Unsolved problems about primes and number theory collect
 

1. [URL="https://en.wikipedia.org/wiki/Grand_Riemann_hypothesis"]Grand Riemann hypothesis[/URL]
1a. [URL="https://en.wikipedia.org/wiki/Extended_Riemann_hypothesis"]Extended Riemann hypothesis[/URL]
1aa. [URL="https://en.wikipedia.org/wiki/Generalized_Riemann_hypothesis"]Generalized Riemann hypothesis[/URL]
[I]4. [URL="https://en.wikipedia.org/wiki/Mertens_conjecture"]Mertens conjecture (disproved)[/URL][/I]
1aaa./4a. [URL="https://en.wikipedia.org/wiki/Riemann_hypothesis"]Riemann hypothesis[/URL]
[B]1aab. [URL="https://en.wikipedia.org/wiki/Class_number_problem"]class number problem for imaginary quadratic number fields, i.e. there is no d>163 such that -d has class number 1 (proved)[/URL][/B]

2. [URL="https://en.wikipedia.org/wiki/N_conjecture"]n conjecture[/URL]
2a. [URL="https://en.wikipedia.org/wiki/Abc_conjecture"]abc conjecture[/URL]
2aa. [URL="https://en.wikipedia.org/wiki/Fermat%E2%80%93Catalan_conjecture"]Fermat–Catalan conjecture[/URL]
2aaa. [URL="https://en.wikipedia.org/wiki/Beal_conjecture"]Beal conjecture[/URL]
[I]5. [URL="https://en.wikipedia.org/wiki/Euler%27s_sum_of_powers_conjecture"]Euler's sum of powers conjecture (disproved)[/URL][/I]
5a. [URL="https://en.wikipedia.org/wiki/Lander,_Parkin,_and_Selfridge_conjecture"]Lander, Parkin, and Selfridge conjecture[/URL]
[B]2aaaa./5aa. [URL="https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem"]Fermat's Last Theorem (proved)[/URL][/B]
2ab. [URL="https://en.wikipedia.org/wiki/Pillai%27s_conjecture"]Pillai's conjecture[/URL]
[B]2aab./2aba. [URL="https://en.wikipedia.org/wiki/Catalan%27s_conjecture"]Catalan's conjecture (proved)[/URL][/B]
2b. [URL="https://en.wikipedia.org/wiki/Szpiro%27s_conjecture"]Szpiro's conjecture[/URL]

3. [URL="https://en.wikipedia.org/wiki/Bateman%E2%80%93Horn_conjecture"]Bateman–Horn conjecture[/URL]
3a. [URL="https://en.wikipedia.org/wiki/Schinzel%27s_hypothesis_H"]Schinzel's hypothesis H[/URL]
3aa. [URL="https://en.wikipedia.org/wiki/Bunyakovsky_conjecture"]Bunyakovsky conjecture[/URL]
3aaa. [URL="https://en.wikipedia.org/wiki/Landau%27s_problems"]Landau 4th problem[/URL]
3ab. [URL="https://en.wikipedia.org/wiki/Dickson%27s_conjecture"]Dickson's conjecture[/URL]
3aba. [URL="https://en.wikipedia.org/wiki/First_Hardy%E2%80%93Littlewood_conjecture"]Hardy–Littlewood 1st conjecture[/URL]
[B]3b. [URL="https://en.wikipedia.org/wiki/Prime_number_theorem_for_arithmetic_progressions"]PNT in AP (proved)[/URL][/B]
[B]3aab./3abb./3ba. [URL="https://en.wikipedia.org/wiki/Dirichlet%27s_theorem_on_arithmetic_progressions"]Dirichlet's theorem on arithmetic progressions (proved)[/URL][/B]
[B]3abc./3bb. [URL="https://en.wikipedia.org/wiki/Primes_in_arithmetic_progression"]length of primes in arithmetic progression has no upper bound (proved)[/URL][/B]
3abd. [URL="https://en.wikipedia.org/wiki/Cunningham_chain"]length of (1st or 2nd) Cunningham chain has no upper bound[/URL]
3abaa. [URL="https://en.wikipedia.org/wiki/Polignac%27s_conjecture"]Polignac's conjecture[/URL]
3abab. [URL="https://en.wikipedia.org/wiki/Second_Hardy%E2%80%93Littlewood_conjecture"]Hardy–Littlewood 2nd conjecture is false[/URL]
3abaaa. [URL="https://en.wikipedia.org/wiki/Twin_prime_conjecture"]Twin prime conjecture[/URL]
[B]3abaaaa. [URL="https://en.wikipedia.org/wiki/Chen_prime"]There are infinitely many Chen primes (proved)[/URL][/B]

(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.