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How Do Mathematicians Know Their Proofs Are Correct?

The Joy of Why

CHAPTER

How Many Twin Primes Are Less Than a Big Number?

There's no formula for the prime numbers. Yet, this is something that, in the case of primes, is a very serious, interesting question. What fraction of numbers less than a big number are prime? And as you say, you can make a statistical model that gets that right. The same model can be used to then predict how many twin primes, there would be less than abig number. Does the same model do a good job in that case?

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