def is_circular_prime(number):
"""if number is a circular prime, return True, else False.
>>> is_circular_prime(37)
True
>>> is_circular_prime(197)
True
>>> is_circular_prime(101)
False
>>> is_circular_prime(123)
False
"""
num_string = str(number)
for i in range(len(num_string)):
if not util_euler.is_prime(int(num_string)):
return False
num_string = rotate(num_string)
return True
def sum_of_primes_below(n):
sum_primes = 2
for i in range(3, n, 2):
if is_prime(i):
sum_primes += i
return sum_primes
import util_euler
if __name__ == "__main__":
truncatable_primes = []
number = 10
while True:
number += 1
if all(util_euler.is_prime(int(str(number)[i:])) for i in range(len(str(number)))):
if all(util_euler.is_prime(int(str(number)[:-i])) for i in range(1,len(str(number)))):
truncatable_primes.append(number)
print(truncatable_primes)
if len(truncatable_primes) == 11:
break
print("sum of truncatable primes is {0}".format(sum(truncatable_primes)))
import util_euler
if __name__ == "__main__":
LIMIT = 999
A = 0
B = 0
MAX_N = 0
for a in range(-LIMIT, LIMIT + 1):
for b in range(-LIMIT, LIMIT + 1):
n = 0
consecutive_prime_count = 0
while True:
formula = n * n + a * n + b
if not util_euler.is_prime(formula):
break
consecutive_prime_count += 1
n += 1
if consecutive_prime_count > MAX_N:
A, B, MAX_N = a, b, consecutive_prime_count
print("a:{0} b:{1} max_n:{2}".format(A, B, MAX_N))
print("answer:{0}".format(A * B))
import util_euler
if __name__ == "__main__":
count = 0
numbers_on_diagonal = 1
primes_on_diagonal = 0
number = 1
layer = 1
while True:
number += 2 * layer
count += 1
if util_euler.is_prime(number):
primes_on_diagonal += 1
numbers_on_diagonal += 1
if count % 4 == 0:
if primes_on_diagonal / numbers_on_diagonal < 0.1:
side_length = 2 * layer + 1
break
count = 0
layer += 1
print("answer: {0}".format(side_length))
import util_euler
from math import sqrt
if __name__ == "__main__":
number = 3
while True:
odd_divisors = util_euler.find_divisors(number, proper=True)
odd_divisors.remove(1)
for d in odd_divisors:
if d % 2 == 0:
odd_divisors.remove(d)
if not all((number / d) % 2 == 0 for d in odd_divisors):
if all(not util_euler.is_prime(number - (i ** 2) * 2) for i in range(int(sqrt(number)))):
answer = number
break
number += 2
print("answer: {0}".format(answer))