Example 2:

Prediction of the 300^th prime

From Expression (3), given b = 1891, the number of primes within [2, 1891] is counted as

$\pi \left(1891\right)=4+48\times \left(8+1\right)-{\displaystyle \sum }_{i=1}^{48}\left|L_b\left(i\right)\right|=4+432-146=290$ .

The 290^th prime is 1889, which is located at $\left(i,k\right)=\left(47,8\right)$ as shown in Figure 4. Therefore, the 300^th prime is counted to be 1987, at the location of $\left(i,k\right)=\left(21,9\right)$ .