Primes are like Weeds (PNT) - Numberphile
The Prime Number Theorem shows that primes are like weeds, popping up everywhere! Dr James Grime explains --- Little bit extra cut from this video: http://youtu.be/TMRZYSQGAcw More links &...
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DR. JAMES GRIME: So another prime-generating formula is actually the most important one of all. It's called the prime number theorem. So let me write it out. I think it deserves being written out. Really important result in mathematics. It's so important that you can refer to by its TLA. You can refer to it by its three-letter acronym. Just call it PNT. People know what PNT is. It's the prime number theorem. It's that important. And the prime number theorem is about how many primes are there, less than a number n. So how many primes are there less than a billion? Something like that. And so the formula says that the number of primes less than n-- well, the symbol for that is pi of n. Now, don't be confused. This pi is not 3.14...
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DR. JAMES GRIME: So another prime-generating formula is actually the most important one of all. It's called the prime number theorem. So let me write it out. I think it deserves being written out. Really important result in mathematics. It's so important that you can refer to by its TLA. You can refer to it by its three-letter acronym. Just call it PNT. People know what PNT is. It's the prime number theorem. It's that important. And the prime number theorem is about how many primes are there, less than a number n. So how many primes are there less than a billion? Something like that. And so the formula says that the number of primes less than n-- well, the symbol for that is pi of n. Now, don't be confused. This pi is not 3.14...
