A244529 Prime numbers whose decimal expansion contains no repeated digits or zeros, whose digits cannot be rearranged to form another prime number.

2, 3, 5, 7, 19, 23, 29, 41, 43, 47, 53, 59, 61, 67, 83, 89, 257, 263, 269, 431, 487, 523, 541, 827, 829, 853, 859, 2861, 5623, 5849

Offset: 1

Author

Andreas Boe, Jun 29 2014

Keywords

• nonn
• base
• fini
• full

Comments

There are only thirty prime numbers which meet the criteria.

The largest prime in this sequence happens, as noted by Farideh Firoozbakht, to have the property pi(5849) = (pi(5)*pi(8)*pi(4)*pi(9)) * (pi(pi(5))*pi(pi(8))*pi(pi(4))*pi(pi(9))), where pi = A000720. Note that 5849 is the earliest multi-digit prime with this property. - Jonathan Vos Post, Jun 30 2014

Examples

			541 (prime) -> 145, 154, 415, 451, 514 (all nonprime).
		

Links

• Prime Curios, 5849

Crossrefs

Cf. A000720.

Programs

Maple

with(combinat):
T:= n-> sort(map(h-> h[], select(z-> nops(z)=1,
    map(x-> map(y-> select(isprime, parse(cat(y[]))),
    permute(x)), choose([$1..9], n)))))[]:
seq(T(n), n=1..4);  # Alois P. Heinz, Jun 29 2014

Mathematica

nrdQ[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,0]&&Length[Union[idn]] == Length[idn]&&Count[FromDigits/@Permutations[idn],?PrimeQ]==1]; Select[ Prime[ Range[800]],nrdQ] (* _Harvey P. Dale, Apr 27 2018 *)