Timeline for Infinite sets of primes of density 0
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Jan 28, 2013 at 14:06 | vote | accept | Andrea Mori | ||
| Mar 2, 2010 at 14:26 | comment | added | Kevin Buzzard | @Franz: In some sense my example of a set of density 0 is no more or less natural than the n^2+1 example! For the set of numbers of the form n^2+1 is growing a lot more slowly than the primes: there are only about sqrt(x) of these less than x, but there are x/log(x) primes! So in some sense the two examples are "the same". | |
| Mar 2, 2010 at 13:55 | comment | added | Kevin Buzzard | @Andrea: OK, I added some comments on an explicit example---infinitude of supersingular primes. | |
| Mar 2, 2010 at 13:54 | history | edited | Kevin Buzzard | CC BY-SA 2.5 |
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| Mar 2, 2010 at 13:42 | comment | added | Franz Lemmermeyer | I think what he wants are "natural" sets of primes with density 0, such as twin primes or primes of the form n^2+1. The set of primes of the form x^2 + y^4 is infinite - does it have positive density? | |
| Mar 2, 2010 at 13:40 | comment | added | Andrea Mori | Kevin, I believe you're answering to the problem of constructing an "explicit" infinite set of primes of density 0. My admittedly vague question goes a bit in the other direction: suppose you start with some set of primes (defined by some conditions) and suppose that you can establish that its density is 0. What can you do next if you insist on proving that the set is infinite? It's just a case-by-case situation or there are some standard techniques you can try to apply? Are there interesting examples in the literature where a set of primes is shown to be infinite although its density is 0? | |
| Mar 2, 2010 at 12:22 | history | answered | Kevin Buzzard | CC BY-SA 2.5 |