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2019-04-07, 11:20   #31
ThiloHarich

Nov 2005

101 Posts

Hmm.

why should my model be very rough?

I have trained it with 30 million Factorizations on hard numbers (no factor below n^1/3). For different fixed multipliers m and collection good k = k' * m.
We have only 10.000 = 2^13,33 = 2^(40/3) multipliers 'k' for n below 40 bits. So I think the model is well trained. Increasing the training does not improve the results.

Surprisingly I get best results for the fixed multiplier m = 45.
I do not get the same speed for m=1 or other multiplier below.

So my conclusion is:
It still looks like when factoring one number it is better to go with one fixed multiplier (for us 315), then to go with good multipliers working for other numbers.

Quote:
 maximum(S/(m^1/3)) and m < n^1/3,
m < n^1/3 is clear , but i did not get the first limit. And limit on what?

I understand that constructing 'k' as a product of small numbers sounds promising, since it covers many u*v of u/v ~ q/p. But my tries in using this fail. I tired:
- increase multiple different m in parallel
- construct smooth numbers
- use good 'k' from other factorizations.

Last fiddled with by ThiloHarich on 2019-04-07 at 11:20