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 would provide a trivial example for any sufficiently large prime.) Most SKOPs for large prime periods are rectifier loops.
Reflector-based
The first such oscillator was built by Gabriel Nivasch on August 7, 2003.[1] 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).[2][note 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.[note 2] 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 282589933-1 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.[3]
Engine-based
- See also category Prime-period oscillators
Not counting Snark loops for p43+, or conduit-based oscillators for p57+, there are relatively few known engine-based prime-period oscillators above 16, although more are starting to be found with symmetric CatForce. See also category "Prime-period oscillators" for oscillators that have dedicated pages.
The largest known prime number for which an engine-based oscillator is known is period 199, achieved by 84P199. Attached is a list of the largest known prime periods for engine-based oscillators:
- 199: One known: p199 R-pentomino hassler.
- 173: One known: p173 dependent reflector loop
- 139: One known: p139 century hassler.
- 127: Two known: p127 century hassler and p127 R-pentomino hassler.
- 113: One known: 86P113 (aside from the conduit-based Nihonium)
- 109: One known: p109 R-pentomino hassler.[4]
- 107: One known: 86P107.
- 101: One known: 116P101.
Notes
References
- ↑ Jason Summers' jslife-oversize pattern collection. Retrieved on October 28, 2020.
- ↑ Adam P. Goucher (December 27, 2009). 13395-digit prime-period oscillator (discussion thread) at the ConwayLife.com forums
- ↑ Dave Greene (July 16, 2019). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
- ↑ Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums