Jabari, I like your enthusiasm. Please study some good references on the prior work.
Your second sentence seems to show you don't know what the prime95 code does. The database for candidate exponents contains only prime candidate exponents (meaning the exponents have _already_ been sieved, at a trivial portion of the effort). It also uses an optimized form of sieving like what you propose, for _trial factors_. Read http://www.mersenne.org/math.htm, for a sense of the variety of approaches used to tackle primality testing the immensely huge Mersenne numbers in an optimized way using multiple approaches with highly optimized compiled code with hand tuned assembler language components. Optimizations are processor version specific with use of the builtin performance measurement in later pentium family processors. Optimizations include best number theory approaches, knowledge of the special form of mersenne candidates' potential factors, and much more. (My apologies to George Woltman if I've misstated the nature of the code somehow. I've been following it since V12, well before primenet was created.) You may benefit by reading some number theory books. I like Hans Riesel's. Another good read is Donald Knuth, Seminumerical Algorithms, if you can find it. Or back issues of Byte magazine; there was an article in the 1980's on sieving. http://primes.utm.edu/mersenne/LukeMirror/lit/lit_024s.htm for the first computer based Mersenne prime discoveries. Sieving is terribly ineffective compared to the Lucas-Lehmer test for determining primality of Mersenne numbers of prime exponent that have not yielded to factoring attempts on the number. Sieving scales as >2^n, while LLtesting scales as ~n^2, where n is the mersenne prime candidate's exponent. Sieving in an interpreted language compounds the inefficiency. Your program's best rate of sieving (delta time of ~0.9sec for 20M to 30M span) covers ~11M span per second. Given that if you started sieving today you would not reach >1 million bits = 10^301030 within the lifetime of the sun at that rate, I don't see what use your sieve has for GIMPS. (Also the rate is unsustainable since multiple precision requirements, storage size & speed issues, etc for larger numbers would drag the rate down considerably. See Knuth for more on that.) Ten billion years estimated remaining life expectancy of Sol = _only_ ~3.2x10^17 seconds or 3.5x10^24 sieve range, adequate to sieve only to 2^81.5 at 0.9second/M, yet requiring double precision on a 64-bit processor and mammoth memory space. All mersenne numbers below Mn<2^127 can be found without computers using the Lucas Lehmer test. I could have made a factor of a million error in one of those time calculations without changing the conclusion. Ken At 11:15 AM 6/8/2008 -0500, Jabari Zakiya wrote: > Hi John, > >Yes, I am fully aware of what GIMPS is, and have been running primes95 >for >over 8 years on variuos computers. But all you're doing is finding >smaller primes >to use as exponents to find the Mersenne primes. If you can >deterministically >find P exponents faster and with certainty then you are more ahead of the >game. > >Also, my primality tester can be applied to the Meresenne prime >candidates. >You just need to implement this very siimple, and deterministic, method >to deal >with the size of numbers you are dealing with, like you are trying to do >with primes95. >After all, modulo n operations are just successive subtractions of n from >the number >until it is <= n. That's a whole lot easier than what primes95 is trying >to do. > >Hotep (Peace) > >Jabari > > > ----- Original Message ----- > From: "John R Pierce" > To: "The Great Internet Mersenne Prime Search list" > Subject: Re: [Prime] Ultimate Prime Sieve - Sieve of Zakiya (SoZ) > Date: Sat, 07 Jun 2008 22:29:02 -0700 > > > Jabari Zakiya wrote: > > This is to announce the release of my paper "Ultimate Prime Sieve > -- > > Sieve of Zakiiya (SoZ)" in which I show and explain the development > of > > a class of Number Theory Sieves to generate prime numbers. > > > do you understand that the GIMPS project is working with prime > numbers > that have a million digits (2^3,000,000 or more)? > > the amount of storage, and computational time for /any/ sort of sieve > algorithm would be astronomical > _______________________________________________ > Prime mailing list > [email protected] > http://hogranch.com/mailman/listinfo/prime > > > > > >-- >See Exclusive Videos: 10th Annual Young Hollywood Awards >http://www.hollywoodlife.net/younghollywoodawards2008/ > >_______________________________________________ >Prime mailing list >[email protected] >http://hogranch.com/mailman/listinfo/prime > _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
