It does not unravel our whole society or even our ability for secure encryption but however can be significantly used in the field of encryption/ decryption...not a world shaker though, not yet...it does have much promise.... I think it's real significance is yet to be fully understood. I would argue that it will have major implications on understanding fractals which in turn would go along way in understanding "natural" formations such as he points out snowflakes , and i believe perhapspossible other patterns demonstrated maybe even in gravity effects like macro mass distribution and maybe even other effects that may otherwise seem random but in essence are only following a "prime number" like wave distribution "patterns".....I put patterns in quotations because until the pattern is recognizable and demonstrable then it appears and is assumed to be just random, just as the distribution of prime numbers did before this work demonstrated a very sophisticated function that repeats in cycles , .............................thus a wave form. ----- Original Message ---- From: philip madsen <pma15027@xxxxxxxxxxxxxx> To: geocentrism@xxxxxxxxxxxxx Sent: Tuesday, September 4, 2007 4:27:35 PM Subject: [geocentrism] Re: calculating primes curiosity got me! I know I'm biased, but is mathmatics a game, or is the following indicative of doing anything useful? Can it help make a machine? McCanny claimed it could be used to decode cyphers.. what does that accomplish or do? He inferred this meant breaking in (hacking) any computer was easy. Mystified.. Phil. Calculating Prime Numbers We now consider the question of how to find prime numbers. The prime number theorem shows that if we pick an integer n at random, it will be prime with probability . So even if n 2512, our random n is prime with probability 0.0028. This is perfectly reasonable; in principle then we can find primes quickly. So the important question is how easy is it to tell if a number n is prime. It is certainly infeasible to check the primality of n directly from the definition. We've seen an elementary method of finding primes, namely the prime sieve, in Section 4.5, and we will make use of it shortly, but this method would also take infeasibly long and use an infeasible amount of storage. However, using our sieve to generate a list of small primes, we can quickly decide that many such prime candidates n are composite. We simply check in turn whether each small prime is a factor of n. And any prime candidate which is accepted by such a filter is fairly likely to be prime.11.5 Note the result of such a test on a prime candidate n: either we demonstrate that n is composite; or it remains unknown whether or not n is prime. We will call this a one-sided test for primality. We are about to meet more such tests. Recall Fermat's Little Theorem (11.6). If n is prime, and we choose any a with 1 < a < n - 1 then an-1 1(mod n). Conversely, if we ever find such an a for which an-1 1(mod n), we have demonstrated that n is composite. We call a number n which passes this ``Fermat's Little Theorem (FLT)'' test for a given base a, but which is not actually a prime, a pseudoprime with respect to the base a. Such pseudoprimes are very rare; very much rarer than primes themselves. Of course we can apply the FLT test again using a different a; each such test passed successfully increase our confidence that n is prime. However there are numbers, called Carmichael numbers which are composite, but which satisfy the FLT test for every base a.11.6 Indeed fairly recently it has been confirmed that there are an infinite number of Carmichael numbers.