import sys
from itertools import *
import c_prime
primes = c_prime.get_primes(10000)
#primes = c_prime.get_primes(10000000)
primes_s = set(primes)
cache = {}
def check(a, b):
# print a, b
if (a,b) in cache:
return cache[(a,b)]
else:
p1 = int(str(a)+str(b))
p2 = int(str(b)+str(a))
retval =(p1 in primes_s and p2 in primes_s) or (c_prime.is_prime(p1) and c_prime.is_prime(p2))
cache[(a,b)] = retval
return retval
range_max = len(primes)
sol_sum_min = None
sol_min = None
from itertools import islice
import c_prime
PRIME_MAX = 1000000
primes = c_prime.get_primes(PRIME_MAX, set)
def quad(a, b):
n = 0
while True:
yield n**2+a*n+b
n=n+1
#print primes
sol_max = 0
for a in xrange(-1000, 1001):
for b in xrange(-1000, 1001):
sol = 0
for idx, n in enumerate(quad(a, b)):
# print idx, n
if n > PRIME_MAX:
raise ValueError(str(n))
if n<1:
break
if n not in primes:
sol = idx
break
import c_prime
from itertools import permutations
primes = [x for x in c_prime.get_primes(10000) if x>1000]
primes_set = set(primes)
solved = False
for prime in primes:
# print prime
for digits in permutations(map(int, str(prime)), 4):
if digits[0] == 0 or digits[-1]%2 == 0:
continue
num = digits[0]*1000 + digits[1]*100 + digits[2]*10 + digits[3]
if num == prime:
continue
if num<prime:
continue
if num in primes_set and prime+(num-prime)*2 in primes_set and set(str(prime)) == set(str(prime+(num-prime)*2)):
print "found", prime, num, prime+(num-prime)*2, num-prime, str(prime)+str(num)+str(prime+(num-prime)*2)
break
import c_prime
from itertools import product
primes = [x for x in c_prime.get_primes(1000000)]
primes_set = set(map(str, primes))
digits_s = map(str, range(10))
solved = False
# very brute force
# plenty of spaces for improvements
for prime in primes:
prime_s = str(prime)
for src in sorted(set(prime_s)):
if prime_s[0] == src:
dsts = digits_s[1:]
else:
dsts = digits_s[:]
dsts.remove(src)
cnt = 1
for dst in dsts:
prime_tmp = prime_s.replace(src, dst)
if prime_tmp in primes_set:
cnt += 1
if cnt>=8:
print prime, src, cnt
print "--"