Difference between revisions of "Large prime 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]] 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.}}
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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]] on August 7, {{year|2003}}.<ref>{{CiteSummersPattern|name=jslife-oversize|accessdate=October 28, 2020}}</ref> 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).<ref name="post1688" />{{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.  
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The next record-holding oscillator was 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&times;4005 instead of 18493&times;7074.
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On 16th July {{year|2019}}, [[Dave Greene]] constructed an oscillator with period 2<sup>82589933</sup>-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.<ref name="post79686" />
  
 
==Notes==
 
==Notes==
 
<references group="note" />
 
<references group="note" />
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==References==
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<references>
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<ref name="post1688">{{LinkForumThread
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|format = ref
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|title  = 13395-digit prime-period oscillator
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|p      = 1688
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|author = Adam P. Goucher
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|date  = December 27, 2009
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}}</ref>
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<ref name="post79686">{{LinkForumThread
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|format = ref
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|title  = Re: Thread for basic questions
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|p      = 79686
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|author = Dave Greene
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|date  = July 16, 2019
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}}</ref>
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</references>
  
 
==External links==
 
==External links==
 
{{LinkLexicon|lex_l.htm#largeprimeoscillator}}
 
{{LinkLexicon|lex_l.htm#largeprimeoscillator}}
{{LinkForumThread|f=2|t=316|title=13395-digit prime-period oscillator|author=Adam P. Goucher}}
 

Latest revision as of 01:50, 29 October 2020

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 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 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 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.

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