Large prime oscillator

From LifeWiki
Revision as of 05:49, 1 November 2023 by Confocal (talk | contribs) (revert to Snarks)
Jump to navigation Jump to search

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.) 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]

Notes

  1. This oscillator can be found in Golly's Very Large Patterns collections, accessible via Help › Online Archives › Very Large Patterns › Mersenne-44497.
  2. A copy can be found here.

References

  1. Jason Summers' jslife-oversize pattern collection. Retrieved on October 28, 2020.
  2. Adam P. Goucher (December 27, 2009). 13395-digit prime-period oscillator (discussion thread) at the ConwayLife.com forums
  3. Dave Greene (July 16, 2019). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums

External links