Editing Fermat number (section)

===Largest known generalized Fermat primes===
The following is a list of the ten largest known generalized Fermat primes.<ref name="Top Twenty's Generalized Fermat Primes">{{cite web|title=The Top Twenty: Generalized Fermat|url=http://primes.utm.edu/top20/page.php?id=12|work=The Prime Pages|first=Chris K.|last=Caldwell|access-date=5 October 2024}}</ref> The whole top-10 is discovered by participants in the [[PrimeGrid]] project.

{| class="wikitable" style="text-align:right"
|-
! Rank
! Prime number
! Generalized Fermat notation
! Number of digits
! Discovery date
! ref.
|-
| 1
| 4×5<sup>11786358</sup>&nbsp;+&nbsp;1
| ''F''<sub>1</sub>(2×5<sup>5893179</sup>)
| 8,238,312
| style="text-align:left" | Oct 2024
|<ref>[https://t5k.org/primes/page.php?id=138596 4×5<sup>11786358</sup>&nbsp;+&nbsp;1]</ref>
|-
| 2
| 3843236<sup>1048576</sup>&nbsp;+&nbsp;1
| ''F''<sub>20</sub>(3843236)
| 6,904,556
| style="text-align:left" | Dec 2024
|<ref>[https://t5k.org/primes/page.php?id=138830 3843236<sup>1048576</sup>&nbsp;+&nbsp;1]</ref>
|-
| 3
| 1963736<sup>1048576</sup>&nbsp;+&nbsp;1
| ''F''<sub>20</sub>(1963736)
| 6,598,776
| style="text-align:left" | Sep 2022
|<ref>[https://t5k.org/primes/page.php?id=134423 1963736<sup>1048576</sup>&nbsp;+&nbsp;1]</ref>
|-
| 4
| 1951734<sup>1048576</sup>&nbsp;+&nbsp;1
| ''F''<sub>20</sub>(1951734)
| 6,595,985
| style="text-align:left" | Aug 2022
|<ref>[https://t5k.org/primes/page.php?id=134298 1951734<sup>1048576</sup>&nbsp;+&nbsp;1]</ref>
|-
| 5
| 1059094<sup>1048576</sup>&nbsp;+&nbsp;1
| ''F''<sub>20</sub>(1059094)
| 6,317,602
| style="text-align:left" | Nov 2018
|<ref>[https://t5k.org/primes/page.php?id=125753 1059094<sup>1048576</sup>&nbsp;+&nbsp;1]</ref>
|-
| 6
| 919444<sup>1048576</sup>&nbsp;+&nbsp;1
| ''F''<sub>20</sub>(919444)
| 6,253,210
| style="text-align:left" | Sep 2017
|<ref>[https://t5k.org/primes/page.php?id=123875 919444<sup>1048576</sup>&nbsp;+&nbsp;1]</ref>
|-
| 7
| 81×2<sup>20498148</sup>&nbsp;+&nbsp;1
| ''F''<sub>2</sub>(3×2<sup>5124537</sup>)
| 6,170,560
| style="text-align:left" | Jun 2023
|<ref>[https://t5k.org/primes/page.php?id=136165 81×2<sup>20498148</sup>&nbsp;+&nbsp;1]</ref>
|-
| 8
| 4×5<sup>8431178</sup>&nbsp;+&nbsp;1
| ''F''<sub>1</sub>(2×5<sup>4215589</sup>)
| 5,893,142
| style="text-align:left" | Jan 2024
|<ref>[https://t5k.org/primes/page.php?id=136831 4×5<sup>8431178</sup>&nbsp;+&nbsp;1]</ref>
|-
| 9
| 4×3<sup>11279466</sup>&nbsp;+&nbsp;1
| ''F''<sub>1</sub>(2×3<sup>5639733</sup>)
| 5,381,674
| style="text-align:left" | Sep 2024
|<ref>[https://t5k.org/primes/page.php?id=138515 4×3<sup>11279466</sup>&nbsp;+&nbsp;1]</ref>
|-
| 10
| 25×2<sup>13719266</sup>&nbsp;+&nbsp;1
| ''F''<sub>1</sub>(5×2<sup>6859633</sup>)
| 4,129,912
| style="text-align:left" | Sep 2022
|<ref>[https://t5k.org/primes/page.php?id=134407 25×2<sup>13719266</sup>&nbsp;+&nbsp;1]</ref>
|}

On the [[Prime Pages]] one can find the [https://t5k.org/top20/page.php?id=12 current top 20 generalized Fermat primes] and the [https://t5k.org/primes/search.php?Comment=Generalized+Fermat&OnList=all&Number=100&Style=HTML current top 100 generalized Fermat primes].