# Quadratic primes

# Consider quadratics of the form:
# n^2 + an + b, where abs(a) < 1000 and abs(b) <= 1000

# Find the product of the coefficients, a * b, for the quadratic expression that
# produces the maximum number of primes for consecutive values of n, starting from n = 0

import numpy as np
import math

def quad(a, b, n):
	return n**2 + a * n + b

# Thing that immediately stands out is that b always needs to be prime itself,
# since for n=0 only b remains, so that thins the pool a lot
# So get the prime thingy out again

def getPrimes(n):
	primes = [1 for p in range(n)]
	primes[0] = 0
	primes[1] = 0

	x = 2
	while x < np.sqrt(n):
		if primes[x] == 1:

			for i in range(x+x, n, x):
				primes[i] = 0

		x += 1

	result = []
	for i in range(n):
		if primes[i]:
			result.append(i)

	return result

def getPrimeSequenceLength(a, b, primes):
	n = 0
	while True:
		if quad(a, b, n) in primes:
			n += 1
		else:
			break

	return n - 1

def main():
	print("Hello, this is Patrick")

	ps = getPrimes(1000000)
	littleps = list(filter(lambda p: p < 1000, ps))

	maxprod = 0
	maxlength = 0
	for b in littleps:
		for a in range(-b, 1000):
			psl = getPrimeSequenceLength(a, b, ps)
			if psl > maxlength:
				maxlength = psl
				maxprod = a * b

	print(f"The maximum prime sequence {maxlength} was found for {maxprod}")
	

if __name__ == "__main__":
	main()