Using the principle of inclusion-exclusion determine the number of prime numbers not exceeding 100.
How would you approach this problem?
2026-04-02 18:42:52.1775155372
Using the principle of inclusion-exclusion determine the number of prime numbers not exceeding 100.
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You might take out those divisible by $2,3,5,7$ (all the primes up to $\sqrt{100}$). Doing this is a pretty straightforward includsion-exclusion counting, and this has the effect of counting the number of primes between $10$ and $100$. After you add back in the $4$ primes up to $10$, you'll have counted the number of primes up to $100$.
Does that make sense?