Time to update this.
This is the list of currently active guesses (those stricken through were previous guesses that have been replaced under the rules). A number of them we have tested all of the exponents to that number, some we have passed the predicted date. All except those guessed in the last 24 hours have been tested and shown not to be a prime.
Code:
Who When guessed Exponent When found
MattcAnderson 9/11/2019 84000013 4/1/2020
Uncwilly 12/28/2018 84000017 2/28/2019
firejuggler 1/2/2019 85020577 1/1/2020
Neutron3529 12/13/2018 85615531 10/1/2019
firejuggler 1/2/2019 87522767 1/3/2021
Petrw1 12/12/2018 87654361 12/25/2019
dcheuk 3/11/2019 87668491 3/14/2019
moebius 12/14/2018 87885437
Neutron3529 12/13/2018 87946949
kriesel 12/21/2018 88318673 6/14/2019
dcheuk 3/11/2019 89065523 3/14/2020
Uncwilly 12/29/2018 89999999 4/15/2020
MattcAnderson 2/25/2021 90000049 12/25/2022
firejuggler 1/2/2019 90098611 2/1/2022
Viliam Furik 12/3/2019 91305491 1/18/2020
patrik 12/18/2018 91502209 12/4/2020
dcheuk 3/11/2019 91761547 3/14/2021
Neutron3529 12/13/2018 92074531
christian_ 12/27/2018 93456799 4/7/2019
axn 12/21/2018 94029857 3/17/2021
sweety439 8/30/2019 94539113* 5/9/2021 *factored
Uncwilly 12/30/2018 95000167 9/24/2021
EWMayer 12/12/2018 96000193 5/1/2021
ixfd64 12/27/2018 96052357* 5/21/2021 *factored
Dylan14 12/14/2018 97200647 2/2/2021
Spherical Cow 12/27/2018 97211981 10/30/2019
dcheuk 3/10/2020 98350193 6/1/2020
Uncwilly 2/11/2020 99998441 7/31/2020
Uncwilly 7/24/2020 100002751 10/6/2020
lukerichards 101834393* 8/1/2020 *factored
Primeinator 2/25/2021 102218101 3/1/2021
ZFR 11/24/2020 102685711 2/4/2021
ZFR 11/24/2020 102685769 2/4/2021
ZFR 11/24/2020 103037743 2/4/2021
Primeinator 2/25/2021 103103437 3/31/2022
Raydex 2/15/2021 103237441 4/26/2021
tuckerkao 11/24/2020 103305173
tuckerkao 10/14/2020 103347613
Primeinator 2/25/2021 104115637 8/31/2024
Uncwilly 9/29/2021 106456279 10/31/2021
christian_ 12/27/2018 106456799 1/22/2020
axn 12/21/2018 107054317 8/31/2023
Prime95 12/16/2018 107448181 6/1/2022
Spherical Cow 2/11/2020 107448791* 2/9/2021 *factored
Zhangrc 8/4/2021 108765463 11/1/2021
ZFR 5/7/2021 109287103 12/14/2021
ZFR 5/7/2021 109287119 12/14/2021
ZFR 5/7/2021 109287131 12/14/2021 <==FTC complete above this
Kvasir 12/9/2021 110235199 12/2/2022
Batalov 12/12/2018 110691517 6/19/2022
ixfd64 12/27/2018 110691683 1/3/2025
dannyridel 7/26/2020 111906173 1/2/2021
Uncwilly 9/29/2021 111999799 5/27/2022
firejuggler 5/8/2021 114034099 12/24/2022
congsz 8/24/2022 115230449 5/1/2023
masser 8/3/2019 115856161 7/4/2023
masser 12/12/2018 117003179 11/24/2022
firejuggler 5/8/2021 118034167 5/24/2023
masser 12/12/2018 118788157 8/8/2020
ixfd64 12/27/2018 121596589 10/8/2027
kriesel 12/21/2018 121882753 5/21/2025
axn 12/21/2018 121882903 7/12/2026
Petrw1 10/13/2020 123456841 4/3/2021
Raydex 12/5/2020 125000089 5/2/2021
Jan S 12/10/2021 126551093 10/15/2023
sweety439 8/4/2021 127027489 4/21/2023
moebius 12/19/2020 131508427 1/1/2026
congsz 8/24/2022 141421417 1/1/2027
christian_ 12/27/2018 146456881 2/3/2022
masser 10/13/2020 149929849 9/2/2024
Ensigm 10/13/2020 150714349 12/11/2024
congsz 8/24/2022 173205119 12/1/2030
Dobri 8/20/2021 194004047 8/15/2022
Dobri 8/20/2021 194004049 8/15/2022
tuckerkao 12/8/2021 196828523
Brian-E 12/21/2018 258150181 5/15/2027
GP2 1/4/2019 282362693 3/3/2025
tuckerkao 10/14/2020 310347613
Dobri 8/2/2021 332192957 8/23/2024
dcheuk 9/1/2019 333898333 11/1/2019
kriesel 12/21/2018 402143633* 3/12/2052 *factored
ONeil 12/5/2020 852348659 12/31/2024
moebius 12/14/2018 1/13/2020
tServo 12/14/2018 12/31/2019
greenskull 10/12/2021 2/10/2022