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.
import math,time def isOk(temp): if temp < 0: return False for i in range(2,int(math.sqrt(temp))+1): if temp%i==0 : return False return True begin = time.time() maxValue=0 lastValue=1 for a in range(-1000,1001): for b in range(-1000, 1001): n = 0 resu = 0 while True: temp = n*n + a*n + b if(isOk(temp)): resu+=1 n+=1 else : break if resu>maxValue: maxValue = resu lastValue = a*b print lastValue end = time.time() print end-begin