title: Quadratic primes
url: http://projecteuler.net/problem=27

desc: |
  Euler discovered the remarkable quadratic formula:
  n² + n + 41
  It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 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 n = 0 to 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

solution: Bruteforce

solutions:
  solve.php:
    desc: Basic Solution - needs BCMath
    language: php