In Mersenne Digest Number 808 on Sunday, January 14 2001 Nathan Russell wrote on Mon, 08 Jan 2001 > (...) > > While I think that's a tad too much criticism directed at a > non-technical, local newspaper, and I know newspapers very rarely > print any more than a retraction of 3 or 4 lines in an inside corner > somewhere, I do have to dispute a few things said in that article: > > "Nor has anybody developed an easy way to tell whether a number is > prime: You’ve got to try dividing it by every possible factor, > which is a time-consuming pain in the patoot." > > I think it's marginally possible to prove M127 in that fashion, but > not M521 or any higher Mersenne. > (...) The thesis in above quotation from a local newspaper is not quite true. A few monthes ago I found rather simple method (algorithm) for checking if any natural is prime or not and it is not under necessity of "to try dividing by every possible factor". It does not need to know anything about any odd primes less then examined natural n (exactly less then sqrt(n)). And I proved correctness of this method. But it is time-consuming. M521 is not so big - it is "only" in 521-bits arithmetic in comparison to e.g. 8-megabits arithmetic. -- regards, Waclaw W. Psiurski [EMAIL PROTECTED] [EMAIL PROTECTED] _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
