On 26 May 2013, at 00:54, John Mikes wrote:
Bruno and others:
did you read
the information about prof. Zhang's discovery (U of New Hampshire)?
It is still in the conjecture of mathematical proof and 'truth' with
a position of "primes are greater
than 1" - with the interesting conclusion that 'primes' are the
ATOMS of the number world.
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
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).
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