Folk who use their spare cycles for purposes other than number theory have found an odd signal: http://www.newscientist.com/news/print.jsp?id=ns99996341...
This is a belated reply to the post by David Broadhurst of July 18 as I saw it just about a week ago. At "15k Search" we did some investigation what caused 23...
Thanks, Pedrag, for the link ... Here is another modest bit of checking. Thomas Masser kindly sent me his LLR residues for 97*2^n-1 with n up to 200000. I have...
Dear Tom, My congratulations and applause for your 18-digit Riesel number in base 3, quite an improvement on my initial 27-digit finding! I guess it must have ...
Hi, here's a smaller 14-digit k with 9 elements in the covering set: k=17630689120601, covering set {5,7,13,17,19,37,41,193,757} It's shamelessly based off of...
Hello All, I hope, at the very least, you find humorous, the latest rewrite of my web site. Please check it out. http://www.imathination.net - Dick Boland...
Hi Mikael, Congrats to you too! But, as you suspected already yourself, still not optimal : 15618563306548 is the one to beat now (same covering set). Who's...
Well, I'm afraid you are both wrong!! I tested 97*2^157221-1 using many versions (all for Windows) and found the following: 97*2^157221-1 is not prime. Res64:...
Thanks, Predrag, for that alarming detective work. To compound the confusion, I obtained ... from one linux version, and ... from another. Each identitfies...
9337#+835401121+n*17676, n=0,1,2 is a _probable_ 4003-digit CPAP-3, which, when proved prime*, would fit into the top-10 of this type of prime constellations...
... Brilliant! Now we're getting to the range where testing all lower k might be possible. I've been testing plus and minus up to 10 million, however going up...
... k ... million, ... candidates. ... Thanks for the reminder about these, if I go much higher I will use this however up to 10 million I'll try to get as...
Hi Andrew ... Small exponent duals (which can easily be *proved* prime) can sieve out MANY of the candidates (up to %80). I strongly recommend testing them...
... as ... was ... out MANY ... just from ... narraw ... smallest k. ... I intend to do the duals as well, what I plan is: a) Search both without duals up to...
Hi, here's an 11-digit candidate for the 2*k*3^n+1 case: k=62525488043, covering set {5,7,13,17,19,37,41,193,757} Does anyone have a smaller k? Mikael...
First of all my congratulations and standing ovation for Mikael Klasson !!! Very "klassy", Mikael! I never expected such a low k-value was possible! Meanwhile...
... Klasson !!! ... k=31532322469 ... will ... way, from ... values less ... Only up to about k=40,000 or so, more for k<10^6 ... possible ... values were ... ...
... Actually a post has just come through to the number theory mailing list from Eric Brier stating: "If a number n is such that n*2^k + 1 is composite for all...
... There is a check of LLR for N=k*2^n-1 when neither N nor k is divisible by 3. Simply take u[0]=V(4,1,k), u[j+1]=u[j]^2-2, compute u[n-2] mod N and output...
Thank you, Guido. For the curious, I've searched through all k less than 31532322469, checking if any of them has a covering set under the following...
Thanks, Predrag, for our collegial off-line work, which established (via Pari-GP) the correctness of 97*2^157221-1 is not prime. Res64: 47863748031D7E7A and...
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