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problem_027.py
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problem_027.py
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# coding: utf-8
'''
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.
'''
from helpers import is_prime
def binome(a, b):
def f(n):
return n ** 2 + a * n + b
return f
def result(n):
_max = 1
_max_a = 1
_max_b = 1
first_primes = [j for j in range(n + 1) if is_prime(j)]
for a in range(- n, n + 1):
for b in first_primes:
i = 0
while is_prime(binome(a, b)(i)):
i += 1
if i >= _max:
_max = i
_max_a = a
_max_b = b
return _max_a * _max_b
def main():
return result(1000)
if __name__ == "__main__":
print(main())
# -59231 in 597ms