Shor and Jones (Jones's Period Proxy Algorithm) use the same algorithm, however, Shor focusses on using a quantum computer and Jones looks for hyper-reduced reptends to solve in polynomial time.
At best, the even period of
:<math>f(x) = a^x\ \mbox{mod}\ N</math>,
will be the period of 1/N. In most cases it is a multiple of the period of 1/N.
Can a quantum computer be used to find the period of 1/N ? If so, I think applying [Jones's Period Proxy] algorithm would be more effective than Shor's algorithm since it would eliminate guessing.
I'm not positive, but I think the smallest odd period (p) of Shor's other than 1 will be related to one of the factors (f) such that f = 2 * p + 1 and will be found when 'a' is in close proximity to the other factor.
