g(s)+LnR(5s)/5s=Int(1,Infinite)K(s,t)g(t)dt for a certain symmetrical Kernel K(s,t) see the paper adjoint this Kernel is:

K(s,t)=nexp(-n^2(t-s)^2)+2^2(t+s)/2^5st-1

R(s) is Riemman,s Zeta function

with this calculating the prime number counting function is obvious,...just solve the integral equation by some approximate method to get Pi(2^2t)/2^2t

my results give an expresion for Pi(t) as

Pi(t)=Sum(n)a(n)fn(log2(t))

being fn(t) a set of orthonormal function.....

yes,i treid to submit to journals but the snobbish referees (which only want famous names in the papers) did not give me a chance.