--description--

Euler discovered the remarkable quadratic formula:

It 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.

The 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.

Considering quadratics of the form:

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 $n = 0$.

--hints--

quadraticPrimes(200) should return a number.

assert(typeof quadraticPrimes(200) === 'number');

quadraticPrimes(200) should return -4925.

assert(quadraticPrimes(200) == -4925);

quadraticPrimes(500) should return -18901.

assert(quadraticPrimes(500) == -18901);

quadraticPrimes(800) should return -43835.

assert(quadraticPrimes(800) == -43835);

quadraticPrimes(1000) should return -59231.

assert(quadraticPrimes(1000) == -59231);

--seed--

--seed-contents--

function quadraticPrimes(range) {

  return range;
}

quadraticPrimes(1000);

--solutions--

// solution required