Author: Dann Corbit
Date: 15:15:19 05/27/05
Go up one level in this thread
On May 27, 2005 at 17:57:47, Vincent Diepeveen wrote: >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. For special primes like Mersenne primes, you can use Lucas Lemur test. About 50 days on special hardware (IIRC). Links to source can be found at the GIMPS page. >>>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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