FactHacks

The p-1 method

     def p1exponent(cutoff):
       return lcm(range(1,cutoff))
     
     def p1(n,cutoff):
       # Pollard's p-1 method
       g = gcd(n,Integer(pow(2,p1exponent(cutoff),n))-1)
       return [g,n/g]
     
     # example:
     print p1(38568900844635025971879799293495379321,2^14)
     # output: [17495058332072672321, 2204559716953267001]