Prime Number Formula XXII

p_n=1+\displaystyle\sum_{k=1}^{2 \cdot (\lfloor n\ln(n) \rfloor+1)}\left(1-\left\lfloor \frac{1}{n} \cdot \displaystyle\sum_{j=2}^k \left\lceil \frac{3-\displaystyle\sum_{i=1}^j \left\lfloor \frac{\left\lfloor \frac{j}{i} \right\rfloor}{\left\lceil \frac{j}{i} \right\rceil} \right\rfloor}{j} \right\rceil \right\rfloor\right)

Try it !

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4 thoughts on “Prime Number Formula XXII

  1. Hi,

    Checked your formula in Matlab code for n up to 115 and works pretty good!

    False answers are given for the following n:

    n=49 -> p(49)=227, formula(49)=229
    n=98 -> p(98)=521, formula(98)=523
    n=103 -> p(103)=563, formula(103)=569
    n=107 -> p(103)=587, formula(103)=593

    Note: In those “false” cases, your formula gives the (n+1)th prime, instead of the (n)th prime.

    Overall: Impressive formula!

    Is it possible to get in contact with you?

    • Try to run this maxima code :

      n:49;
      1+sum((1-floor((1/n)*sum(ceiling((3-sum(floor((floor(j/i))/(ceiling(j/i))),i,1,j))/j),j,2,k))),k,1,2*(floor(n*log(n))+1));

      It should work fine . You probably have to set precision in Matlab to arbitrary .

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