if N < 2:
return False
if N == 2:
return True
if N % 2 == 0:
return False
if N < 1000:
return (primes[N] != 0)
i = 3
while i**2 <= N:
if N % i == 0:
return False
i += 2
return True
primes = raw_sieve(1000)
A = False
B = False
MAX_N = 0
# When n == 0, n^2 + a*n + b = b, so b must be prime
for b in reversed(primes):
if b < MAX_N:
continue
for a in xrange(-999, 1000):
n = 0
while is_prime(n**2 + a*n + b, primes):
n += 1
if n > MAX_N:
MAX_N = n
from sieve import raw_sieve
nums = raw_sieve(1000000)
# Loop through. If any rotation isn't prime, 0 it out.
def rotated(n):
yield n
N = str(n)
for i in range(1, len(N)):
yield int(N[i:] + N[:i])
for n in nums:
if n != 0:
if any([nums[p] == 0 for p in rotated(n)]):
nums[n] = 0
# Filter and count
print len([x for x in nums if x != 0])