I think I hav the formula for the number of p[rimes less than a given prime p, but the mathamatician I am dealing with says I cannot use von-Staudt Clausen theorem to prove that it is the prime counting function. But i proved it using von Staudt clausen. i something wrong with that? Can I not use a theorem in the proof of a theorem? Please help me I believe I solve Riemann.
N = (sum(arctan(tan(Pi*bernoulli(2*n)*GAMMA(2*n+1)))*(2*n+1)/Pi, n = 0 .. (P/2)-1/2))

= number of primes less than P exactly!! Can you help me break through the red tape of Riemann and Primes?

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