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).