[Webmath] Add informations about arithmetics progressions ruling primes

[francillette thierry]

Hello,

      Finding on the web, a mail  I sent to webmath on May 2006 talking 
about equations ruling prime by studying why others weren't, I saw that the 
first one was wrote with an error :

3R+1 is prime if R(even) is not:
                                  (8+10n) + k(10+12n)  or  (16+14n)+ 
k(14+12n) and not"16n"

When I talk about (n) growing with no end, I thought about greats factor but 
if the not wong
formulas have been compute, people can see that (n) grow until a value like 
:

           n=  ( t-1 ) ,   if  from N = X1 * X2,   X2 = 6* t + 1    6* t -1

In the same way fro  X1 = 6* K +1 or -1,  the final  (k) is   ( K-1 ).

The advantage is to check about N/3 in the Altheyr R

                                      R (even) = (N-1)/3   or   R(odd)= 
(N-2)/3
3R+2 is prime if R(odd) is not:
                                 (11+14n)+ k (10+12n)  or  (11+10n) + k  
(14+12n).

   If   R  is  write as  X + k* Y :
                                                Y = 2  * X2,      with  X2 = 
7+6n  or 5 + 6n

If  X2  =  P + 6n   with  P = 6z+1 or 6z-1 ,  X = R - kY  can be found by 
for ormulas for

each of the four types of  N = X1* X2  depending of combinate form of X, 
more or less 1.

            Checking  with simple programms,  I know I'm not wrong and it is 
a new way to
study Primes,  looking why Altheyr= R, of some N  don't give a prime by  
3R+1 or 3R+2.


                                          FRANCILLETTE  Thierry

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