Phil Carmody and I have found the record generalized BiTwins with one link: 570323880*(16500#/673949)*8087388^n +/- 1, for n = 1,2 (7120,7127 digits) ...
I ended up with the following problem while trying to solve one of the problems in graph theory, i felt this problem had something to do with prime numbers and...
In a message dated 02/10/2004 16:53:40 GMT Daylight Time, ... An interesting problem, even though rather OT. Firstly, there are many more "trivial" solutions...
I wrote ... I asked David Broadhurst for help on this and, guru that he is, he has come up with the goods. To quote his email:- ... So, the rank is indeed 1,...
Let n be (p(p+2)+1)/2 where p and p + 2 are potential twin primes. If p and p+2 are twin primes then the sum of the products of (n+x)(n-x) that divide...
I've just noticed that if p and p+2 are prime then (p+2)^p % p = 2 p^(p+2) % (p+2) = p If the first condition is met then p is prime and if the second...
... (p+2)^p % p = 2^p % p, for all numbers. Numbers satisfying 2^p % p = 2 are called base 2 probable primes, or 2-prp. Fermat's little theorem says all primes...
Hi all, (Hope this formatting comes out) n-2 ____ \ / (x+n)(x-n) ... k=0 I think (?) this is the sum of all (x+n)(x-n) for all n starting from 0 to n-2. But...
Thanks, Jens! ... (p+2)^p % p = 2^p % p, for all numbers. Numbers satisfying 2^p % p = 2 are called base 2 probable primes, or 2-prp. Fermat's little theorem...
SIr/Madam I would like to ask if there is a way on how to generate 100 digits prime numbers with the use of Java? One thing i had read about prime number is...
I'm (attempting) to make a quadratic and no resources are making it clear on how I choose the size of the factor base to use. Can anyone help me on how to do...
... The website http://www.utm.edu/research/primes/ gives a lot of information. Especially see the section "Finding primes, proving primality". That gives...
... Regan, Yes, Java already has built-in methods to do this for you. For example, the constructor: BigInteger(int bitLength, int certainty, Random rnd) ...
Hi, ... There are no hard and fast rules because the optimal factor base size varies depends on whether you are using the simple quadratic sieve, the multiple...
I'll definitely do that, only thing is how much changes in the second edition? Does the first edition include the CFRAC example? I need to decide if its...
Hi, ... I only have the second edition so I can't really say. On the subject of factoring I believe the second edition adds a more complete description of the...
I'll get this right in a minute :-( What I am looking for is a proof that for x^2 = 1 mod p where p is an odd composite and x is not 1 that x is always even. ...
... Well, first, the choice of 'p' to represent an odd composite is, well, a bit *odd*... :) Other than that, how about a counter-example: x = 11 p = 15...
Hi Jack, Your counter example threw me there for a minute. I need to tighten the constraints a little. I should specify that I am looking for the first value...
Hi Jack, Thanks for that. I must admit that I wasn't looking at low numbers, but larger bi-primes. I'll have to revisit my stratgey to handle composites which...
Hi Jens, I think that my point is that every odd composite has an even 'x' where x^2 = 1 mod p. In the case of p = 55 then x is 34. So what I am getting at,...
... Okay, let's look at this a couple of things at a time... First, I'll change the modulus from 'p' to 'm' because 'p' is usually reserved for primes: x^2 ==...
Hello members ! In last weeks I found the smallest titanic-3 and -4 prime tuplets. -3: 10^999+1598241813 {+0,+4,+6} -4: 10^999+4114571944591 {+0,+2,+6,+8} ...
I also am getting redunant messages. But no, they just appear redunant, because the senders have not thought through the problem. They just publish one tiny...
Milton Brown
miltbrown@...
Oct 8, 2004 7:13 am
15371
Guys, Here is a new Carol Prime....(2^175749 - 1)^2 - 2. This number has 105812 digits. This is a new record. To date, it is the largets Carol/Kynea prime...
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