--description--

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 $F({10}^3) = 431$ and $F({10}^4) = 78\,728$.

Find $F({10}^7)$.

--hints--

primeConnection() should return 46479497324.

assert.strictEqual(primeConnection(), 46479497324);

--seed--

--seed-contents--

function primeConnection() {

  return true;
}

primeConnection();

--solutions--

// solution required