Unsolved problems about primes and number theory collect

[sweety439]

1. Grand Riemann hypothesis
1a. Extended Riemann hypothesis
1aa. Generalized Riemann hypothesis
4. Mertens conjecture (disproved)
1aaa./4a. Riemann hypothesis
1aab. class number problem for imaginary quadratic number fields, i.e. there is no d>163 such that -d has class number 1 (proved)

2. n conjecture
2a. abc conjecture
2aa. Fermat–Catalan conjecture
2aaa. Beal conjecture
5. Euler's sum of powers conjecture (disproved)
5a. Lander, Parkin, and Selfridge conjecture
2aaaa./5aa. Fermat's Last Theorem (proved)
2ab. Pillai's conjecture
2aab./2aba. Catalan's conjecture (proved)
2b. Szpiro's conjecture

3. Bateman–Horn conjecture
3a. Schinzel's hypothesis H
3aa. Bunyakovsky conjecture
3aaa. Landau 4th problem
3ab. Dickson's conjecture
3aba. Hardy–Littlewood 1st conjecture
3b. PNT in AP (proved)
3aab./3abb./3ba. Dirichlet's theorem on arithmetic progressions (proved)
3abc./3bb. length of primes in arithmetic progression has no upper bound (proved)
3abd. length of (1st or 2nd) Cunningham chain has no upper bound
3abaa. Polignac's conjecture
3abab. Hardy–Littlewood 2nd conjecture is false
3abaaa. Twin prime conjecture
3abaaaa. There are infinitely many Chen primes (proved)

(e.g. conjecture * covers conjecture *a, *b, *c, ..., where * is any string, tell me if I miss any conjectures in these families)

These 1 (Grand Riemann hypothesis, stronger than Riemann hypothesis), 2 (n conjecture, stronger than abc conjecture), and 3 (Bateman–Horn conjecture, stronger than Schinzel's hypothesis H), I call these three conjectures "three classed unsolved problems in number theory" and hope that they are all true, at least 1' (Riemann hypothesis), 2' (abc conjecture), and 3' (Schinzel's hypothesis H) are all true.