I'm fascinated by prime numbers, and over the years, I've found multiple applications and natural occurrences for them. But can anyone suggest some alternatives that aren't in my list?

**Applications of Prime Numbers**

- Public key cryptography algorithms
- The lengths of hash tables (not recommended)
- Prime polynomials can be used for hash functions and CRC algorithms
- Programs that search for large prime numbers can be used as “torture tests” for compilers, multitasking operating systems, memory, processors, etc.
- Pseudo-random-number generators
- Hard disk interleaving
- Error-correction codes (quadratic residue codes)
- Since no known natural process generates prime numbers, extraterrestrials might use them at the beginning of a radio transmission so we can distinguish it from a natural process (as in Carl Sagan's
*Contact*). - Generating organically tiling images

**Applications of Coprimality**

- If the number of teeth on a sprocket and the number of links in a chain are coprime, then the sprocket-chain system will experience even wear (cyclical wear will be minimized).
- Nanotech symmetrical sleeve bearings, in which the outer sleeve has m-fold rotational symmetry and the inner sleeve has n-fold rotational symmetry, would in theory function most smoothly when m and n are coprime. (Nanosystems, K. Eric Drexler, p. 286)

**Natural Occurrences of Prime Numbers**

- The 13- and 17-year life cycles of periodical cicadas (genus magicicada) may be an evolutionary advantage (minimizing exposure to predators and competing broods).