## Prome Numbers

A "Prome" number is any prime number consisting of only odd digits. For example 177 is a prome because it is prime and all its digits ("1", "7" and "7") are all odd. Whereas 163 is not a prome because "6" is even. Let \(S(N)\) denote the sum of all prome numbers less than \(N\). For example \(S(40) = 3+5+7+11+13+17+19+31+37 = 143\).Part A | Determine \(S(1000)\) | |
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Part B | Determine \(S(10^8)\) |