In the first 100 numbers having all of the non-prime digits, the interloping primes can occur only in the 7-digit numbers as we haven't arrived at 8-digit numbers yet. The interloping prime can only be 3 or 7 and not 5, as the non-primes, 0, 1, 4, 6, 8 and 9, add up to 28 and the addition of 5 would make 33, so all such numbers would be a multiple of 3 and therefore not prime. You'd have to get into the 8-digit numbers, with either a repetition of a non-prime, or another prime (or a second 5) to get a case with all the primes and also at least one 5.

Posted by Charlie on 2017-04-28 15:38:57