Prime Number Formula XV

p_n=1+\displaystyle\sum_{k=1}^{2\cdot(\lfloor n\ln(n)\rfloor+1)}\left(2-\left\lceil \frac{1}{n}\cdot \left(\displaystyle\sum_{j=2}^k\left\lceil \frac{\displaystyle\sum_{i=1}^j \left\lceil \frac{2}{\gcd(i,j)}-1 \right\rceil-j+2}{j-1} \right\rceil+1\right)\right\rceil\right)

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