In order to factorize a given 'N' with 'n' number of bits. The GNFS had a time complexity

O(N) = exp( ((64/9)^(1/3) + 1)(ln n)^(1/3)(ln ln n)^(2/3) )

And i had a method which complexity as follows

K = ceiling( sqrt( ( (ceiling( sqrt(N)))^2 - N )))

Then O(N) = k +1 if k is even

= (k -1)/2 + 1 if k is odd.

Then which complexity is best. Mine or GNFS.

For eg. N = 67, ceiling(sqrt(N)) = 9

Then k = ceiling( sqrt ( 9^2 - N ))

= ceiling( sqrt (81 - 64))

= ceiling( sqrt ( 17 )) = 5

Then O(N) = (5 - 1)/2 = 2