8539 equal divisions of the octave (8539edo), or 8539-tone equal temperament (8539tet), 8539 equal temperament (8539et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 8539 equal parts of about 0.141 ¢ each.
While it may strike many people as too large to be practical, 8539edo has seen actual use as a bookkeeping device to keep track of higher-limit intervals which have been allowed to freely modulate, and has been proposed as a unit of interval measure, the tina (see Tonalsoft Encyclopedia | Tina). This is because it is a very strong higher-limit system, distinctly consistent through the 27-odd-limit, and is both a zeta peak, zeta integral, and zeta gap tuning. In the 13-limit, the only smaller systems with a lower logflat badness are 72, 270, 494, 5585 and 6079; in the 17-limit, that becomes 72, 494, 1506, 3395 and 7033. In the 19-limit, where it really shines, nothing beats it in terms of logflat badness until 20203. Some 17-limit commas it tempers out are 28561/28560, 31213/31212 and 37180/37179; in the 19-limit it tempers out are 27456/27455 and 43681/43680.
Subsets and supersets
8539edo is the 1065th prime edo. On that basis the tina as a unit of measure could be criticized; however, some people prefer primes for this sort of job, as they do not imply a preference for one smaller edo over another.