Author: Dann Corbit
Date: 10:01:19 05/27/05
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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 >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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