Thankyou for your reply.

I am interested with using a ray because the method would be analogue and could therefore check every possible factor in the same short amount of time, regardless of the size of the semi prime. Whereas the computer program's speed at determining the correct factor decreases as the amount of possible factors increases.

The bad part of using an anaologue ray method is that as the number to be factorised increases, so would the accuracy of the machine. In the second part of my previous question, I am asking if there is a machine that uses an analogue method and also does not have the problems of being limited by accuracy.

I am not aware of any other ray factorisation device ? I have created a method of using a ray. Please see the attachments. This machine uses these 2 facts:

1) that if you square the number being tested and add the squareroot of the modulus against the semi prime (87), a multiple of the modulus is revealed

109^2 = 11881 mod(11881, 87)= 49 mod(109+49^0.5,87)=58

2) that if you square a multiple of a factor and then calculate the modulus, the answer is always another multiple of a factor.

Example of how multiple of factor repeats : 58 = 2 x 29 58^2=3364 mod(3364,87)=58

Example of how non factor doesn't repeat : 57 57^2=3249 mod(3249,87)= 30

Other non factors, on the other hand become 'noise'. Over sufficient interations, this factor pattern becomes measurable above the noise. My machine could also be re-calibrated over smaller intervals, where an irregularity in the noise occurs. This allows 'zoom' , thereby removing the limitation of the maximum accuracy of the machine. The only limitation is the amount of reflections a ray could have until it losses all of it's energy !

I can send you a spreadsheet that demonstrates this for any semi prime, and shows the angles at all stages, if require.

Thanks again for your time.

Zander Hack