11.- R^+ prime coding functions.

Amongst the R^+ coding functions, it will be interesting to select
those given by f_m : [m, m+1] -> R (m=0, 1, 2, ...), satisfying:

( i ) f_m (x) = a_m (x-m ) + B_m
( B_0 =0, B_m= Sum { j = 0 to m-1 } ( a_j ), for every m e N.
( Affine functions ).
( ii ) 0 < a_i < a_( i + 1 ) for every i e N.

We call any of these functions " R^+ prime coding functions ". Easily
proved, R^+ prime coding functions identify prime numbers by means
of vortex points. Next step wiil be to create the conditions for
characterizing Goldbach Conjecture using the "essential region" concept.


Fernando.

P.S. For previous comments see:

http://mathforum.org/kb/thread.jspa?threadID=1615410&tstart=75
.