欧拉计划(python) problem 27

Quadratic primes

Problem 27

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.

python code:

import math
def IsPrime(x):
    if x<3:
        return False
    for i in range(2,int(math.sqrt(x))+1):
        if x%i==0:
            return False
    return True

def func(a,b):
    k=0
    while True:
        if IsPrime(k*k+a*k+b):
            k+=1
        else:
            break
    return k-1

maxa,maxb=0,0
num=0
for j in range(-999,1000):
    if IsPrime(j):
        for i in range(-999,1000):
            temp=func(i,j)
            if temp>num:
                num=temp
                maxa,maxb=i,j
print(maxa*maxb)

time : 3s