What is the trick to counting prime numbers?

So, the question is, what's the secret sauce to counting prime numbers efficiently? Are there any shortcuts or special methods we can use to make the process quicker and more accurate? Is there a trick to identifying prime numbers that sets them apart from the rest? Or do we simply have to follow a systematic approach and check each number one by one? I'm eager to hear your insights on the most effective strategies for counting prime numbers and why they work.