How many primes are less than or equal to 100 by Inclusion Exclusion Rule And by using Mathematica

Published On :2020-12-21 17:32:00

Let P1=Integers that are less than or equal 100 and divisible by 2 $99-\left[\frac{100}{2}\right]-\left[\frac{100}{3}\right]-\left[\frac{100}{5}\right]-\left[\frac{100}{7}\right]+\left[\frac{100}{2·3}\right]+\left[\frac{100}{2·5}\right]+\left[\frac{100}{2·7}\right]+\left[\frac{100}{3·5}\right]+\left[\frac{100}{3·7}\right]+\left[\frac{100}{5·7}\right]$
$-\left[\frac{100}{2·3·5}\right]-\left[\frac{100}{2·3·7}\right]-\left[\frac{100}{3·5·7}\right]-\left[\frac{100}{2·5·7}\right]+\left[\frac{100}{2·3·5·7}\right]$