(6 x + 1) (12 x + 1) (18 x + 1) is a Carmichael number if all three factors are simultaneously prime and where x>0 is integer. I searched for other such...
It seems the following concept ought to be important: "k-Generalized Carmichael numbers." DEFINITION: If N is composite and squarefree and: for all primes p...
Have a look please at this family of polygonal matricially structured m x m fractals with layers of which Sierpinski Triangle and Carpet are just particular...
I figure this group might like this. In the OEIS, the sequences A190124 and A190303 are defined and computed to 0.265563275... and 0.446684307... respectfully....
Hello, group members. To a degree, I am able to locate and work with what I am interested in, but perhaps somebody can facilitate my efforts either with...
Hi, I have a new composite test for odd n with any x and a: 2<x<(n+1)/2 1<a<(n+1)/2: kronecker(x^2-4,n)==-1 gcd(a^3-a,n)==1 gcd(a,x)==1 with sub-tests: ...
Let pi(N) = number of primes p with p<=N. A well known question is whether pi(A)+pi(B) <= pi(A+B) always. Usually this is true, but Hensley & Richards...
... Welcome to the list, Robert, great to have a mind as sharp as yours on board! ... One might just describe them as merely expressions with higher kolmogorov...
Hi Following on from the emails relating to factorization, here is a little brain teaser. Work out the difference mod 6, 7 and 11 on the following number: ...
Hi, Can any one tell me Whats the exact logic lie behind the worst time complexity of fermat factorization method? In order to factorize N = pq any semiprime...
A beautifull day, i am looking for a counterexample concerning the following prime test: 1. Let jacobi (a, p) = -1 and a^[(p-1)/2]=-1 mod p 2 if (a+sqrt...
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...
