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A172508
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Prime numbers such that the differences between any pair of digits is prime.
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3
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2, 3, 5, 7, 13, 29, 31, 41, 47, 53, 61, 79, 83, 97, 163, 257, 461, 479, 503, 613, 631, 641, 683, 853, 863, 947, 2749, 4297, 4729
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OFFSET
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1,1
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COMMENTS
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As Robert G. Wilson v points out, there are only 4 different single-digit primes, 2, 3, 5 and 7. Therefore the difference between any pair of a term cannot be zero; the terms can only have a maximum of 5 different digits. A full search covering this range shows that the sequence terminates with the 4729. - R. J. Mathar, Feb 25 2010
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LINKS
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MAPLE
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isA172508 := proc(n) local res, dgs, k, l ; dgs := convert(n, base, 10) ; if nops(dgs) < 2 or not isprime(n) then return false; else for k from 1 to nops(dgs)-1 do for l from k+1 to nops(dgs) do if not isprime(abs( op(k, dgs)-op(l, dgs) )) then return false; end if; end do ; end do ; end if; return true; end proc: for i from 1 to 500000 do p := ithprime(i) : if isA172508(p) then printf("%d, \n", p) ; end if; end do: # R. J. Mathar, Feb 16 2010
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MATHEMATICA
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Select[Prime[Range[638]], And@@PrimeQ[#[[1]]-#[[2]]&/@ Subsets[ IntegerDigits[ #], {2}]]&] (* Harvey P. Dale, Nov 29 2012 *)
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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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EXTENSIONS
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STATUS
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approved
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