As you know 1/7 is periodic and its period length is 6. 1/17 is periodic and its period length is 16. 1/29 is periodic and its period length is 28. What 7, 17...
I am new here and only here for one reason... To show to you my theory about the distribution of primes and to show that they are not random. It is actually...
Here is a primality test but I don't know if it is computationally efficient. Define the serie U by U(0)=1 and U(n+1)= U(n)*(4-2/(n+2)) The primality test is: ...
Let p a prime, p>5, and q=2*p+1. q is prime if and only if there exists a, a>1, such that: a^p=1 mod q. In particular, a can be any number such that...
Torbjörn Alm has retaken the 8-tuplet record: 97510235*421# + 322355908991 + 0, 2, 6, 8, 12, 18, 20, 26 (180 digits) I just realized it was 18 months ago I...
let p be a prime number and r is product of all primes from2 including p r=2*3*5*7*......*p s is anumber so that s>r+1 and s is prime. If t=s-r then t is...
Hello ! I found (perhaps) that 2^p-1 is mersenne prime, if a^p-1 <> 0 (mod 2^p-1) for all a , a<>2^n, n element N. Is it trival ? 2^11-1 not prime -> 39^11-1 =...
Hi All, Being particularly interested in Multifactorials I noticed the above recent addition to the top 5000. I manage a search for multifactorial primes ...
It has taken me several days to figure it out, but I now understand why the first relationship (X+4) works. However I'm totally mystified as to how/why the...
does anybody know where to find such k's for which neither 6k-1 nor 6k+1 is prime or a program that finds such k's. please e-mail me if you have such...
Hi all, What can I use to sieve for N=35*10^k - 1? And, would this form be considered near-repunit? I did not see this form in Multisieve, but I suspect that...
14.1.05 I have a growing interest in prime numbers and recently read Prof Marcus du Sautoy book the music of primes. In his book he mentions Eulers formula x2...
Is it possible to find such a and b that for all c's ( a<c<b and c is multiple of 6) either c-1 or c+1 is prime? I am interested in very big a and b. Also...
Lets s(n) be sum of first n primes. For which n is s(n) prime? It is clear that n has to be even. Can you tell me where to find information about this subject?...
1 REM This is a program showing that below every even number y the superficial prime pairs fulfils Goldbach's conjecture:as y increases the number of even...
Congratulations to Predrag Minovic for finding a new record Sophie Germain Prime pair. 7068555 · 2121302-1 36523 L100 2005 Sophie Germain (2p+1) 7068555 ·...
Guys, I've been looking at the following equation; R=4^k +/- P*2^(k-1) - 1, where k = 2,3,4 ... and P is a prime number. The two (or four) most interesting...
This program is a rough test for the solution of Goldbach's conjecture presented in the message titled: final corrected version of trying solving goldbach's...
hi, Consider 1. If p is prime and p+k is prime then p+k divides p^(p+k) + k. 2. the converse If p is prime and p+k is composite and p+k divides p^(p+k) +k,...
Hello! I have created a ms EXCEL macro to create a colorful graphic using a sequential list of prime numbers 2 through 19997 (about 2262 in the list). The...
I've recently discovered primes and find it fashinating, i'm currently trying to find as many primes as possible that follow the pattern of (x^x)+1 = prime. So...
I want to try and get the follow congruencies to combine it with Proth's theorem. Any suggestions? 1) Let N = the number to test a^(2*N) - a^(N-1)*(a^2+1) + 1...
