Fibonacci and Primes

\[\large S(N)=\sum F_p\]

Define the summation above for all primes \(p\) less than \(N\).

The Fibonacci sequence \(\{F_n\}\) is defined by \(F_0=0,F_1=1\) and \(F_n=F_{n-1}+F_{n-2}\) for all integers \(n\geq 2\).

It is given that

\[\begin{eqnarray} S(10)&=&21 \\ S(10^2)&\equiv & 350775433\pmod{10^9+7} \\ S(10^3)& \equiv & 347000363\pmod{10^9+7} \end{eqnarray} \]

Find the value of \(S(10^7)\) modulo \(10^9+7\).

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