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A244529
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Prime numbers whose decimal expansion contains no repeated digits or zeros, whose digits cannot be rearranged to form another prime number.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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541 (prime) -> 145, 154, 415, 451, 514 (all nonprime).
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MAPLE
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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)))))[]:
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,base,fini,full
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AUTHOR
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STATUS
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approved
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