Solution to Project Euler Problem 27: Quadratic primes - Euler discovered the remarkable quadratic formula: Find the product of the coefficients, and , for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n = 0.


Updated: Nov. 28, 2020 — Training Time: 4 minutes
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Topic: Project Euler Problem 27: Quadratic primes.

Difficulty: Easy.

Objective: Euler discovered the remarkable quadratic formula:
n2 + n + 41
It turns out that the formula will produce 40 primes for the consecutive integer values 0 ≤ n ≤ 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and certainly when n = 41, 412 + 41 + 41 is clearly divisible by 41.
The incredible formula n2 - 79n + 1601 was discovered, which produces 80 primes for the consecutive values 0 ≤ n ≤ 79. The product of the coefficients, −79 and 1601, is −126479.
Considering quadratics of the form:
n2 + an + b, where |a| < 1000 and |b| ≤ 1000
where |n| is the modulus/absolute value of n
e.g. |11| = 11 and |-4| = 4
Find the product of the coefficients, a and b, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n = 0.

Input: None.

Expected Output: -59231.

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