Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3).
Navigation
Topics Help • Register • News • History • How to • Sequences statistics • Template prototypes

Difference between revisions of "PrimeGrid Generalized Fermat Prime Search"

From Prime-Wiki
Jump to: navigation, search
(Start a page for GFN search)
 
m (Fix date of one linked forum post (2022 instead of 2023))
 
(5 intermediate revisions by 2 users not shown)
Line 1: Line 1:
The '''Generalized Fermat Prime Search''' is a [[PrimeGrid]] sub-project, launched in 2009.<ref>[https://www.primegrid.com/forum_thread.php?id=5674 Welcome to the Generalized Fermat Prime Search - PrimeGrid forums]</ref> It is searching for [[Generalized Fermat number#Dubner|Generalized Fermat]] prime numbers.
+
The '''Generalized Fermat Prime Search''' is a [[PrimeGrid]] sub-project, launched in 2009.<ref>[https://www.primegrid.com/forum_thread.php?id=5674 Welcome to the Generalized Fermat Prime Search - PrimeGrid forums]</ref> It is sometimes abbreviated to "Genefer" or "GFN". It is searching for [[Generalized Fermat number#Dubner|Generalized Fermat]] prime numbers.
  
 
== Purpose ==
 
== Purpose ==
The project is searching for primes of the form {{Kbn|+|1|b|2<sup>{{Vn}}</sup>}} where:
+
The project is currently searching for primes of the form {{Kbn|+|1|b|2<sup>{{Vn}}</sup>}} where:
* 15 ≤ {{Vn}} ≤ 22
+
* 16 ≤ {{Vn}} ≤ 22
 
* {{Vb}} ≤ 2 • 10<sup>9</sup>
 
* {{Vb}} ≤ 2 • 10<sup>9</sup>
  
"Genefer 17" (where {{Vn}} = 17) was split into two sub-projects:
+
[[PrimeGrid GFN-17]] (where {{Vn}} = 17) was split into two sub-projects:
* "Genefer 17 Low", testing {{Vb}} < 42,597,774, completed.
+
* [[PrimeGrid GFN-17 Low]], testing {{Vb}} &lt; {{Num|42597774}}, completed
* "Genefer 17 Mega", testing {{Vb}} ≥ 42,597,774 (the smallest {{Vb}} necessary to find megaprimes)
+
* [[PrimeGrid GFN-17 Mega]], testing {{Vb}} &ge; {{Num|42597774}} (the smallest {{Vb}} necessary to find megaprimes)
  
There is also "Do You Feel Lucky?", a variant of Genefer 22 (where {{Vn}} = 22) designed to find world record primes. It is currently searching {{Vb}} ≥ 846,398, the smallest {{Vb}} necessary such that any prime found would be larger than [[M51]], making it a world record prime number. If a new world record is found outside of PrimeGrid then this project will jump up to the minimum {{Vb}} needed to surpass that number.<ref>[https://www.primegrid.com/forum_thread.php?id=8422&nowrap=true#125716 Do You Feel Lucky? - PrimeGrid forums]</ref>
+
There is also "Do You Feel Lucky?", a variant of [[PrimeGrid GFN-22]] (where {{Vn}} = 22) designed to find world record primes. It is currently searching {{Vb}} &ge; {{Num|846398}}, the smallest {{Vb}} necessary such that any prime found would be larger than [[M51]], making it a world record prime number. If a new world record is found outside of PrimeGrid then this project will jump up to the minimum {{Vb}} needed to surpass that number.<ref>[https://www.primegrid.com/forum_thread.php?id=8422&nowrap=true#125716 Do You Feel Lucky? - PrimeGrid forums]</ref>
  
 
== Primes found ==
 
== Primes found ==
As of July 2023 over 7,000 primes have been found. [https://www.primegrid.com/primes/primes.php?project=GFN&factors=+&only=ALL&announcements=ALL&sortby=size&dc=no&search= Full list from PrimeGrid's website]
+
As of July 2023 over {{Num|7000}} primes have been found. [https://www.primegrid.com/primes/primes.php?project=GFN&factors=+&only=ALL&announcements=ALL&sortby=size&dc=no&search= Full list from PrimeGrid's website]
  
The largest four finds have been GFN-20s:
+
The largest four finds have been [[PrimeGrid GFN-20]]:
 
* 2022-09-24: {{Kbn|+|1|1963736|1048576}}
 
* 2022-09-24: {{Kbn|+|1|1963736|1048576}}
 
* 2022-08-09: {{Kbn|+|1|1951734|1048576}}
 
* 2022-08-09: {{Kbn|+|1|1951734|1048576}}
Line 23: Line 23:
 
== Status ==
 
== Status ==
 
[https://www.primegrid.com/stats_genefer.php Live status at PrimeGrid]
 
[https://www.primegrid.com/stats_genefer.php Live status at PrimeGrid]
 +
 +
== Completed ==
 +
* 2022-01: [[PrimeGrid GFN-17 Low]], testing {{Vb}} &lt; {{Num|42597774}} ({{HistLink|2021-11-14|P#9796}}: Forum / {{HistLink|2022-01-23|P#9796#153518}}: Post)
 +
* 2023-11-15: [[PrimeGrid GFN-15]] was terminated at {{Vb}} = {{Num|460000000}}. ({{HistLink|2023-09-14|P#10333}}: Forum / {{HistLink|2023-11-08|P#10333#166430}}: Post)
  
 
== References ==
 
== References ==

Latest revision as of 06:38, 29 December 2023

The Generalized Fermat Prime Search is a PrimeGrid sub-project, launched in 2009.[1] It is sometimes abbreviated to "Genefer" or "GFN". It is searching for Generalized Fermat prime numbers.

Purpose

The project is currently searching for primes of the form b2n+1 where:

  • 16 ≤ n ≤ 22
  • b ≤ 2 • 109

PrimeGrid GFN-17 (where n = 17) was split into two sub-projects:

There is also "Do You Feel Lucky?", a variant of PrimeGrid GFN-22 (where n = 22) designed to find world record primes. It is currently searching b ≥ 846,398, the smallest b necessary such that any prime found would be larger than M51, making it a world record prime number. If a new world record is found outside of PrimeGrid then this project will jump up to the minimum b needed to surpass that number.[2]

Primes found

As of July 2023 over 7,000 primes have been found. Full list from PrimeGrid's website

The largest four finds have been PrimeGrid GFN-20:

  • 2022-09-24: 19637361048576+1
  • 2022-08-09: 19517341048576+1
  • 2018-10-31: 10590941048576+1
  • 2017-08-29: 9194441048576+1

Status

Live status at PrimeGrid

Completed

References

PrimeGrid