
``The Goldbach comet is the graph of the
function which tells in how many ways an
integer 2n can be written as a sum of two
primes. While it is preposterous trying to
prove that the function is positive (this
is the Goldbach conjecture), one can investigate
the comet statistically and experiment with variations or in
other number systems. I'm personally convinced
that every mathematician has secretly worked on
the problem, but of course few admit it
as there is a serious danger to reach a high score on the
``Prime numbers crackpot index" of Chris Caldwell
Having not much to lose in matters of reputation,
I can tell about my own foolish attempts which
started 35 years ago both trying to find a
root of the comet as well as trying to
prove that none exists. There will be also a bit of
history. While serious mathematicians
use heavy analytic number theory, I will explain a simple
real analysis attempt which only uses single
variable calculus and relates to the Riemann
zeta function. There is no reason for excitement:
the approach does not prove it but there are
interesting patterns and opportunities
to experiment with computer algebra systems.``
