, 775, 778, 779, 1118, 3337, 7771, 77779

Offset: 1

Author

Jayanta Basu, May 01 2013

Keywords

• nonn
• base

Examples

			772 is a member since both 727 and 277 are primes.
		

Crossrefs

Cf. A003459, A068652, A068653.

Programs

Mathematica

t={}; Do[p=Permutations[IntegerDigits[n]]; c=Length[p]; cn=Length[Select[Table[FromDigits[k],{k,p}], PrimeQ]]; If[!PrimeQ[n] && c>1 && cn==c-1, AppendTo[t,n]], {n,10,100000}]; t

Python

from sympy import isprime
from itertools import count, islice, permutations
def agen(): yield from (k for k in count(1) if len(set(s:=str(k)))!=1 and not isprime(k) and all((t:=int("".join(m)))==k or isprime(t) for m in permutations(s)))
print(list(islice(agen(), 28))) # Michael S. Branicky, Dec 29 2023