--description--

For any positive integer $n$ the function $\text{next_prime}(n)$ returns the smallest prime $p$ such that $p > n$.

The sequence $a(n)$ is defined by: $a(1) = \text{next_prime}({10}^{14})$ and $a(n) = \text{next_prime}(a(n - 1))$ for $n > 1$.

The fibonacci sequence $f(n)$ is defined by: $f(0) = 0$, $f(1) = 1$ and $f(n) = f(n - 1) + f(n - 2)$ for $n > 1$.

The sequence $b(n)$ is defined as $f(a(n))$.

Find $\sum b(n)$ for $1≤n≤100\,000$. Give your answer $\bmod 1\,234\,567\,891\,011$.

--hints--

primonacci() should return 283988410192.

assert.strictEqual(primonacci(), 283988410192);

--seed--

--seed-contents--

function primonacci() {

  return true;
}

primonacci();

--solutions--

// solution required