Unique Lehmer primes 1) Definition of a unique Lehmer prime: If, for a given integer P > 2 and choice of sign, the Lehmer sequence U(P,1,n+1) +/- U(P,1,n) with...
... Hmmm, not quite so far to go now. The largest known unique Lehmer prime now has 4730 digits. Here it is as a Lehmer primitive part: Calling N+1 BLS with...
... But I got there, thanks to OpenLenstra: http://primes.utm.edu/primes/page.php?id=87993 I'm not confident about proving gigantic unique Lehmer PPRs like...
... There are 14 bible-belt gigantic unique Lehmer PPRs with index = 71^2. So far I have inspected 9/14, with a decent dose of GMP-ECM, and proven one with...
He means : " Proposition: If p,q,r,s are consecutive primes, then valuation( ps+rs, P )=1 for some prime P. Corollary: If p,q,r,s are consecutive primes, then...
...and I meant: " Proposition: If p,q,r,s are consecutive primes, then valuation( ps+qr, P )=1 for some prime P. Corollary: If p,q,r,s are consecutive primes,...
... [snip] ... A cool concept, and analysis, David. I have a small query about your Statistics, really about the semantics of the expression "proably unique...
... Welcome. ... Pythagorean triplets have already been enumerated. They're all of the form { k(x^2+y^2), kxy, k(x^2-y^2) }. ... Attachments are not permitted...
Hi, I have played with consecutive primes p1,p2,p3,p4 and determined (see link) that any combinition of pi*pj + pk*pl is possibly square if 3 of them are 4k+3...
... Congrats. As far as I know, that is the largest proven pair, and the largest prp pairs are in http://mersenneforum.org/showthread.php?t=11381#10 I don't...
Hello, This email message is a notification to let you know that a file has been uploaded to the Files area of the primenumbers group. File : /Prime...
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May 7, 2009 2:57 pm
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... I have today uploaded a file containing the results of my search for all primes of this form for 2<=b<=1000, 2<=p<10000, done in the years 2000-2008. It is...
For integer R>=1, Q>=1, and odd n>=1, define the Lehmer sequence LV(R,Q,n) = (x^n+y^n)/(x+y) where x = sqrt(R)/2+sqrt(R-4*Q)/2 and y=sqrt(R)/2-sqrt(R-4*Q)/2 ...
... The Society for Suppression of Square Roots hopes to be able to announce, within a few days, the proof of a unique Lehmer prime with more than 15000 digits...
... I was careless in defining the exact ranges of Q and R. The transformation (R=>-R, Q=>-Q) leaves LV() invariant; so w.l.o.g. we can require Q>0 (if we...
... Then he ammended this puzzle, in response to a delightful posting by ... Hence I faithfully reparse Mike's revised puzzle as this: For integer Q > 0 and...
... (Thanks, Mike !) ... Thanks, David! (Remark: These tiny urls are nice, but can be quite annoying when they point to a website that re-arranged its...
... When presented with something a bit difficult, Einstein was wont to say "I must a little t'ink..." I don't know at the moment how to fix my puzzle to stop...
... OK Boss, message received and understood. Sometimes such discoveries are best not cast as puzzles. Discovery: Mike Oakes has found a (Q,R) integer pair...
... With Q = 2 and R = 7 we get precisely 3 units, at n = 3, 5, 13. I assume that this is Mike's discovery, but as he is being cagey, I cannot be sure. David...
... I think you are wrong, Maximilian. With Q = 3 and R = 10, I did not obtain 3 units from (x^n+y^n)/(x+y) with x = sqrt(R)/2 + sqrt(R-4*Q)/2 y = sqrt(R)/2 -...
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