def main():
power_list = euler.prime_list_with_zeros(LIMIT1)
fast_list = power_list[:]
max_divisors = euler.max_divisors(range(LIMIT1))
total = 0
for i in range(len(power_list) - 1, -1, -1):
if power_list[i]:
temp = i
while temp < LIMIT1:
power_list[temp] = 1
temp *= i
for n in range(2, LIMIT1):
if power_list[n]:
total += 1
elif not n & 1 and fast_list[n >> 1]:
total += (n >> 1) + 1
else:
max_divisor = max_divisors[n]
r = n // max_divisor
for a in range(r - 1, 0, -1):
a_m = a * max_divisor
if not a_m * (a_m + 1) % n:
total += a_m + 1
break
if not a_m * (a_m - 1) % n:
total += a_m
break
return total
def main():
lst = euler.prime_list_with_zeros(LIMIT)
count = 0
for n in lst:
if n:
for rounding in get_round(n):
if lst[rounding] == 0:
break
else:
count += 1
return count
def main():
lst = euler.prime_list_with_zeros(LIMIT**2)
double_squares = [2 * i**2 for i in range(1, LIMIT + 1)]
number = 33
while True:
number += 2
if lst[number] == 0:
for i in range(LIMIT):
must_be_prime = number - double_squares[i]
if must_be_prime > 0:
if lst[must_be_prime] != 0:
break
else:
return number
def main():
lst = euler.prime_list_with_zeros(LIMIT)
prime_list = [n for n in lst if n != 0]
length = len(prime_list)
prime = 0
max_j = 0
for i in range(length):
for j in range(1, length - i):
total = sum(prime_list[i:i + j])
if total > 1000000:
if j < max_j:
return prime
break
if lst[total] != 0:
prime = max(prime, total)
max_j = max(max_j, j)
return prime
def main():
lst = euler.prime_list_with_zeros(LIMIT)
total = 0
for i in range(10, LIMIT):
if lst[i] != 0:
ind = i
while ind > 10:
ind = ind // 10
if lst[ind] == 0:
break
else:
ind = i
while ind > 10:
ind = ind % 10**int(math.log(ind, 10))
if lst[ind] == 0:
break
else:
total += i
return total
def main():
primes_for_square = euler.prime_list_with_zeros(int(LIMIT ** 0.5))
primes_for_cube = euler.clean_zeros(
primes_for_square[:int(LIMIT ** (1 / 3))]
)
primes_for_forth_power = euler.clean_zeros(
primes_for_square[:int(LIMIT ** 0.25)]
)
primes_for_square = euler.clean_zeros(primes_for_square)
numbers = set()
for i in primes_for_forth_power:
for j in primes_for_cube:
temp = i ** 4 + j ** 3
if temp >= LIMIT:
break
for k in primes_for_square:
n = temp + k ** 2
if n < LIMIT:
numbers.add(n)
return len(numbers)
def main():
lst = euler.prime_list_with_zeros(10000)
for i in range(1000, 10000):
if (
lst[i] != 0 and
lst[i] != 1487
):
for diff in range(500, (10000 - i) // 2):
if (
lst[i + diff] != 0 and
lst[i + 2 * diff] != 0 and
(
set(str(lst[i])) ==
set(str(lst[i + diff])) ==
set(str(lst[i + 2 * diff]))
)
):
return int(
str(lst[i]) +
str(lst[i + diff]) +
str(lst[i + 2 * diff])
)
return 0
import itertools
import euler
ANSWER = 71
LIMIT = 5000
PRIME_LIST_WITH_ZEROS = euler.prime_list_with_zeros(LIMIT)
PRIME_LIST = euler.clean_zeros(PRIME_LIST_WITH_ZEROS)
def sum_two(n, index):
result = 0
prime = PRIME_LIST[index]
n_2 = n // 2
while prime <= n_2:
if PRIME_LIST_WITH_ZEROS[n - prime]:
result += 1
index += 1
prime = PRIME_LIST[index]
return result
def sum_count(n, count, index=0):
if n < count * 2:
return 0
if count == 2:
return sum_two(n, index)
prime = PRIME_LIST[index]
smallest = n // count
result = 0
import euler
ANSWER = 1739023853137
LIMIT = 10**8
LIMIT2 = LIMIT + 2
PRIME_LIST = euler.prime_list_with_zeros(LIMIT2)
def check(n):
sqrt = int(n**0.5) + 1
for i in range(3, sqrt):
if not n % i:
if not PRIME_LIST[i + n // i]:
return False
return True
def main():
total = 1
for i in range(2, LIMIT // 2 + 3):
q = 2 * i - 4
if PRIME_LIST[i]:
if PRIME_LIST[q + 1]:
if check(q):
total += q
return total
if __name__ == '__main__':
print(main())