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]] 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).<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 17:23, 15 March 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 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 (244497-1).[1][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.[2]

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. Adam P. Goucher (December 27, 2009). 13395-digit prime-period oscillator (discussion thread) at the ConwayLife.com forums
  2. Dave Greene (July 16, 2019). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums

External links