# Problem 425: Prime connection
Two positive numbers A and B are said to be connected (denoted by "A ↔
B") if one of these conditions holds: (1) A and B have the same length
and differ in exactly one digit; for example, 123 ↔ 173. (2) Adding one
digit to the left of A (or B) makes B (or A); for example, 23 ↔ 223 and
123 ↔ 23. We call a prime P a 2's relative if there exists a chain of
connected primes between 2 and P and no prime in the chain exceeds P.
For example, 127 is a 2's relative. One of the possible chains is shown
below: 2 ↔ 3 ↔ 13 ↔ 113 ↔ 103 ↔ 107 ↔ 127 However, 11 and 103 are not
2's relatives. Let F(N) be the sum of the primes ≤ N which are not 2's
relatives. We can verify that F(103) = 431 and F(104) = 78728. Find
F(107).