def solution():
limit = 10000
primes_list = set(seive_of_erat(limit))
n = 9
while n < limit:
if n not in primes_list:
primes_below = seive_of_erat(n)
conjecture_false = True
for p in primes_below:
if sqrt((n - p) / 2).is_integer():
conjecture_false = False
if conjecture_false:
return n
n += 2
def solution():
four_digit_primes = [p for p in seive_of_erat(10000) if p > 999]
for i, prime1 in enumerate(four_digit_primes):
if prime1 == 1487:
continue
for prime2 in four_digit_primes[i + 1:]:
prime3 = 2 * prime2 - prime1
if prime3 in four_digit_primes:
if set(str(prime1)) == set(str(prime2)) == set(str(prime3)):
return str(prime1) + str(prime2) + str(prime3)
def solution():
list_of_primes = seive_of_erat(1000000)
set_of_primes = set(list_of_primes)
num_circ_primes = 0
for prime in list_of_primes:
circ = True
for rotation in rotations(prime):
if rotation not in set_of_primes:
circ = False
if circ:
num_circ_primes += 1
return num_circ_primes
def find_family(n, limit=100000):
"""Finds lowest prime in family of n primes, searches up to limit"""
primes_list = seive_of_erat(limit)
primes_set = set(primes_list)
for p in primes_list:
digits = get_digits(p)
for d in digits:
family = replace_digits(p, d)
if family:
size = len([m for m in family if m in primes_set])
if size + 1 == n:
return p
return False
def solution():
best_len = 0
best_pair = None
primes_list = set(seive_of_erat(10000))
for a in range(-999, 1000):
for b in range(-999, 1000):
n = 0
while quadratic_function(n, a, b) in primes_list:
n += 1
if n - 1 > best_len:
best_len = n - 1
best_pair = (a, b)
return best_pair, best_len, best_pair[0] * best_pair[1]
def solution():
limit = 1000000
primes_list = seive_of_erat(limit)
primes_set = set(primes_list)
best = (0, 0)
for i, pstart in enumerate(primes_list):
running_sum = pstart
point = i
while running_sum < limit and point < len(primes_list) - 1:
point += 1
running_sum += primes_list[point]
if running_sum in primes_set and point - i + 1 > best[1]:
best = (running_sum, point - i + 1)
return best[0]
def sum_n_primes(n):
"""Returns sum of all primes below n"""
return sum(seive_of_erat(n))