Euler discovered the remarkable quadratic formula:
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 | Â | Â |
| (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.
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