Thanks for that post henryzz. I will read the paper you linked to see what a real Mathematician thinks.
I noted with the integrated probability equation that if you make the reasonable assumptions: ln k << B ln b, and ln k << A ln b, (where w is the weight, b is the base, k is the k, testing range from n=A to n=B)
and use some logarithmic identities that the equation: #Primes = w * (ln(ln k + B*ln b)  ln(ln k + A*ln b))/ln b
becomes #Primes = w * log_{b}B/A
Quote a bit simpler!
Also I used the term k*b*n1 for the weight of a random set of odd numbers of the same magnitude and I got 18.23% for R620. Much closer to 19.5%.
I'll compare all the 1 k's for the old and new methods in your spreadsheet and see what I can find.
