def get_more_primes():
global working_combos, all_primes
all_primes = get_prime_numbers_until(10000)
all_primes.remove(2)
all_primes.remove(5)
for cur_prime in all_primes:
for prime in list(working_combos.keys()):
left = int(str(prime) + str(cur_prime))
right = int(str(cur_prime) + str(prime))
if is_prime(left) and is_prime(right):
working_combos[prime].add(cur_prime)
working_combos[cur_prime].add(prime)
working_combos[cur_prime] = set()
def second_try():
max_consecutive = 0
primes = get_prime_numbers_until(1000000)
last_prime = primes[len(primes) - 1]
for index, prime in enumerate(primes):
if prime * max_consecutive > last_prime:
break
prime_sum = 0
index_offset = 0
while prime_sum < last_prime:
prime_sum += primes[index + index_offset]
if index_offset > max_consecutive and prime_sum in primes:
max_consecutive = index_offset
max_consecutive_prime = prime_sum
index_offset += 1
return max_consecutive, max_consecutive_prime
def first_try():
primes = get_prime_numbers_until(1000000)
max_consecutive_prime = 0
max_consecutive = 2
for prime in reversed(primes):
starting_primes = [p for p in primes if p < prime / max_consecutive]
for index, sp in enumerate(starting_primes):
prime_sum = 0
index_offset = 0
while prime_sum < prime:
prime_sum += primes[index + index_offset]
index_offset += 1
if prime_sum == prime and index_offset > max_consecutive:
max_consecutive = index_offset
max_consecutive_prime = prime
print(prime, index_offset, len(starting_primes))
break
elif prime_sum > prime and index_offset < max_consecutive:
break
return max_consecutive, max_consecutive_prime
from helpers import get_prime_numbers_until print(sum(get_prime_numbers_until(2 * (10**6)))) print(get_prime_numbers_until(100))
from helpers import get_prime_numbers_until
number = 600851475143
root = number ** 0.5
prime_numbers = get_prime_numbers_until(int(root))
result = 0
for prime_number in reversed(prime_numbers):
if number % prime_number == 0:
result = prime_number
break
# for num in reversed(range(2, int(number ** .5))):
# if number % num == 0:
# if is_prime(num):
# result = num
# break
print(result)
from helpers import is_prime, get_prime_numbers_until
highest_combo = (0, 0, 0)
primes = get_prime_numbers_until(1001)
for a in range(-999, 1000):
for b in primes:
n = 0
while True:
number = n**2 + a * n + b
if number < 2 or not is_prime(number):
n -= 1
if n > highest_combo[2]:
print('new high', a, b, n)
highest_combo = (a, b, n)
break
n += 1
print(highest_combo[0] * highest_combo[1])
from helpers import get_prime_numbers_until
target = 50 * 10 ** 6
primes_1 = get_prime_numbers_until(int(target ** (1/2)) + 1)
primes_2 = get_prime_numbers_until(int(target ** (1/3)) + 1)
primes_3 = get_prime_numbers_until(int(target ** (1/4)) + 1)
numbers = set()
itters = 0
for prime_1 in primes_1:
prime_1_square = prime_1 ** 2
for prime_2 in primes_2:
prime_2_cube = prime_2 ** 3
if prime_1_square + prime_2_cube > target:
primes_2 = [prime for prime in primes_2 if prime < prime_2]
for prime_3 in primes_3:
prime_3_fourth = prime_3 ** 4
if prime_1_square + prime_3_fourth > target:
primes_3 = [prime for prime in primes_3 if prime < prime_3]
num = prime_1_square + prime_2_cube + prime_3_fourth
if num < target:
numbers.add(num)
itters += 1
print(itters)
print(len(numbers))