## Thinking Mathematically (6th Edition)

Consider another formula to find the prime numbers, $f\left( n \right)={{n}^{2}}-79+1601$ Now, verify the formula for prime numbers by substituting$\left( n=0,1,2,3,4,5.....79 \right)$.Then, the prime numbers are shown below in the table,
Now, check the above formula for$n=80$. \begin{align} & f\left( 80 \right)={{80}^{2}}-79\times 80+1601 \\ & =1681 \\ & ={{41}^{2}} \end{align} The prime number is the number that divisible by itself or 1. From the above table, the above formula shows the prime numbers between $\left( n=0 \right)$to$\left( n=79 \right)$. But at $\left( n=80 \right)$ the formula fails. Hence, from the above observation, no unique formula is true for all prime numbers.