def main():
primes = get_all_primes_until(10000)[168:]
for step in range(1111,5000):
for prime in primes:
if is_prime(prime + step) and is_prime(prime + 2 * step):
if is_permutation(prime, prime + step) and is_permutation(prime, prime + 2 * step):
print(prime, prime + step, prime + step * 2)
def is_circular_prime(n):
if is_prime(n):
flag = True
for i in range(1, len(str(n))):
if not is_prime(int(str(n)[-i:] + str(n)[:-i])):
flag = False
return flag
else:
return False
def is_truncatable_prime(n):
flag_right = False
flag_left = False
for i in range(len(str(n)) - 1, 0, -1):
if is_prime(n % (10 ** i)):
flag_left = True
else:
return False
for j in range(1, len(str(n))):
if is_prime(int(n / 10 ** j)):
flag_right = True
else:
return False
if flag_right and flag_left:
return True
return False
def main():
ans = 0
max_con = 21
primes = get_all_primes_until(10000)
for i in range(len(primes)):
for j in range(i + 1):
q = sum(primes[j:len(primes) - 1 - i + j])
if is_prime(q) and q < 1000000:
if len(primes) - i > max_con:
max_con = len(primes) - i
ans = q
print(ans, max_con)
def main():
primes = 0
number = 10
ans = 0
while primes < 11:
if is_prime(number):
if is_truncatable_prime(number):
print(number)
primes += 1
ans += number
number += 1
print(ans)
def main():
ans = 0
numbers = list(itertools.permutations(
['1', '2', '3', '4', '5', '6',
'7'])) # there is no pandigital prime with 8/9 digits O_o
for i in reversed(numbers):
number = ''
for digit in i:
number += digit
if is_prime(int(number)):
ans = int(number)
break
print(ans)
def main():
current = 9
prime_counter = 3
counter = 5
h = 3
while (prime_counter * 100) / counter >= 10:
h += 2
for i in range(4):
current += h - 1
if is_prime(current):
prime_counter += 1
counter += 1
print(h)
def main():
for i in range (9, 100000000000000 , 2):
if not goldbach(i) and not is_prime(i):
print(i)
break
def get_all_primes_until(n):
primes = [1, 2]
for i in range(3, n, 2):
if is_prime(i):
primes.append(i)
return primes