A couple of easy counterexamples can be found, for n = 16 and n = 36, both of which meet your hypothesis, but both of which are known not to be prime....
Hi Bill, ... I believe you were trying to say something like this (at least that's what your sample calculation suggests): If n >= 2 and F(n) = 2^(2^n) + 1....
Hi, All. It would be great if I could get some feedback on this. I have completed a third proof of the Riemann Hypothesis, this one being the only one I...
whoa, I got a lot of responses!; didn't have time to look at any of them. I made the correction to the typo earlier, but sent the e-mail to myself; this proof...
... did you mean "if" ? But it's still wrong for n=16 (and n=36) : F(16) = -1 (mod 2^15+1) but F(16) is known to be composite, as Peter wrote, it is divisible...
I happened to look at http://primes.utm.edu/bios/top20.php?type=person&by=PrimesRank and was struck by the fact that Bouk de Water, without needing to prove...
A quick question if I may. If a prime number does not have the same digit occuring within it more than once, what is that number called (and yes I know there...
... They are simply called primes with distinct digits in http://www.research.att.com/~njas/sequences/A029743 which says: "This sequence has 283086 terms, the...
Oh my, what a disappointment. I thought for sure they would have a name. Perhaps we can name them? Three possibilities among many occur to me: "Unidigital...
Xeno Riddle An anthropologist and a mathematician strolled through the forest. Suddenly they came upon an extratresterial camp. The two extratresterials,...
That mathematician is good. All I can see is that the pattern in the first is repeated somewhere in each of the succeeding eight patterns. And, the 1st, 3rd...
Here are new AP16 & AP17 records at 42 digits:- (263013824+18107251*n)*83#+1 is prime for n=0..16 All confirmed prime with PFGW -tc Input/output statistics:- ...
... Congratulations! http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated. That AP17 may last a while. I'm not trying to retake it. -- Jens Kruse...
Greetings all, let o_p(2) = order of 2 in F_p. in other words, o_p(2) = card{ 2^0 (mod p), 2^1 (mod p), ... , 2^p (mod p) } we know that it is an open...
... Counterexample: o_137(2) = (137 - 1)/2 = 68 o_p(2) is provably a divisor of p-1 for prime p. By the Artin conjecture, it is a proper divisor of p-1 for...
David, you are absolutely correct, i misstated that conjecture. the conjecture asks whether o_p(2) = p-1 for infinitely many primes. this would correspond to ...
You might be interested in the following two variable function. Define F(m,k) recursively as follows. F(1,1) = 15 F(m+1,k) = F(m,k) + 4*(2*m + k + 2) F(m,k+1)...
Hello Kermit, it seems that my emails can't reach you due to some unexplainable blacklist on some router near you. So I answer on the list : ... <snip> ... can...
Given any prime expressed as a+b, is there always some a,b such that 2^a*3^b is one away from a prime? I doubt it but have yet to find a counterexample. Below...
... I expect infinitely many counter examples but there are none below 7500. I only computed one prime for each prime sum a+b. -- Jens Kruse Andersen...
... I think you're right Jens, infinitely many. By observation, the average number of solutions for a given prime seems to be roughly constant, around 10. For...
1a. Re: Composite integer function Posted by: "Yann Guidon" whygee@... yasep16 Date: Wed Nov 18, 2009 9:02 am ((PST)) Hello Kermit, it seems that my...
... Post hoc, ergo propter hoc? ... Your nebulous "algorithm" was surpassed 2200 years ago: http://www.gap-system.org/~history/Biographies/Eratosthenes.html ...
Congratulations to Henry Lifchitz for finding a record Fibonacci PrP http://www.primenumbers.net/prptop/detailprp.php?rank=5 Lélio [Non-text portions of this...
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