Define the sequence $a_1,a_2,a_3,\dots$ as:

• $a_1=1$
• $a_{n+1}=6a_n^2+10a_n+3$ for $n\ge 1$.

Examples:
$a_3=2359$
$a_6=269221280981320216750489044576319$
$a_{6}mod1000000007=203064689$
$a_{100}mod1000000007=456482974$

Define $B(x,y,n)$ as $\sum (a_{n}modp)$ for every prime $p$ such that $x\le p\le x+y$.

Examples:
$B({10}^9,{10}^3,{10}^3)=23674718882$
$B({10}^9,{10}^3,{10}^{15})=20731563854$

Find $B({10}^9,{10}^7,{10}^{15})$.