John, On 26 May 2013, at 00:54, John Mikes wrote:

Bruno and others: did you read http://www.slate.com/articles/health_and_science/do_the_math/2013/05/yitang_zhang_twin_primes_conjecture_a_huge_discovery_about_prime_numbers.single.html the information about prof. Zhang's discovery (U of New Hampshire)?It is still in the conjecture of mathematical proof and 'truth' witha position of "primes are greaterthan 1" - with the interesting conclusion that 'primes' are theATOMS of the number world.Any thoughts?

`Primes (1 is usually not considered as a prime number) are atoms of`

`the numbers when conceived multiplicatively, because all numbers can`

`be described uniquely as a product of primes. That is the existence`

`and unicity of decomposition of numbers into prime factors (without`

`taking the order of the multiplication into account). This is the so`

`called fundamental theorem of arithmetic. It is easy to prove the`

`existence of the decomposition into primes, but less easy to prove the`

`uniqueness.`

`For the twin conjecture, (it exists an infinity of pair of primes p`

`and q with p - q = 2) it looks like an important step has been proved,`

`(the case with p - q just bounded) but we are still far from proving`

`the twin one. Most mathematician believe that the twin conjecture is`

`true (like most believe that the Riemann conjecture is true). If they`

`were false, the distribution of primes would not be "statistically`

`random", and that would mean something very special is at play, a bit`

`like a number conspiracy! Why not, of course. We just don't know, but`

`a non random behavior of the primes is a bit like the UFO of number`

`theory. Well, except that for the UFO, there are (at least) some`

`evidences (from time to time, most are eventually explained in`

`general), but there is no evidence at all that the primes behave non-`

`randomly (in the statistical sense, not in Chaitin-Kolmogorov sense as`

`we can generate mechanically the distribution of primes).`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.