GFN divisibilities found for primes of the form k * 2^n + 1 since double checking started on 7/30/2022
Prime found date is from PrimePages or PrimeGrid.
Divisibility found date is always the "Run ended" date in my output file.

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Divisibilities missed for a short time (more than 2 weeks but less than 3 months)

---------- Primes extracted from PrimePages (T5K)
New divisibility: +++++                        81 * 2^5100331 + 1 divides GF(5100327,6)
Prime found 8/23/2022 by L4965 (Propper), divisibility found 10/26/2022

New divisibility: +++++                        81 * 2^5115131 + 1 divides GF(5115128,12)
Prime found 8/24/2022 by L4965 (Propper), divisibility found 10/26/2022

New divisibility: +++++                        81 * 2^11616017 + 1 divides xGF(11616014,3,2)
Prime found 8/31/2022 by L4965 (Propper), divisibility found 10/26/2022

New divisibility: +++++                        81 * 2^12804541 + 1 divides xGF(12804540,5,4)
Prime found 9/20/2022 by L4965 (Propper), divisibility found 10/26/2022

New divisibility: +++++                        81 * 2^13708272 + 1 divides xGF(13708267,9,8)
Prime found 10/11/2022 by L4965 (Propper), divisibility found 10/26/2022

New divisibility: +++++                        93 * 2^8898285 + 1 divides xGF(8898284,12,7)
Prime found 3/4/2024 by A2 (Propper), divisibility found 3/20/2024

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Divisibilities missed for a long time (more than 3 months)

---------- Primes extracted from PrimePages (T5K), prime found by PrimeGrid
New divisibility: +++++                       935 * 2^1394813 + 1 divides xGF(1394811,11,4)
Prime found 1/26/2012 by L2863 (Orr), divisibility found 8/17/2022

New divisibility: +++++                     1,071 * 2^3523944 + 1 divides xGF(3523943,9,5)
Prime found 5/29/2018 by L1675 (Schwieger), divisibility found 12/6/2022


---------- Primes extracted from Proth Search (Proth-k-10000-II.txt), prime found by PrimeGrid, too small for PrimePages
New divisibility: +++++                     5,919 * 2^390702 + 1 divides xGF(390700,9,2)
Prime found 7/5/2012 by Chris Granger, divisibility found 12/11/2023

New divisibility: +++++                     7,995 * 2^396591 + 1 divides GF(396585,7)
Prime found 7/17/2012 by BartKus (Lennart Vogel), divisibility found 12/11/2023

New divisibility: +++++                     2,465 * 2^398291 + 1 divides xGF(398290,12,11)
Prime found 7/20/2012 by BartKus (Lennart Vogel), divisibility found 12/11/2023

New divisibility: +++++                     2,829 * 2^399877 + 1 divides xGF(399875,9,2)
Prime found 7/23/2012 by orita (Lennart Vogel), divisibility found 12/11/2023

New divisibility: +++++                     4,117 * 2^404704 + 1 divides xGF(404701,11,8)
Prime found 8/4/2012 by Dirk (Dirk D'huyvetters), divisibility found 12/11/2023

New divisibility: +++++                     4,869 * 2^413322 + 1 divides xGF(413321,7,6)
Prime found 10/1/2012 by Sysadm@Ngb (Ulrich Fries), divisibility found 12/11/2023

New divisibility: +++++                     2,713 * 2^422420 + 1 divides GF(422418,10)
Prime found 11/10/2012 by Scott Brown, divisibility found 12/11/2023

New divisibility: +++++                     4,033 * 2^433000 + 1 divides xGF(432999,11,4)
Prime found 12/13/2012 by pabliedung (Philipp Bliedung), divisibility found 12/11/2023

New divisibility: +++++                     2,527 * 2^436710 + 1 divides xGF(436706,7,4)
Prime found 12/20/2012 by parabol (Vince Splain), divisibility found 12/11/2023

New divisibility: +++++                     5,653 * 2^441594 + 1 divides GF(441593,12)
Prime found 12/27/2012 by rebirther (Ronny Willig), divisibility found 12/11/2023

New divisibility: +++++                     5,951 * 2^446347 + 1 divides xGF(446346,6,5)
Prime found 1/1/2013 by Gary Craig, divisibility found 12/11/2023


---------- Primes extracted from Proth Search (Proth-k-10000-III.txt), prime found by PrimeGrid, too small for PrimePages
Note: These divisibilities were found at the time of prime discovery but were not added to PrimeGrid due to a "glitch".

New divisibility: +++++                     9,573 * 2 ^ 1709798 + 1 divides xGF(1709797,11,8)
Prime found 9/19/2022 by vaughan (Vaughan Davies), divisibility re-found 12/16/2023

New divisibility: +++++                     5,351 * 2 ^ 1737647 + 1 divides xGF(1737646,8,3)
Prime found 3/30/2023 by vaughan (Vaughan Davies), divisibility re-found 12/17/2023