Brute force

The problem is to find the best combination of \( a \) and \( b \) such that the formula:

\[ n^2 + an + b \]

produces the largest number of primes for consecutive values of \( n \). The absolute value of \( a \) and \( b \) must be less than \( 1000 \).

The brute force solution is to iterate from \( -1000 \) to \( 1000 \) for \( a \) and \( b \) and count the number of consecutive primes each time.

def quadratic_primes(limit=1000):
    res = 0
    max_primes = 0
    for a in range(-limit, limit):
        for b in range(-limit, limit):
            n = 0
            while isprime(n ** 2 + a * n + b):
                n += 1
            if n > max_primes:
                max_primes = n
                res = a * b

    return res