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.
A productive hunch
Chemists and physicists typically study the structure of a material by firing X-rays at a sample and observing how the rays scatter off the atoms within it. This process is known as X-ray diffraction, where different materials produce different patterns depending on how symmetrically their atoms are arranged.