README for the file [URL="https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml"]https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml[/URL]:

* 12{3}45 means family {1245, 12345, 123345, 1233345, 12333345, 123333345, ...}

* A means digit value 10, B means digit value 11, C means digit value 12, ...

* z means digit value base-1, y means digit value base-2, x means digit value base-3, w means digit value base-4, ...

* the numbers in the list is the length of the smallest primes or PRPs in this family in this base (only count numbers > base) (e.g. family 3{z} in base 72, the smallest prime is 4*72^1119849-1, which has 1119850 digits in base 72, thus the number for family 3{z} for base 72 is 1119850)

* NB: this family is not interpretable in this base (e.g. family 7{0}1 and 7{z} in bases <=7, family {z}x in bases <=3) (including the case which this family has either leading zeros (leading zeros do not count) or ending zeros (numbers ending in zero cannot be prime > base) in this base)

* RC: this family can be proven to only contain composite numbers (only count numbers > base)

* unknown: this family has no primes or PRPs found, nor can this family be proven to only contain composite numbers (only count numbers > base)

Test limit of the length of the families for the file [URL="https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml"]https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml[/URL] (for bases 2<=b<=1024):

1{0}1: >=8388608 (reference: [URL="http://www.noprimeleftbehind.net/crus/GFN-primes.htm"]http://www.noprimeleftbehind.net/crus/GFN-primes.htm[/URL], also see [URL="http://jeppesn.dk/generalized-fermat.html"]http://jeppesn.dk/generalized-fermat.html[/URL])

{1}: >=100000 (thanks to Michael Stocker, reference: [URL="http://www.primenumbers.net/prptop/searchform.php?form=%28b%5En-1%29%2Fa&action=Search"]http://www.primenumbers.net/prptop/searchform.php?form=%28b%5En-1%29%2Fa&action=Search[/URL], also see [URL="https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html"]https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html[/URL] and [URL="http://www.fermatquotient.com/PrimSerien/GenRepu.txt"]http://www.fermatquotient.com/PrimSerien/GenRepu.txt[/URL])

2{0}1, 3{0}1, 4{0}1, 5{0}1, 6{0}1, 7{0}1, 8{0}1, 9{0}1, A{0}1, B{0}1, C{0}1, 1{z}, 2{z}, 3{z}, 4{z}, 5{z}, 6{z}, 7{z}, 8{z}, 9{z}, A{z}, B{z}: >=100000 (reference: [URL="https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n"]https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n[/URL], [URL="https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n"]https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n[/URL])

z{0}1: >=100000 (reference: [URL="https://www.rieselprime.de/ziki/Williams_prime_MP_least"]https://www.rieselprime.de/ziki/Williams_prime_MP_least[/URL])

y{z}: >=200000 (reference: [URL="https://www.rieselprime.de/ziki/Williams_prime_MM_least"]https://www.rieselprime.de/ziki/Williams_prime_MM_least[/URL], also see [URL="https://harvey563.tripod.com/wills.txt"]https://harvey563.tripod.com/wills.txt[/URL])

1{0}2, {z}y, 1{0}z, {z}1, {y}z: >=5000 (by me)

other families: >=2500 (by me)