freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-27-quadratic-primes.english.md

id, challengeType, title, forumTopicId

id	challengeType	title	forumTopicId
5900f3871000cf542c50fe9a	5	Problem 27: Quadratic primes	301919

Description

Euler discovered the remarkable quadratic formula: $n^2 + n + 41$ 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:

n^2 + an + b, where |a| < range and $|b| \le range$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.

Instructions

Tests

tests:
  - text: <code>quadraticPrimes(200)</code> should return -4925.
    testString: assert(quadraticPrimes(200) == -4925);
  - text: <code>quadraticPrimes(500)</code> should return -18901.
    testString: assert(quadraticPrimes(500) == -18901);
  - text: <code>quadraticPrimes(800)</code> should return -43835.
    testString: assert(quadraticPrimes(800) == -43835);
  - text: <code>quadraticPrimes(1000)</code> should return -59231.
    testString: assert(quadraticPrimes(1000) == -59231);

Challenge Seed

function quadraticPrimes(range) {
  // Good luck!
  return range;
}

quadraticPrimes(1000);

Solution

// solution required