To explain this pattern, you also have to explain why, 31 with A and B 13 and 19 divides elements 13 (155), and 19 (341) of the pattern, same with 59 with...
7842
djbroadhurst
Jul 3, 2002 3:24 am
... I believe not; you can do it mod 6, mod 12, mod 24 and then there are exceptions. Easy to see why: we require a modulus M such that n^2=1 mod M for all n...
7843
djbroadhurst
Jul 3, 2002 4:02 am
A while ago, in another place, Peter Shaw observed that there is a simple quadratic Ansatz that will generate BLS-provable triplets. It's trivial to extend...
7844
Jon Perry
jon_perryuk
Jul 3, 2002 8:33 am
(sorry about the complete tripe in previous post - the n.sigma(n) eqv. 2 mod phi(n) is only true for n=p, and n=4,6,22). -- Continuing Jack's work: for...
7845
Bouk de Water
bdewater
Jul 3, 2002 10:05 am
... Actually I did browse them for proofs. One or two could be proven with a large ECM effort. This one is a good very good one to try: 2^64695-2^15-1 with...
7846
Bouk de Water
bdewater
Jul 3, 2002 10:13 am
And for die-hards: 2^118843-2^43+1 with 35776 digits. N-1: 2^43*(2^118800-1) T 118800={ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 25, 27, 30,...
7848
Phil Carmody
thefatphil
Jul 3, 2002 5:17 pm
According to someone on sci.crypt, Message-ID: <c193a9.0207011528.25e38767@...> , Dr Dobbs' Journal is carrying an article that claims to prove...
7849
jim_fougeron
Jul 3, 2002 5:21 pm
Hello all, A new Fermat Factor has been found during the very last .5% or so of a long search I have been performing (searching all values from 8388608*2^2015...
7850
jbrennen
Jul 3, 2002 9:27 pm
... I explored this sequence further, and have essentially fully characterized it... It is periodic, as Phil already figured out. The period is 14802818350320...
7851
Cletus Emmanuel
cemmanu
Jul 3, 2002 10:18 pm
Hi all, (273*2^51488)^2-2 and (273*2^51972-1)^2-2 are prime. These prime numbers are even more dense than the original Carol or even Kynea Primes. To date ...
7852
Alan T.W. Wong #Q=#N
twawong@...
Jul 3, 2002 10:27 pm
What are Carol and Kynea primes again? AW ... -- /* **************************************************************** */ Alan T.W. Wong Gilliland Gold Young...
7853
djbroadhurst
Jul 3, 2002 10:56 pm
Here is a previous article by, probably, the same Peter Smith: http://cypherpunks.venona.com/date/1998/01/msg00377.html...
7854
Cletus Emmanuel
cemmanu
Jul 3, 2002 10:59 pm
... Carol Numbers are of the form (2^k-1)^2-2 = 4^k - 2^(k+1)-1 and Kynea Numbers are of the form (2^k+1)^2-2 = 4^k + 2^(k+1)-1. These numbers have factors...
7855
Cletus Emmanuel
cemmanu
Jul 4, 2002 12:21 am
Hi all, Can anyone prove that no Carol of Kynea Numbers are Carmichael Numbers? _________________________________________________________________ Join the...
7856
paulunderwooduk
Jul 4, 2002 12:36 am
... Numbers? see: http://groups.yahoo.com/group/primenumbers/message/5927 especially the foot note. Extrapolating ...? Perhaps David Broadhurst can give us an...
7857
Jon Perry
jon_perryuk
Jul 4, 2002 10:32 am
Remember the conjecture that S[n]<=200, where S[n] is defined by the sum of sigma(1,n)+...sigma(x,n) such that x divides S[n]? It is fairly easy to prove that...
7858
Paul Jobling
paul_joblinguk
Jul 4, 2002 11:03 am
... In fact, François Grieu on the sci.crypt thread says "The algorithm test[s] any odd candidate p. It simply performs two Lucas tests, one with any P such...
7859
subhendu paul
serampour
Jul 4, 2002 11:20 am
I have been submitted a paper in Amer . Math . Monthly entitle ' P-chart and an onto mapping from natural numbers to primes . Here I introduce a chart of...
7860
Bouk de Water
bdewater
Jul 4, 2002 12:01 pm
... It's also good fun (more actually) to generalize them with their exponent. Cletus has already done this with primes of the form (2^k+1)^4-2 and ...
7861
djbroadhurst
Jul 4, 2002 12:25 pm
... Deterministic is the opposite of probabilistic; it is _not_ the opposite of probable. The author is almost certainly claiming a deterministic test of...
7862
Phil Carmody
thefatphil
Jul 4, 2002 2:27 pm
... I can _prove_ that a single Fermat PRP test, a single Lucas test and a single ECM curve up to 1000:100000 can be combined to make a _DETERMINISTIC_ test. ...
7863
Phil Carmody
thefatphil
Jul 4, 2002 2:30 pm
... [quoting other] ... Scratch my last reply. "Declared prime". No guesswork involved. Phil ===== -- "One cannot delete the Web browser from KDE without ...
7864
Bouk de Water
bdewater
Jul 4, 2002 3:21 pm
... It is a bit of a dead end indeed, but it IS something at least. This is the total factorization of N+1 (for both cases): (2^k-1)^4-1 = 2^(k+2)*(2^k-1)* the...
7865
djbroadhurst
Jul 4, 2002 3:26 pm
... nope! it nicer than that: (2^k-1)^3-1 = 2*(2^(k-1)-1)* (product over d of Phi(6*k/d,2) where d|k and d is coprime to 6) Check: ...
7866
Jon Perry
jon_perryuk
Jul 4, 2002 5:22 pm
Anyone know if 3/n=1/a+1/b for all n>1, a,b integers, has ever been solved? Jon Perry perry@... http://www.users.globalnet.co.uk/~perry/maths ...
7867
Jon Perry
jon_perryuk
Jul 4, 2002 5:26 pm
Anyone know if 3/n=1/a+1/b for all n>1, a,b positive integers, has ever been solved? Jon Perry perry@... ...
7868
Jack Brennen
jbrennen
Jul 4, 2002 7:29 pm
... What do you mean "solved"? There are an infinite number of solutions -- (n,a,b) = (2*x,x,2*x) is one family... Even the set of "primitive" solutions...
7869
Cletus Emmanuel
cemmanu
Jul 4, 2002 7:45 pm
... _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: ...
7870
Cletus Emmanuel
cemmanu
Jul 4, 2002 7:54 pm
Sorry some difficulties...re-sending this message... ... Phil, True, not in general. But if we have p divides s and s>p and p == 1 or 7 (mod 8), then 2^(s-1)...
7872
David Underbakke
dlunderbakke
Jul 4, 2002 10:41 pm
Congratulations to Andy J. Penrose, Jim Fougeron, and Yves Gallot for the discovery of the largest know GFN prime, and the first 400,000 digit GFN prime. 9999...
