Prime Numbers Show Unexpected Patterns of Fractal Chaos

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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'Prime numbers' discovery upends thousands of years of accepted beliefs and could disrupt encryption methods

 

Numbers rarely make headlines, yet a fresh claim about prime numbers is stirring excitement well beyond math circles. Primes are those stubborn figures that resist division. For thousands of years, their locations have seemed as unpredictable as meteor showers.

Now comes a bold assertion: primes are not as random as we thought. If that statement holds, it rewrites a story mathematicians have told since the ancient Greeks. It also challenges the security systems that shield our bank transactions and private messages.

Understanding prime numbers
Every whole number on your calculator can be built from primes. Need 15? Multiply 3 and 5. Need 323? Break it into 17 × 19. Yet no one has found a simple shortcut that lists every prime in order without missing one or adding impostors.

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