Hi group, 138^196873-137^196873 is PRP for bases 2, 3, 5, 7, 11, 13, 17, 19, 31, 71 and 101. This number has 421285 digits. Moreover, 138^p-137^p is composite...
I have established the following result:- For each of the 6 currently remaining candidates for the smallest Sierpinski number, no covering set of primes, with...
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...
There are lots of these. but here is another nice one by M. Chaves: Theorem. A necessary and sufficient condition for the integers n>7 and n+2 to be twin...
I thank David Broadhurst for indirectly reminding me that not all Pythagorean Triples are primitive. I thank Mike Oakes for indirectly reminding me that in...
Here is a small puzzle:- Find fixed integers a, b, x, y such that the expression a*x^n+b*y^n is prime for all n in the range 1 <= n <= n_max, where n_max is to...
Primes in algebraic number systems: Consider the extension to the integers, {A + B * sqrt(d) }, where A, B are variable integers, and d is a fixed integer. (a1...
I've define a set of prime numbers. hypothesis and the Goldbach's conjecture of Riemann that I think would work. a certain number of N, so that, the sum of...
Perhaps someone would enjoy applying some Gaussian concepts to this basic stuff!: Previously, in September, '08 it was conjectured that: x, A(x), B(x), k,...
http://chitatel2000.blogspot.com/ Update The Number Theory "Number of primes in intervals" "A million dollar problem" [Non-text portions of this message have...
... (Forwarded) The 'numbertheory' Yahoo group was very well-maintained, had a membership of 1200 and the discussion was of a high level of sophistication. ...
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...
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...
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...
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)...
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 ...
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...
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:- ...
Xeno Riddle An anthropologist and a mathematician strolled through the forest. Suddenly they came upon an extratresterial camp. The two extratresterials,...
If one could prove that the residue of mod(P) over all larger primes was equally likely to be 1,2,3...p(n-1), would that in any way prove or be equivalent to...
Hello, Professor Caldwell. I like your website. Could you please post the following conjecture: if n>= 2 and F(n)= 2^(2^n)+1, then iff [F(n) mod (2^(n-1)+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...
A Ramanjan Prime Corollary: 2*p_(i-n) > p_i for i > k where k = primepi(p_k) = primepi(R_n). That is, p_k is the n'th Ramanujan Prime, R_n, and the k'th prime....
