Let p_n be the nth prime: 2, 3, 5, 7, 11, ..., and let r be the remainder when (p_n−1)ⁿ + (p_n+1)ⁿ is divided by p_n².

For example, when n = 3, p₃ = 5, and 4³ + 6³ = 280 ≡ 5 mod 25.

The least value of n for which the remainder first exceeds 10⁹ is 7037.

Find the least value of n for which the remainder first exceeds 10¹⁰.