© Olena Shmahalo/Quanta Magazine
Often known as "the building blocks of mathematics," prime numbers have fascinated mathematicians for centuries due to their highly unpredictable and seemingly random nature.
However, a team of researchers at Princeton University have recently discovered a strange pattern in the primes' chaos. Their novel modelling techniques revealed a surprising similarity between primes and certain naturally occurring crystalline materials, a similarity that may carry significant implications for physics and materials science.
What are primes?
Prime numbers are integers (whole numbers) that can only be divided by themselves or the number 1, and they appear along the number line in a highly erratic way.
They begin as 2, 3, 5, 7, 11 and continue to appear intermittently all the way to infinity. However, the further along the number line you go, the more random the distribution of primes appears to be. The lack of any obvious pattern was
best summarized by British mathematician R.C. Vaughan: "It is evident that the primes are randomly distributed but, unfortunately, we do not know what 'random' means."
This disorder is not without its uses. Some of the most important types of modern cryptography are based upon the extreme unpredictability of very large prime numbers. For example, the widely used RSA encryption algorithm relies on the fact that it's easy to take two very large prime numbers and multiply them, but extremely difficult to take a very large number and figure out which primes were multiplied together to make that large number (the specifics of how this works
in the context of RSA encryption are explained in-depth here.)
Nonetheless, primes are still responsible for a number of unsolved problems in mathematics-such as the infamous
Reimann Hypothesis-and remain at the cutting edge of the field since they were first documented by the ancient Greeks.
Comment: So scientists have a better idea of where sprites originate, but as of right now, few seem to have been able to identify why they, and a variety of other atmospheric phenomena, have surged in recent years:
- Chemtrails, Disinformation and the Sixth Extinction
- Our changing atmosphere: Stunning iridescent cloud over Mexico, complex solar halo over Russia and a triple rainbow over Norway
- Rare green flash sunset photographed flickering into even rarer blue in Norway
- Rare blue auroras seen in the Arctic Circle
- Strange auroral arc 'STEVE' observed in US, farther south than usual
- 'Strange' Arctic rainbow and red 'summer' sprites in winter - rare atmospheric events on the increase
- Strange skies: Red Sprites in Oklahoma, aurora Steve in Canada, iridescent clouds in Illinois and noctilucent clouds in Denmark
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