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 2021-08-02, 11:13 #1 sweety439   "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 72·73 Posts Unsolved problems about primes and number theory collect 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. Last fiddled with by sweety439 on 2021-08-05 at 05:48

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