Timeline for Infinite sets of primes of density 0
Current License: CC BY-SA 2.5
7 events
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| Mar 3, 2010 at 15:19 | history | edited | Álvaro Lozano-Robledo | CC BY-SA 2.5 |
Added first sentence, explaining this is a simple example of usage of Dirichlet's
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| Mar 2, 2010 at 17:25 | comment | added | Álvaro Lozano-Robledo | Yes, this is a somewhat ad-hoc construction, but it's simply an example of a standard technique, as the poster asked, of how one can use Dirichlet's theorem to find sets of density zero. | |
| Mar 2, 2010 at 17:09 | comment | added | Regenbogen | This is an ad-hoc construction. You could have just required that $p_n$ is the first prime after $n!$, or the prime just before $10^n$, and you would have got a set of density zero primes. | |
| Mar 2, 2010 at 16:54 | comment | added | Álvaro Lozano-Robledo | @Harrison, thanks! I guess I didn't need to define $P$ in that way, so I edited the definition, and I think it now should make sense. | |
| Mar 2, 2010 at 16:52 | history | edited | Álvaro Lozano-Robledo | CC BY-SA 2.5 |
Minor ... the -> a
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| Mar 2, 2010 at 16:43 | comment | added | Harrison Brown | Hm, I don't think part (1) is correct -- certainly a $p$ such that $p = 1 mod p_1p_2...p_n$ exists, but there are likely new primes in between $p_n$ and $p$. In fact, unless I'm seriously misunderstanding you, (1) is false by Bertrand's postulate. | |
| Mar 2, 2010 at 16:36 | history | answered | Álvaro Lozano-Robledo | CC BY-SA 2.5 |