Den söndag 17 januari 2016 kl. 10:44:47 UTC+1 skrev jonas.t...@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. -- https://mail.python.org/mailman/listinfo/python-list
