A244529 - OEIS

%I #41 Nov 10 2024 02:23:23

%S 2,3,5,7,19,23,29,41,43,47,53,59,61,67,83,89,257,263,269,431,487,523,

%T 541,827,829,853,859,2861,5623,5849

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

%C There are only thirty prime numbers which meet the criteria.

%C 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

%H Prime Curios, <a href="https://t5k.org/curios/page.php?short=5849">5849</a>

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

%p with(combinat):

%p T:= n-> sort(map(h-> h[], select(z-> nops(z)=1,

%p     map(x-> map(y-> select(isprime, parse(cat(y[]))),

%p     permute(x)), choose([$1..9], n)))))[]:

%p seq(T(n), n=1..4);  # _Alois P. Heinz_, Jun 29 2014

%t 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 *)

%Y Cf. A000720.

%K nonn,base,fini,full

%O 1,1

%A _Andreas Boe_, Jun 29 2014