Exploding sequence

Define the sequence a₁, a₂, a₃, ... as:

• a₁ = 1
• a_n+1 = 6a_n² + 10a_n + 3 for n ≥ 1.

Examples: a₃ = 2359 a₆ = 269221280981320216750489044576319 a₆ mod 1 000 000 007 = 203064689 a₁₀₀ mod 1 000 000 007 = 456482974

Define B(x,y,n) as ∑ (a_n mod p) for every prime p such that x ≤ p ≤ x+y.

Examples: B(10⁹, 10³, 10³) = 23674718882 B(10⁹, 10³, 10¹⁵) = 20731563854

Find B(10⁹, 10⁷, 10¹⁵).

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