Prime numbers are sometimes called math’s “atoms” because they can be divided by only themselves and 1. For two millennia, mathematicians have wondered if the prime numbers are truly random, or if some unknown pattern underlies their ordering. Recently number theorists have proposed several surprising conjectures on prime patterns—in particular, probabilistic patterns that show up in large groups of the mathematical atoms.
The patterns in the primes trace back to an 1859 hypothesis involving the legendary Riemann zeta function. Mathematician Bernhard Riemann derived a function that counts the number of primes up to a number x. It includes three main ingredients: a smooth estimate, a set of corrective terms coming from the Riemann zeta function, and a small error term.
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