Difference between revisions of "Large prime oscillator"

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(Mention where to find Calcyman's period 2^44497-1 oscillator.)
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{{Glossary}}
 
{{Glossary}}
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 current record holder is an oscillator constructed by [[Adam P. Goucher]] 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.}}
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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 current record holder is 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 next higher Mersenne-prime oscillator, period 2<sup>86243</sup>-1, could be constructed with [[semi-Snark]]s and would actually be smaller than the current record holder, but as of the end of {{year|2017}} the construction of this pattern has not yet been completed.  
 
The next higher Mersenne-prime oscillator, period 2<sup>86243</sup>-1, could be constructed with [[semi-Snark]]s and would actually be smaller than the current record holder, but as of the end of {{year|2017}} the construction of this pattern has not yet been completed.  

Revision as of 13:49, 4 February 2018

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 current record holder is an oscillator constructed by Adam P. Goucher in 2009 with a period that is a Mersenne prime with 13,395 digits (244497-1).[note 1]

The next higher Mersenne-prime oscillator, period 286243-1, could be constructed with semi-Snarks and would actually be smaller than the current record holder, but as of the end of 2017 the construction of this pattern has not yet been completed.

Notes

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

External links