A172508 Prime numbers such that the differences between any pair of digits is prime.

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

Offset: 1

Author

Claudio Meller, Feb 05 2010

Keywords

• nonn
• base
• fini
• full

Comments

No further term between 4729 and 7368787 = A000040(500000). - R. J. Mathar, Feb 16 2010

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

Programs

Maple

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

Mathematica

Select[Prime[Range[638]],And@@PrimeQ[#[[1]]-#[[2]]&/@ Subsets[ IntegerDigits[ #],{2}]]&] (* Harvey P. Dale, Nov 29 2012 *)

Extensions

Three more terms from R. J. Mathar and Robert G. Wilson v, Feb 16 2010

Edited by N. J. A. Sloane, Feb 24 2010

Keywords:fini,full added by Ray Chandler and R. J. Mathar, Feb 25 2010