Primality sieve challenge

[jonas.thornvall at gmail.com]

Den söndag 17 januari 2016 kl. 10:44:47 UTC+1 skrev jonas.t... at gmail.com:
> Maybe we could have a challenge finding the base with best reducion factor upto base 100 000000? One probably do not want to store more vectors than that in memory, and i guess
> 
> Reducing composites in the integer field
> http://jt.node365.se/composite.html
> 
> 
> I've made my own kind of primality sieve that work by reducing lthe number field into composite "legs" and prime "egs". The legs that contain just composites in the numberfield will be thrown away sieved?
> 
> I asked the people at sci.math if there was a known upper limit for the reduction using this type of counters in the integer field, they said no.
> 
> I wonder if there is a name for this type of sieve/counter within information theory?
> 
> My idea is to find a base with very high percentage of composite legs, remove all start numbers that produce only composites in their legs, and then store the other egs that contain prime in an array.
> 
> That array will than serve the purpose modelling the new integer field, using the searched base with highest composite reduction.
> 
> 
> The script seaching the bases take a few seconds, so there could be alot of improvements. I have a feeling that using bignumb bases as sieves will be out of range for us mere mortals, but who knows maybe for computer theorists.

At least i am impressed how well it reduce the composite integer field but of course you need a big array...

The math guys said just construct the base using the primes 2*3*5*7*11*13*17... and so on.

NEWBASE = 510510 ------------------------------------------
BASE= 510510 Composite legs= 92.91551585669234% ===============
One could say it is a bit clumsy but i think it is neat be able to peel of numbers that do not even need to be considered for primality test.