Hi folks, Things have gone very quiet here lately, I imagine there's a lot of theory and searching going on! I've been taking a little vacation and also...
735
R Dohmen
r_dohmen@...
May 1, 2000 9:58 pm
So expressions like n!x+n!y+1 (were x and y are the number of !'s) are evaluated false and the prime results are not valid? (unless you find the corresponding...
736
Dick
richard042@...
May 1, 2000 10:39 pm
I think I've found another one which may or may not be related, but, I put the following in as recurrences f(1) = 1 f(2) = p(n)#/p(k) f(3) = p(n)#/p(k) f(4) =...
737
Paul Jobling
Paul.Jobling@...
May 2, 2000 9:05 am
(Apologies for cross-posting) An Arithmetic Progression of 6 Titanic Primes ... Paul Jobling ... Previously the longest known arithmetic progression of titanic...
738
Dirk Augustin
augustd@...
May 2, 2000 10:46 am
Congratulations to Paul for this very impressive record. I never thought that this would be possible! Calculating the possibility and expected time is one...
739
Chris Nash
chris_nash@...
May 2, 2000 12:32 pm
Hi folks ... Paul does it again! My heartiest congratulations on what not so long ago seemed a very difficult search. ... This seemed a very curious...
740
Paul Jobling
Paul.Jobling@...
May 2, 2000 12:55 pm
Hi all, ... That is quite right. ... I can't remember what my code did, but I seem to recall that I found 2347# (mod p) first (call that x), then found x^(p-2)...
741
Giovanni La Barbera
giolaba@...
May 3, 2000 8:54 am
... expansion" mode. You will discover that the result PrimeForm outputs is NOT zero. applied. ... remain from the first one. ... Of course there is a simple...
742
Chris Nash
chris_nash@...
May 6, 2000 7:01 pm
Hi folks, Here's an interesting puzzle you might like to think about. Carmichael numbers are composite numbers that are (Fermat) pseudoprimes to all bases that...
743
Chris Caldwell
caldwell@...
May 7, 2000 1:57 am
... And when I heard Pomerance say this, he added "furthermore, the first Carmichael number is expressible as a sum of two first powers in more ways than any...
744
Chris Nash
chris_nash@...
May 7, 2000 2:38 am
Hi folks ... *grins* Presumably everything falls apart with the fourth Carmichael number... It does have something to do with the form of the prime factors -...
745
Warut Roonguthai
warut@...
May 7, 2000 11:55 am
... No, I haven't found that yet. Warut...
746
Michael Bell
mbell@...
May 7, 2000 4:39 pm
... If p-1 has *all* factors small then all these primes should be provable: Let p=c+1 therefore, p^2+p-1 = (c^2+2c+1)+(c+1)-1 = c(c+3)+1 and, (p^3+p^2-p+1)/2...
747
Chris Nash
chris_nash@...
May 7, 2000 4:48 pm
Hi folks ... the ... number - ... Whoops.... my apologies to Warut :) Perhaps then it was Henri Lifchitz who found three Proth primes, each of over 1000...
748
Chris Nash
chris_nash@...
May 7, 2000 4:58 pm
Hi folks ... is just ... Amazing! I knew an answer to this question before I asked the PF list about it. Remarkably, Michael found a different answer than I...
749
Michael Bell
mbell@...
May 9, 2000 8:45 pm
... Hi, Because Proth is significantly faster than primeform it is best to find p's of the form k.2^n+1, then use PF to check if for any of these p^3+p^2-p+1 ...
750
Giovanni La Barbera
giolaba@...
May 14, 2000 9:50 am
Hi to you all! I have 3 questions : 1) How can you compute the probability that a P.F. prob. prime is prime? 2) You can increase the probabilty this way: ...
751
Chris Nash
chris_nash@...
May 14, 2000 6:35 pm
Hi folks, It's been quiet around here lately. Although I am pretty sure I will give you all something to be excited about very shortly. Watch this space. ... ...
752
Paul Jobling
Paul.Jobling@...
May 15, 2000 12:41 pm
(apologies for cross posting) A BiTwin chain of titanic primes. Dirk Augustin and Paul Jobling. A BiTwin chain of one link consists of four primes, these being...
753
R Dohmen
r_dohmen@...
May 16, 2000 8:02 am
Hi all! Congratulations Paul and Dirk, a suberb continuation of your methods! And then a short note to inform you that 13830!/2-1 is prime! (Far over 50,000...
754
Chris Nash
chris_nash@...
May 18, 2000 1:59 am
Hi folks ... over ... Congratulations yet again to Rene! Once again he claims the PrimeForm record, and this time, the 50,000 digit barrier has been broken......
755
Chris Nash
chris_nash@...
May 18, 2000 6:33 am
Dear Colleagues, I am very pleased to be able to announce that a very early demonstration of the next version of PrimeForm is now available for some...
756
R Dohmen
r_dohmen@...
May 18, 2000 6:36 am
Hi there Chris, could you tell us all how long the search took, ... let's see: 14056!/2-1 now says (about) 60% complete and 70 minutes to go, so that's 175...
757
Pavlos ask
pavlos19@...
May 18, 2000 9:17 am
Hi to all.Can anyone prove the primality of the generalized repunit:((23*23!)^107-1)/(23*23!-1) (2521digits).if the prime exponent is 61 it also yields a...
758
Jud McCranie
jud.mccranie@...
May 18, 2000 6:25 pm
... A general number that large is pretty hard to prove. I tested it on Maple and it says that it is prime. However, Maple uses two different ...
759
Hans.Rosenthal@...
May 18, 2000 9:54 pm
You may try out Tony Forbes' program VFYPR at http://www.ltkz.demon.co.uk/ar2/vfypr110.zip which does not produce a certificate of primality but definitely can...
760
Giovanni La Barbera
giolaba@...
May 19, 2000 8:09 am
Hi to all, ... a 700 digits number with Certifix beta release 0.1 (http://www.znz.freesurf.fr/) takes about 7 h of a 450 mHZ computer. a 500 digits is out in <...
761
Chris Nash
chris_nash@...
May 19, 2000 8:57 pm
... Andy Steward has the following interesting page: http://www.users.globalnet.co.uk/~aads/ about generalized repunits. He has links to all the data for small...
762
Chris Nash
chris_nash@...
May 23, 2000 8:44 pm
Dear Colleagues, After Rene Dohmen recently broke the 50,000 digit barrier with PrimeForm, I did not realize another milestone had been achieved. For the first...
763
R Dohmen
r_dohmen@...
May 24, 2000 12:24 pm
Hi everybody! No doubt Anderson and Robinson have a very nice record: congratulations! Not just because this is a very large number, but also in historical...
