%I
%S 51,69,96,249,294,429,438,474,546,564,1428,1455,1545,2148,2346,3543,
%T 4155,4236,4515,5415,5433
%N Numbers that can be written as a sum of prime numbers, where all of the digits from 1 to 5 appear exactly once in the primes.
%C Only two numbers have more than one solution, 294, which has two:
%C 294 = 43 + 251,
%C 294 = 53 + 241.
%C And 564, which has three:
%C 564 = 23 + 541,
%C 564 = 41 + 523,
%C 564 = 43 + 521.
%C Also, permutations of numbers are extremely common. 69 and 96; 249,294 and 429; 546 and 564; 1428 and 2148; 1455, 1545, 4155, 4515 and 5415; 2346 and 4236; 3543 and 5433. In fact, there are only 3 numbers from a total of 21 that do not have any permutations associated with it. These are 51, 438 and 474.
%C Another odd fact: the sum of the digits of every single value, except 51, is 15. (note: not actually odd. Since 1 + 2 + 3 + 4 + 5 = 15 and digitSum (a + b) = digitSum( digitSum(a) + digitSum(b) ))
%e 51 = 2 + 3 + 5 + 41.
%e 69 = 5 + 23 + 41.
%e 96 = 2 + 41 + 53.
%K nonn,base,fini,full
%O 1,1
%A _Raffa Freitas_, Aug 12 2014
