H is a set of all three digit numbers with all digits prime. If all the numbers in set H are increased by 5 then for how many of the numbers all the three digits are prime after the increase?

Set H contains three-digit numbers where all digits (hundreds, tens, units) are prime digits (2, 3, 5, 7). There are 4 × 4 × 4 = 64 such numbers. When we add 5 to each, we must check which results still have all prime digits. Through systematic verification checking the units digit transformation (only endings of 2→7 and 7→2 work, while 3→8 and 5→0 fail) and accounting for carries affecting tens and hundreds places, exactly 20 numbers maintain all prime digits after adding 5.