data/problems/27.yml
---
:id: 27
:name: Quadratic primes
:url: https://projecteuler.net/problem=27
:content: "Euler discovered the remarkable quadratic formula:\n\n$n^2 + n + 41$\n\nIt
turns out that the formula will produce 40 primes for the consecutive integer values
$0 \\le n \\le 39$. However, when $n = 40, 40^2 + 40 + 41 = 40(40 + 1) + 41$ is
divisible by 41, and certainly when $n = 41, 41^2 + 41 + 41$ is clearly divisible
by 41.\n\nThe incredible formula $n^2 - 79n + 1601$ was discovered, which produces
80 primes for the consecutive values $0 \\le n \\le 79$. The product of the coefficients,
−79 and 1601, is −126479.\n\nConsidering quadratics of the form:\n\n> $n^2 + an
+ b$, where $|a| \\< 1000$ and $|b| \\le 1000$ \n> \n> \n> where $|n|$ is the
modulus/absolute value of $n$ \n> e.g. $|11| = 11$ and $|-4| = 4$\n\nFind 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 $n = 0$.\n\n"