Large prime oscillator

A large prime oscillator is any oscillator with a relatively small bounding box whose period is a very large prime.

(If the bounding-box restriction is removed, then eight gliders travelling in a four-Snark loop or rectifier loop provides a trivial example for any sufficiently large prime. Most SKOPs for large prime periods are rectifier loops.)

The first such oscillator was built by Gabriel Nivasch on August 7, 2003. The record holder for many years was an oscillator constructed by Adam P. Goucher in 2009 with a period that is a Mersenne prime with 13,395 digits (2⁴⁴⁴⁹⁷-1).

The next record-holding oscillator was the next higher Mersenne-prime period, 2⁸⁶²⁴³-1. It was constructed with quadri-Snarks and semi-Snarks in November 2018. The pattern was posted by an unknown author in a comment on an unrelated Catagolue page. It is actually less than a third of the size of the 2⁴⁴⁴⁹⁷-1 oscillator, due to the use of reasonably well-packed quadri-Snarks instead of semi-Snarks: 8875×4005 instead of 18493×7074.

On 16th July 2019, Dave Greene constructed an oscillator with period 2^82589933-1 by attaching a period-512 base gun to a compact rectangular region comprising 41294962 copies of the quadri-Snark. This is, as of the time of writing, the largest explicitly-known prime number.

External links

• Large prime oscillator at the Life Lexicon