Author: Vincent Diepeveen
Date: 14:57:47 05/27/05
Go up one level in this thread
On May 27, 2005 at 13:01:19, Dann Corbit wrote: >On May 27, 2005 at 08:33:04, Vincent Diepeveen wrote: > >>On May 26, 2005 at 19:43:07, Uri Blass wrote: >> >>>On May 26, 2005 at 15:54:18, Dann Corbit wrote: >>> >>>>On May 26, 2005 at 15:52:19, Dann Corbit wrote: >>>> >>>>>On May 26, 2005 at 14:18:37, Sune Fischer wrote: >>>>> >>>>>>On May 26, 2005 at 13:15:04, Dann Corbit wrote: >>>>>> >>>>>>>On May 26, 2005 at 12:02:37, Vincent Diepeveen wrote: >>>>>>>[snip] >>>>>>>>Hello, i can calculate prime numbers up to 10 million digits at my pc nearly, >>>>>>>>though not within 5 minutes. >>>>>>> >>>>>>>Less than a second, I imagine. >>>>>> >>>>>>That's quite an imagination since there aren't any known primes that large :) >>>> >>>>I misread the statement as "finding the first ten million primes" >>>> >>>>>>Last I checked only a handful or so had been found with more than a million >>>>>>digits, and of course only through weeks of massively parallel super computer >>>>>>power. >>>>> >>>>>From: >>>>>http://www.mersenne.org/prime.htm >>>>> >>>>>The record is: >>>>>7,816,230 digits >>>> >>>>There is $100,000 for finding a ten million digit prime. >>> >>>Is finding the number enough or is the prize only for people who also prove that >>>the number they picked is a prime. >>> >>>Suppose one person find a number of 10,000,000 digits and claims that the number >>>is prime with no proof and somebody else proves that the number is a prime >>>number. >>> >>>who get the prize? >>>Uri >> >>It's just a small theoretic difference. The problem is finding the prime. >>Whether you do that with 99.999999999999999999999999999999999999% certainty or >>with 100% certainty is not important at all initially. You just ship the prime >>to them that's all. Then some months later, after being helped by 100 >>mathematicians you can also prove it is a prime. > >A number can be proved prime by a number of algorithms like APR-CLE, ECPP, >Lucas-Lemur [for primes of a certain sort only], etc. > >A good probabilistic algorithm to find if it is almost surely prime is >Miller-Rabin. > >http://www.utm.edu/research/primes/prove/index.html Actually for a 10 million digit prime the fastest way to prove a random prime is going to take too long with todays hardware. 100 days to the power 6 is a pretty long time. Undoubtfully you'll google a bit more to find a solution for that. >>The real problem is finding a number X that most likely is a prime. The proof of >>it you leave to others who are happy to help you in that. But first show them >>some serious 'industry grade' primes. >> >>Vincent
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