Regarding the question of Fermat factorisation, one question that has interested me is the factorisation of the ninth generalised Fermat number in base ten, or...
This won't be log(2). Let q>2 prime (where q!=p) then x^2+(p-x)^2 != 0 mod q has got (q-2) solutions if 4|q-1 and q solutions if 4|q-3. Using this and the...
A beautiful day i made a collection of different quadratic polynoms, which produces primes according a special algorithm. i found 191 different sequences and...
"I we decompose any prime p such that p = x + y, there are (p-1)/2 forms of doing that. Of those, many can produce: x^2 + y^2 = prime. CONJECTURE. Calling...
Hi Guys, We can use MathJax... http://www.mathjax.org/demos/use-in-web-platforms/ MathJax in Use MathJax can be found on websites as well as apps, platforms...
Can anyone prove this : https://docs.google.com/open?id=0B5UBNPPDaeHFS05GT2JEbU96ckk <https://docs.google.com/open?id=0B5UBNPPDaeHFS05GT2JEbU96ckk> best...
Formula for divisibility for a prime p. Maybe it can help to findfactors of a number n ?. I have found a way to find easy a formula for each prime p. Examples:...
I converted Bernhard's test 6 for prime numbers into a factoring algorithm. Here is one successful factoring which makes use of it. ... [168040027, 59509631,...
A beautifull day, i have started a small collection of primes between 1000 and 10000 digit primes. The primes are all of the form p:=x^2+x+1=x(x+1)+1 I...
A famous old conjecture is that infinitely many primes of form n^2+1 exist. I have no idea how to settle that, but can one instead settle this easier problem: ...
Hi to all, A question was asked recently. Are there infinitely many of n, n+1 both square free? A simple bit of algebra came up with the following, BUT it...
Hi, let X=x+2 and Y=x-2 for an integer x: Let M=[X,-1;1,2] N=[Y,-1;1,-2] Form a new matrix: A=M^2-x*M+1 Then A=2*[X,-2;2,-Y]==[2*x+4,-4;4,-2*x+4] This has the...
... You may believe what you like. However, as I understand QED and QCD (admittedly imperfectly) there is a non-zero chance of all three quarks approaching...
Hi! I've just started to study Theory of Numbers and I wonder if there are further evidences to the conjecture that there are infinitely manu prime-pairs...
Nobody expressed any interest in this, but here is one last entry before I turned this program off. This is a tie result. The stem value of 126 is repeated...
Hi, I recently added 2 new sequences to OEIS. A216666 : Smallest integer b such that (b+1)^p - b^p is prime for all primes p <= prime(n). The 8 first terms are...
For several (unconvincing) reasons I doubt it. But anyway, Kalita has a web page http://www.aec.ac.in/Uploads/File/faculty/mca/bichitra_kalita.pdf and here is...
Greetings , all , np ( n ) = n^n + (n+1)^(n+1) has numerous interesting aspects . Two aspects of this expression are prominent . ( 1 ) : The number of prime...
As you know, Dirichlet's theorem says that in any arithmetic progression a+b*n, (where a,b fixed with gcd(a,b)=1 and n is variable) there are an infinitude of...
If we demand that n, 2n-1, and 2n+1 all simultaneously be prime or prime-power, then initial examples found by hand are n, 2n-1, 2n+1 2, 3, 5 3, 5, 7 5, 9*, 11...
How many ways can the square of an odd prime n be expressed as the sum of four non zero squares? The answer surprisingly appears to have the formula: f =...
