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

The sequence $a(n)$ is defined by:
$a(1)=\mathrm{next}\mathrm{\_}\mathrm{prime}({10}^{14})$ and $a(n)=\mathrm{next}\mathrm{\_}\mathrm{prime}(a(n-1))$ 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 $1\le n\le 100000$. Give your answer mod $1234567891011$.