import re
import math

def factor(N,primes): #returns largest prime factor of a number. we can just use primes bc/ all cprimes are 1 less than the sqrt of their primes, so the largest prime factor will always be in primes. (we compute prime factors up to sqrt(n)..)
        for i in primes:
                if (N%i)==0:
                        return i
def main():
        inp = open('primes.txt', 'r')
        rinp = ''.join(inp.readlines())
        primes = map(lambda b: int(b), filter(lambda a: a!= '', [s for s in re.split('[\s\t\n]',rinp)])) #regex takes the huge string and splits it on whitespace/tabs/newlines.
                # then we have a list w/ all primes and lots of empty string occurences.
                # filter expression removes the empty strings. map changes the elements of the list of primes, which at that point are strings, to ints.
        cprimes = [((x**2)-1) for x in primes]
        revp = primes[::-1]
        for i in range(0,1000):
                f = factor(cprimes[i],revp)
                if (f>primes[i]):
                        print("pair found, where a=%d,b=%d"%(primes[i],f))
        print "complete."

if __name__=='__main__':
        main()