def sieve_less(self):
for composite in count(35, 2):
# ignore odd primes
if simple_is_prime(composite):
continue
for i in count():
delta = composite - 2 * i**2
if delta < 2:
return composite
if simple_is_prime(delta):
break
def brute_force(self):
for i in (7, 4): # all other lengths of n are divisible by 3
digits = reversed("123456789"[:i])
for j in permutations(digits):
j = int(''.join(j))
if simple_is_prime(j):
return j
def brute_force(self):
upper_bound = 1_000_000
primes = list(sieve_of_eratosthenes(4000))
max_length = 0
max_prime = 0
for start in range(len(primes)):
current_length = 0
for end in range(start, len(primes)):
s = sum(primes[start:end])
current_length += 1
if s > upper_bound:
break
elif simple_is_prime(s) and current_length > max_length:
max_length = current_length
max_prime = s
return max_prime
def brute_force(self):
"""
Loop through all a and b values such that abs(a|b) < 1000
then count up from 0 (n) and check if the output of the quadratic
n^2 + an + b for each n until the output is no longer a prime
check if we beat the max and then rinse and repeat
"""
best_a, best_b, best_n = 0, 0, 0
for a in range(-1000, 1000):
for b in range(-1000, 1000):
for n in count():
output = (n ** 2) + (a * n) + b
if not simple_is_prime(output):
if best_n < n - 1:
best_a = a
best_b = b
best_n = n - 1
break
return best_a * best_b