Prime Number Formula XXII

Posted on September 8, 2012 by princeps37

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

Prime Number Formula XXI

Posted on September 7, 2012 by princeps37

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

Prime Number Formula XX

Posted on September 6, 2012 by princeps37

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

Prime Number Formula XIX

Posted on September 5, 2012 by princeps37

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

Prime Number Formula XVIII

Posted on September 5, 2012 by princeps37

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

Prime Number Formula XVII

Posted on September 5, 2012 by princeps37

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

Prime Number Formula XVI

Posted on September 4, 2012 by princeps37

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

Prime Number Formula

Collection of prime number formulas

Prime Number Formula XXII

Prime Number Formula XXI

Prime Number Formula XX

Prime Number Formula XIX

Prime Number Formula XVIII

Prime Number Formula XVII

Prime Number Formula XVI

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