# Difference between revisions of "Large prime oscillator"

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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 [[glider]]s travelling in a four-[[Snark]] loop would provide a trivial example for any chosen prime.) The first such oscillator was built by [[Gabriel Nivasch]] in {{year|2003}}. The record holder for many years was an oscillator constructed by [[Adam P. Goucher]] in {{year|2009}} with a period that is a [https://en.wikipedia.org/wiki/Mersenne_prime Mersenne prime] with 13,395 digits (2<sup>44497</sup>-1).{{refn|group=note|This oscillator can be found in Golly's ''Very Large Patterns'' collections, accessible via Help › Online Archives › Very Large Patterns › Mersenne-44497.}} | 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 [[glider]]s travelling in a four-[[Snark]] loop would provide a trivial example for any chosen prime.) The first such oscillator was built by [[Gabriel Nivasch]] in {{year|2003}}. The record holder for many years was an oscillator constructed by [[Adam P. Goucher]] in {{year|2009}} with a period that is a [https://en.wikipedia.org/wiki/Mersenne_prime Mersenne prime] with 13,395 digits (2<sup>44497</sup>-1).{{refn|group=note|This oscillator can be found in Golly's ''Very Large Patterns'' collections, accessible via Help › Online Archives › Very Large Patterns › Mersenne-44497.}} | ||

− | The current record-holding oscillator is the next higher Mersenne-prime period, 2<sup>86243</sup>-1. It was constructed with [[quadri-Snark]]s and [[semi-Snark]]s in November {{year|2018}}. The pattern was posted by a unknown author in a comment on an unrelated [[Catagolue]] page. A copy can be found [http://conwaylife.com/forums/viewtopic.php?p=79385#p79385 here]. | + | The current record-holding oscillator is the next higher Mersenne-prime period, 2<sup>86243</sup>-1. It was constructed with [[quadri-Snark]]s and [[semi-Snark]]s in November {{year|2018}}. The pattern was posted by a unknown author in a comment on an unrelated [[Catagolue]] page. A copy can be found [http://conwaylife.com/forums/viewtopic.php?p=79385#p79385 here]. It is actually less than a third of the size of the 2<sup>44497</sup>-1 oscillator, due to the use of reasonably well-packed quadri-Snarks instead of semi-Snarks: 8875 by 4005 instead of 18493 by 7074. |

==Notes== | ==Notes== |

## Revision as of 01:39, 15 July 2019

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 chosen prime.) The first such oscillator was built by Gabriel Nivasch in 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 (2^{44497}-1).^{[note 1]}

The current record-holding oscillator is the next higher Mersenne-prime period, 2^{86243}-1. It was constructed with quadri-Snarks and semi-Snarks in November 2018. The pattern was posted by a unknown author in a comment on an unrelated Catagolue page. A copy can be found here. It is actually less than a third of the size of the 2^{44497}-1 oscillator, due to the use of reasonably well-packed quadri-Snarks instead of semi-Snarks: 8875 by 4005 instead of 18493 by 7074.

## Notes

- ↑ This oscillator can be found in Golly's
*Very Large Patterns*collections, accessible via Help › Online Archives › Very Large Patterns › Mersenne-44497.

## External links

- Adam P. Goucher. 13395-digit prime-period oscillator (discussion thread) at the ConwayLife.com forums