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....
One thing I have often thought about is trying to build a quasi-alternating series out of the reciprocals of the primes, so that: - the reciprocal of every...
Re ... I can easily see that the positive terms would converge. However, there is a problem with showing that the series noted above converges absolutely. Term...
Is it a known fact that the sum of primes of a twinprime pair is always divisible by 12 ? (divisible by 4 is evident) or is there a counterexample? gr. Rob ...
Hi all, a notion occurred to me that has probably been explored, so I'm looking for references to it. Of the numbers n# +1 or n# -1 (n Primorial plus 1, or...
(i) Does the following series converge or diverge? 1/a[1]+1/a[2]+1/a[3]..... Where a[n] is the nth prime in the series of primes p[1],p[2]..that have...
