hi C_twin=pi^2/12*prod(p>=5 odd primes) (1-2/(p*(p-1)))=0.66016.. You will need tens of thousands of terms to get several decimal places, but the appearance of...
The problem with 19 turned out to be minimal. There is a unique (up to permutations) way to do with 19 for the first 56 primes what was done for 7 with the...
The set {11,13,17,19, 41,43,47, 71,73,79, 101,103,107,109} shows two sets of quadruplets 90 apart, and the intervening "+30" and "+60" decades have triplets...
Dear groupmembers, The conjecture, which did not make a whole lot of sense anyway and was already showing itself unsupported empirically before the following...
Hi, I have devised a new composite test for odd n with x: gcd(x^3-x,n)==1 (mod n) kronecker(x^2-4,n)==-1 and the sub-test: (L+1)^n==-L^3+(x^2-2)*L+1 (mod n,...
Hello, I have an issue testing the following sequence past term 129. <a href="http://oeis.org/search?q=a059459&sort=&language=english&go=Search">A059459</a> It...
Hello, This appears to be a nice group. I have an interest in primes, so I thought I would contribute. What a coincidence, I appear to have the same handle...
Hi It is known that an area close to the square root of a number does not yield any factors. Can anyone give me any references / reports of investigations into...
The classical analysis of the GCD algorithm uses the Fibonacci sequence Theorem: If a>b.ge.0 and the Euclid's algorithm uses k.ge.1 recursive steps then...
Some subscribers to this prime numbers group may be interested in the Unsolved Problems web site at http://unsolvedproblems.org/ and/or the associated Yahoo!...
Ron Maimon asks an interesting question here http://mathoverflow.net/questions/72451/how-many-primes-does-euclids-prime-generating-algorithm-really-produce His...
I use Mathematica 7 and Windows 7. With this implementation the maximum value it can handle is PrimePi[249999999999999]=7783516108362. I don't know where they...
Consider these 4 prime numbers namely, A= 1049681, B= 1049683, C= 1049861, D= 1049863. Some interesting facts are: One, A and B are twins. C and D are twins...
I like how when I write about adding digits in prime numbers or noticing that primes like 113 311 and 131 share a similar property I am somehow in fantasy land...
(Quite likely this is already well known.) Suppose we consider the integers mod M (for some modulus M>1) that are relatively prime to M. The total cardinality...
NewPGen is the fastest primorial sieve app I've every tried. I couldn't understand its sieve method for k*n#+-1 and even I tried to compete with it in the...
Let t be the smaller partner of a prime twin (t, t+2). Who has fast enough hard- and software to calculate the infinite product P t/(t-1), t=3,5,11… ? I...
(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...
