What is the next Prime that is 3 mod 4 from this one?
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From: Pubkeybreaker on 1 Sep 2008 18:52 On Aug 29, 6:04�pm, Thomas Pornin <por...(a)bolet.org> wrote: > According to Mensanator �<mensana...(a)aol.com>: > > > Well, you can add some bits to the probability calculation. > Note that there is no such thing as a "probably prime integer". The > integer is prime, or not. Yes and no. The integer is indeed either prime or composite. But what "probable prime" means is that the integer has been subjected to a test and the TEST ITSELF is sometimes in error. It isn't that the number is "probably prime" in the literal meaning. It is that it has been subjected to a test that sometimes has type-1 errors (i.e. false positives). The "probability" label applies to the test and not the candidate,
From: Pubkeybreaker on 1 Sep 2008 18:54 On Aug 30, 3:18�am, Kristian Gj�steen <kristiag+n...(a)math.ntnu.no> wrote: > Thomas Pornin �<por...(a)bolet.org> wrote: > What's the real likelihood of n rounds Miller-Rabin making a mistake? > I tried five rounds of Miller-Rabin for about a million random 100-bit > numbers, and it didn't make a mistake. Then I did the same for one round Pomerance wrote a paper on this in Math.Comp. (back in the late 80's IIRC). It was titled something like "The probability that a random strong PRP is composite". The probability depends on the size of the candidate and the number of rounds. The HAC discusses this,
From: Pubkeybreaker on 1 Sep 2008 18:57 On Aug 30, 5:20�am, Jean-Claude Arbaut <jeanclaudearb...(a)orange.fr> wrote: > Thomas Pornin wrote: > There is no proof that strong witnesses are random. Yes, there is. See the paper that I cited by Pomerance. I have been reading this thread. There is a LOT of confusion and false statements being tossed about by a number of different posters. STOP IT. If you don't KNOW, then don't respond.
From: WTShaw on 3 Sep 2008 04:40 On Sep 1, 5:57 pm, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > On Aug 30, 5:20 am, Jean-Claude Arbaut <jeanclaudearb...(a)orange.fr> > wrote: > > > Thomas Pornin wrote: > > There is no proof that strong witnesses are random. > > Yes, there is. See the paper that I cited by Pomerance. > > I have been reading this thread. There is a LOT of confusion > and false statements being tossed about by a number of different > posters. > > STOP IT. > > If you don't KNOW, then don't respond. Humm....Possible dogma meets the scientific method...How refreshing! The reasons for experimentation include clarification, defining new theories, and verification..and others. Loss of the right to question rather smacks of pure authoritarianism. Either you are vindicated, wrong, or have need to honestly consider new information and explain it. May the facts win...
From: Pubkeybreaker on 3 Sep 2008 05:57
On Sep 3, 4:40�am, WTShaw <lure...(a)gmail.com> wrote: > On Sep 1, 5:57�pm, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > > On Aug 30, 5:20 am, Jean-Claude Arbaut <jeanclaudearb...(a)orange.fr> > > wrote: > > > > Thomas Pornin wrote: > > > There is no proof that strong witnesses are random. > > > Yes, there is. �See the paper that I cited by Pomerance. > > > I have been reading this thread. �There is a LOT of confusion > > and false statements being tossed about by a number of different > > posters. > > > STOP IT. > > > If you don't KNOW, �then don't respond. > > Humm....Possible dogma meets the scientific method...How refreshing! Horseshit. > The reasons for experimentation include clarification, defining new > theories, and verification..and others. There is no "experimentation" here. Just numerous incorrect statements about prime-testing algorithms. �Loss of the right to question > rather smacks of pure authoritarianism. If you could read, you would realize that noone is ASKING questions. It is they who are being dogmatic in their incorrect assertions. |