The solution of Goldbach's conjectur 1)The conventional statement: BELOW every even natural number 2n >2 ,there is at least one prime pair( P_i , P_ j ) such...
I am happy to announce that ECMNet Client/Server 2.5.6 is finally released. You can find it at http://www.loria.fr/~zimmerma/records/ecmnet.html. At this...
Define a q-residue modulo n as follows: An integer a is a q-residue modulo n if and only if it exists an integer b such as b^(2^q)=a mod n Obviously if q=1...
Is the source include with the release? Rob ... From: Mark Rodenkirch [mailto:mgrogue@...] Sent: Monday, January 03, 2005 8:29 PM To:...
Robert Sitton
rsitton@...
Jan 5, 2005 6:26 am
15852
Congratulations to all at Seventeen or Bust for finding that 28433*2^7830457+1 is prime. This has 2,357,207 digits and is the fourth largest known prime. There...
hleleu ... Define a 2^n-residue modulo m as follows: An integer a is a 2^n-residue modulo m if and only if it exists an integer b such as b^(2^n)=a mod m ...
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...
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...
... You have found all of the known examples (for x an integer). Note first that x=1 is a solution. Assume for the remainder of this discussion that x>1. If x...
I'm sure most of us have seen the proof that there is no largest prime by taking one plus the product of any list of primes and showing that either that number...
In a message dated 08/01/2005 06:12:34 GMT Standard Time, ... No. For one thing, the first term of your series 2,3,7,43,... is = +2 mod 5, the second is = -2...
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...
... What if we get a squareful number? Suppose, for arguments sake, that 2*3*7+1 is 4693 which is -2 mod 5 as required. 4693 = 13*19^2. If we only use one 19...
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,...
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...
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...
Your equations are a special form of the more general form 2^a +/- b*2^c +/- 1 Phil C. wrote a sieve base-10 of this form for me; you could ask him to write a...
Steven, Congrats! On you new Carol Prime. Now you are on top of the Carol/Kynea top 10 list again... It is good to see all the interest in these numbers and...
Congratulations to Predrag Minovic for finding a new record Sophie Germain Prime pair. 7068555 · 2121302-1 36523 L100 2005 Sophie Germain (2p+1) 7068555 ·...
Thank you! I think I was lucky to select n=121300 as the exponent. The new record has the second smallest multiplier among top-20 Sohpie Germain primes. I used...
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...
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...
Hi Cletus, I don't consider 3499...99 is near-repdigit because Chris K. Caldwell's Top Twenty page (http://primes.utm.edu/top20/page.php?id=15) says "Let all...
