def one_list_to_n_numbers(l): # 9 or 10
"""Starting with the pattern list, yield all the valid numbers that it generates"""
start = 1 if (l[0] == 'X') else 0
for i in range(start, 10):
mod_l = [i if (j == 'X') else j for j in l]
num = digit_list_to_num(mod_l)
yield num
max_num_prime = 0
for pattern in candidate_generator():
actual_primes = []
not_prime = 0
num_prime = 0
for possible_prime in one_list_to_n_numbers(pattern):
if is_prime(possible_prime):
num_prime += 1
actual_primes.append(possible_prime)
else:
not_prime += 1
if not_prime >= 10 - max_num_prime:
break
if num_prime > max_num_prime:
max_num_prime = num_prime
print pattern, actual_primes, num_prime
if num_prime >= 8:
print "===="
print actual_primes[0]
break
# Copied from 28, and modified.
# Calculate only the diagonal entries.
from poiler_common import is_prime
prev_n = 1
step = 2
prime_count, diagonal_count = 0,1
while True:
for j in xrange(4):
n = prev_n + step
if is_prime(n):
prime_count += 1
prev_n = n
diagonal_count += 4
step += 2
if prime_count * 10 < diagonal_count:
break
print step-1