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Difference between revisions of "PrimeGrid Fermat Divisor Search"

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(Add note about even-n only searches + Fermat divisor for k=27 find)
m (Title references + add 2nd F divisor found by project)
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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</ref>
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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==
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* 5 ≤ {{Vk}} ≤ 49 for {{Vn}} ≤ 9,000,000, with two exceptions:
 
* 5 ≤ {{Vk}} ≤ 49 for {{Vn}} ≤ 9,000,000, with two exceptions:
 
**{{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>
 
**{{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>
* {{Vk}} = 1323, 2187, 3267 for even<ref>https://www.primegrid.com/forum_thread.php?id=8778&nowrap=true#132677</ref> {{Vn}} ≤ 3,322,000
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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
 
* {{Vk}} = 3125, 3375 for {{Vn}} ≤ 3,322,000
 
* {{Vk}} = 3125, 3375 for {{Vn}} ≤ 3,322,000
 
* {{Vk}} = 19683 for {{Vn}} ≤ 4,000,000
 
* {{Vk}} = 19683 for {{Vn}} ≤ 4,000,000
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*2020-02-16: [[Proth prime 41|{{Kbn|+|41|5651731}}]]
 
*2020-02-16: [[Proth prime 41|{{Kbn|+|41|5651731}}]]
 
*2020-01-28: [[Proth prime 31|{{Kbn|+|31|5560820}}]]
 
*2020-01-28: [[Proth prime 31|{{Kbn|+|31|5560820}}]]
*2020-01-22: [[Proth prime 13|{{Kbn|+|13|5523860}}]]
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*2020-01-22: [[Proth prime 13|{{Kbn|+|13|5523860}}]], divides F(5523858)
 
*2019-12-21: [[Proth prime 45|{{Kbn|+|45|5308037}}]]
 
*2019-12-21: [[Proth prime 45|{{Kbn|+|45|5308037}}]]
 
*2019-11-23: [[Proth prime 39|{{Kbn|+|39|5119458}}]]
 
*2019-11-23: [[Proth prime 39|{{Kbn|+|39|5119458}}]]

Revision as of 03:54, 18 June 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

References

External links