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'''Fermat Divisor Search''' is a [[PrimeGrid]] project searching for large [[Fermat divisor]]s. It began in September 2019, and ended in April 2021.<ref>https://www.primegrid.com/forum_thread.php?id=8778&nowrap=true#149792</ref>
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__TOC__
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'''Fermat Divisor Search''' was a [[PrimeGrid]] project searching for large [[Fermat divisor]]s. It began in September 2019, and ended in April 2021.<ref name="table">[https://www.primegrid.com/forum_thread.php?id=8778&nowrap=true#149792 Fermat Divisor Search, Message 149792 - PrimeGrid Forums]</ref>
  
 
==Purpose==
 
==Purpose==
Searching for [[Fermat divisor]]s of the form {{Kbn|+|k|2|n}} for 5 &le; {{Vk}} &le; 49.
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The project searched for [[Fermat divisor]]s of the form {{Kbn|+|k|2|n}}, for the following ranges:<ref name="table"/>
  
==Status==
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* 5 ≤ {{Vk}} ≤ 49 for {{Vn}} ≤ 9,000,000, with two exceptions:
*[https://www.primegrid.com/stats_div_llr.php Current status]
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**{{Vk}} = 9 and 27 did not search even {{Vn}}-values, because they cannot produce Fermat divisors.<ref>[https://www.primegrid.com/forum_thread.php?id=8783 What primes can be Fermat divisors? - PrimeGrid Forums]</ref>
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* {{Vk}} = 1323, 2187, 3267 for even<ref>[https://www.primegrid.com/forum_thread.php?id=8778&nowrap=true#132677 Fermat Divisor Search, Message 132677 - PrimeGrid Forums]</ref> {{Vn}} ≤ 3,322,000
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* {{Vk}} = 3125, 3375 for {{Vn}} ≤ 3,322,000
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* {{Vk}} = 19683 for {{Vn}} ≤ 4,000,000
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[https://www.primegrid.com/stats_div_llr.php Completed status page]
  
 
==Found primes==
 
==Found primes==
*2021-03-01: [[Proth prime 25|{{Kbn|+|25|8788628}}]]
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*2021-03-01: [[Proth prime 2 25|{{Kbn|+|25|8788628}}]]
*2021-02-17: [[Proth prime 17|{{Kbn|+|17|8636199}}]]
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*2021-02-17: [[Proth prime 2 17|{{Kbn|+|17|8636199}}]]
*2021-01-27: [[Proth prime 25|{{Kbn|+|25|8456828}}]]
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*2021-01-27: [[Proth prime 2 25|{{Kbn|+|25|8456828}}]]
*2021-01-23: [[Proth prime 39|{{Kbn|+|39|8413422}}]]
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*2021-01-23: [[Proth prime 2 39|{{Kbn|+|39|8413422}}]]
*2021-01-19: [[Proth prime 31|{{Kbn|+|31|8348000}}]]
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*2021-01-19: [[Proth prime 2 31|{{Kbn|+|31|8348000}}]]
*2021-01-14: [[Proth prime 27|{{Kbn|+|27|7963247}}]]
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*2021-01-14: [[Proth prime 2 27|{{Kbn|+|27|7963247}}]], divides F(7963245)
*2021-01-14: [[Proth prime 39|{{Kbn|+|39|7946769}}]]
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*2021-01-14: [[Proth prime 2 39|{{Kbn|+|39|7946769}}]]
*2021-01-14: [[Proth prime 29|{{Kbn|+|29|7899985}}]]
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*2021-01-14: [[Proth prime 2 29|{{Kbn|+|29|7899985}}]]
*2020-12-13: [[Proth prime 45|{{Kbn|+|45|7661004}}]]
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*2020-12-13: [[Proth prime 2 45|{{Kbn|+|45|7661004}}]]
*2020-12-06: [[Proth prime 15|{{Kbn|+|15|7619838}}]]
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*2020-12-06: [[Proth prime 2 15|{{Kbn|+|15|7619838}}]]
*2020-11-12: [[Proth prime 45|{{Kbn|+|45|7513661}}]]
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*2020-11-12: [[Proth prime 2 45|{{Kbn|+|45|7513661}}]]
*2020-10-27: [[Proth prime 29|{{Kbn|+|29|7374577}}]]
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*2020-10-27: [[Proth prime 2 29|{{Kbn|+|29|7374577}}]]
*2020-10-25: [[Proth prime 15|{{Kbn|+|15|7300254}}]]
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*2020-10-25: [[Proth prime 2 15|{{Kbn|+|15|7300254}}]]
*2020-10-24: [[Proth prime 19|{{Kbn|+|19|6833086}}]]
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*2020-10-24: [[Proth prime 2 19|{{Kbn|+|19|6833086}}]]
*2020-10-20: [[Proth prime 39|{{Kbn|+|39|6684941}}]]
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*2020-10-20: [[Proth prime 2 39|{{Kbn|+|39|6684941}}]]
*2020-10-20: [[Proth prime 39|{{Kbn|+|39|6648997}}]]
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*2020-10-20: [[Proth prime 2 39|{{Kbn|+|39|6648997}}]]
*2020-08-15: [[Proth prime 39|{{Kbn|+|39|6164630}}]]
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*2020-08-15: [[Proth prime 2 39|{{Kbn|+|39|6164630}}]]
*2020-06-04: [[Proth prime 21|{{Kbn|+|21|6048861}}]]
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*2020-06-04: [[Proth prime 2 21|{{Kbn|+|21|6048861}}]]
*2020-02-16: [[Proth prime 41|{{Kbn|+|41|5651731}}]]
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*2020-02-16: [[Proth prime 2 41|{{Kbn|+|41|5651731}}]]
*2020-01-28: [[Proth prime 31|{{Kbn|+|31|5560820}}]]
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*2020-01-28: [[Proth prime 2 31|{{Kbn|+|31|5560820}}]]
*2020-01-22: [[Proth prime 13|{{Kbn|+|13|5523860}}]]
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*2020-01-22: [[Proth prime 2 13|{{Kbn|+|13|5523860}}]], divides F(5523858)
*2019-12-21: [[Proth prime 45|{{Kbn|+|45|5308037}}]]
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*2019-12-21: [[Proth prime 2 45|{{Kbn|+|45|5308037}}]]
*2019-11-23: [[Proth prime 39|{{Kbn|+|39|5119458}}]]
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*2019-11-23: [[Proth prime 2 39|{{Kbn|+|39|5119458}}]]
*2019-10-16: [[Proth prime 15|{{Kbn|+|15|4800315}}]]
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*2019-10-16: [[Proth prime 2 15|{{Kbn|+|15|4800315}}]]
*2019-10-14: [[Proth prime 31|{{Kbn|+|31|4673544}}]]
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*2019-10-14: [[Proth prime 2 31|{{Kbn|+|31|4673544}}]]
*2019-10-14: [[Proth prime 39|{{Kbn|+|39|4657951}}]]
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*2019-10-14: [[Proth prime 2 39|{{Kbn|+|39|4657951}}]]
*2019-10-12: [[Proth prime 29|{{Kbn|+|29|4532463}}]]
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*2019-10-12: [[Proth prime 2 29|{{Kbn|+|29|4532463}}]]
*2019-10-12: [[Proth prime 25|{{Kbn|+|25|4481024}}]]
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*2019-10-12: [[Proth prime 2 25|{{Kbn|+|25|4481024}}]]
*2019-10-10: [[Proth prime 23|{{Kbn|+|23|4300741}}]]
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*2019-10-10: [[Proth prime 2 23|{{Kbn|+|23|4300741}}]]
*2019-10-02: [[Proth prime 37|{{Kbn|+|37|4046360}}]]
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*2019-10-02: [[Proth prime 2 37|{{Kbn|+|37|4046360}}]]
*2019-09-28: [[Proth prime 29|{{Kbn|+|29|3964697}}]]
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*2019-09-28: [[Proth prime 2 29|{{Kbn|+|29|3964697}}]]
*2019-09-28: [[Proth prime 39|{{Kbn|+|39|3961129}}]]
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*2019-09-28: [[Proth prime 2 39|{{Kbn|+|39|3961129}}]]
*2019-09-22: [[Proth prime 49|{{Kbn|+|49|3837090}}]]
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*2019-09-22: [[Proth prime 2 49|{{Kbn|+|49|3837090}}]]
*2019-09-18: [[Proth prime 25|{{Kbn|+|25|3733144}}]]
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*2019-09-18: [[Proth prime 2 25|{{Kbn|+|25|3733144}}]]
*2019-09-17: [[Proth prime 45|{{Kbn|+|45|3677787}}]]
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*2019-09-17: [[Proth prime 2 45|{{Kbn|+|45|3677787}}]]
*2019-09-16: [[Proth prime 33|{{Kbn|+|33|3649810}}]]
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*2019-09-16: [[Proth prime 2 33|{{Kbn|+|33|3649810}}]]
*2019-09-13: [[Proth prime 3125|{{Kbn|+|3125|3124079}}]]
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*2019-09-13: [[Proth prime 2 3125|{{Kbn|+|3125|3124079}}]]
*2019-09-11: [[Proth prime 3125|{{Kbn|+|3125|2867399}}]]
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*2019-09-11: [[Proth prime 2 3125|{{Kbn|+|3125|2867399}}]]
*2019-09-11: [[Proth prime 2187|{{Kbn|+|2187|2786802}}]]
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*2019-09-11: [[Proth prime 2 2187|{{Kbn|+|2187|2786802}}]]
*2019-09-11: [[Proth prime 1323|{{Kbn|+|1323|2764024}}]]
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*2019-09-11: [[Proth prime 2 1323|{{Kbn|+|1323|2764024}}]]
*2019-09-11: [[Proth prime 3125|{{Kbn|+|3125|2697651}}]]
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*2019-09-11: [[Proth prime 2 3125|{{Kbn|+|3125|2697651}}]]
*2019-09-09: [[Proth prime 3375|{{Kbn|+|3375|2314297}}]]
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*2019-09-09: [[Proth prime 2 3375|{{Kbn|+|3375|2314297}}]]
*2019-09-09: [[Proth prime 3267|{{Kbn|+|3267|2305266}}]]
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*2019-09-09: [[Proth prime 2 3267|{{Kbn|+|3267|2305266}}]]
*2019-09-09: [[Proth prime 1323|{{Kbn|+|1323|2186806}}]]
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*2019-09-09: [[Proth prime 2 1323|{{Kbn|+|1323|2186806}}]]
*2019-09-09: [[Proth prime 1323|{{Kbn|+|1323|2205832}}]]
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*2019-09-09: [[Proth prime 2 1323|{{Kbn|+|1323|2205832}}]]
*2019-09-09: [[Proth prime 3267|{{Kbn|+|3267|2173170}}]]
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*2019-09-09: [[Proth prime 2 3267|{{Kbn|+|3267|2173170}}]]
*2019-09-08: [[Proth prime 3125|{{Kbn|+|3125|1583223}}]]
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*2019-09-08: [[Proth prime 2 3125|{{Kbn|+|3125|1583223}}]]
*2019-09-08: [[Proth prime 19683|{{Kbn|+|19683|2265896}}]]
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*2019-09-08: [[Proth prime 2 19683|{{Kbn|+|19683|2265896}}]]
*2019-09-07: [[Proth prime 19683|{{Kbn|+|19683|2033900}}]]
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*2019-09-07: [[Proth prime 2 19683|{{Kbn|+|19683|2033900}}]]
*2019-09-07: [[Proth prime 19683|{{Kbn|+|19683|1868828}}]]
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*2019-09-07: [[Proth prime 2 19683|{{Kbn|+|19683|1868828}}]]
*2019-09-07: [[Proth prime 19683|{{Kbn|+|19683|1797997}}]]
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*2019-09-07: [[Proth prime 2 19683|{{Kbn|+|19683|1797997}}]]
*2019-09-07: [[Proth prime 19683|{{Kbn|+|19683|901745}}]]
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*2019-09-07: [[Proth prime 2 19683|{{Kbn|+|19683|901745}}]]
*2019-09-06: [[Proth prime 19683|{{Kbn|+|19683|493846}}]]
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*2019-09-06: [[Proth prime 2 19683|{{Kbn|+|19683|493846}}]]
*2019-09-06: [[Proth prime 19683|{{Kbn|+|19683|485845}}]]
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*2019-09-06: [[Proth prime 2 19683|{{Kbn|+|19683|485845}}]]
*2019-09-06: [[Proth prime 19683|{{Kbn|+|19683|366665}}]]
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*2019-09-06: [[Proth prime 2 19683|{{Kbn|+|19683|366665}}]]
  
 
==See also==
 
==See also==
*[[Multi Reservation:20|Multi Reservation]]
 
 
*[[PrimeGrid]]
 
*[[PrimeGrid]]
 
==References==
 
<references/>
 
  
 
==External links==
 
==External links==
 
*[https://www.primegrid.com/forum_thread.php?id=8778 PrimeGrid Forum]
 
*[https://www.primegrid.com/forum_thread.php?id=8778 PrimeGrid Forum]
  
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==References==
 +
<references/>
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{{Navbox PrimeGrid}}
 
[[Category:PrimeGrid Fermat Divisor Search| ]]
 
[[Category:PrimeGrid Fermat Divisor Search| ]]

Latest revision as of 09:13, 7 September 2021

Fermat Divisor Search was a PrimeGrid project searching for large Fermat divisors. It began in September 2019, and ended in April 2021.[1]

Purpose

The project searched for Fermat divisors of the form k•2n+1, for the following ranges:[1]

  • 5 ≤ k ≤ 49 for n ≤ 9,000,000, with two exceptions:
    • k = 9 and 27 did not search even n-values, because they cannot produce Fermat divisors.[2]
  • k = 1323, 2187, 3267 for even[3] n ≤ 3,322,000
  • k = 3125, 3375 for n ≤ 3,322,000
  • k = 19683 for n ≤ 4,000,000

Completed status page

Found primes

See also

External links

References

PrimeGrid