--description--

Let $p_n$ be the $n$th prime: 2, 3, 5, 7, 11, ..., and let $r$ be the remainder when ${(p_n−1)}^n + {(p_n+1)}^n$ is divided by ${p_n}^2$.

For example, when $n = 3, p_3 = 5$, and $4^3 + 6^3 = 280 ≡ 5\ mod\ 25$.

The least value of $n$ for which the remainder first exceeds $10^9$ is 7037.

Find the least value of $n$ for which the remainder first exceeds $10^{10}$.

--hints--

primeSquareRemainders() should return 21035.

assert.strictEqual(primeSquareRemainders(), 21035);

--seed--

--seed-contents--

function primeSquareRemainders() {

  return true;
}

primeSquareRemainders();

--solutions--

// solution required