id	title	challengeType	forumTopicId	dashedName
5900f5151000cf542c510028	Problem 425: Prime connection	5	302095	problem-425-prime-connection

--description--

Two positive numbers A and B are said to be connected (denoted by "A ↔ B") if one of these conditions holds:

A and B have the same length and differ in exactly one digit; for example, 123 ↔ 173.
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({10}^3) = 431 and F({10}^4) = 78\\,728.

Find F({10}^7).

--hints--

primeConnection() should return 46479497324.

assert.strictEqual(primeConnection(), 46479497324);

function primeConnection() {

  return true;
}

primeConnection();

// solution required