Timeline for Primes of the form $d^2+d+1$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 20, 2023 at 15:40 | comment | added | user178594 | I think DHR sieve can help to prove that the number of the positive integers $n\le$ such that $n^2+n+1$ is prime is at least $c\cdot\dfrac{n}{log(n)log(log(n))}$ for some positive constant $c$ and therefore that sum of their reciprocal diverges at least as fast as $log(log(log(n)))$, and that the similar results hold for any other irreducible quadratic polynomial. | |
| Jan 19, 2023 at 18:43 | comment | added | Stanley Yao Xiao | @number yes as a non-number theorist it is indeed surprising that such a basic statement is not known. However number theorists know that we know embarrassingly little about many things, so wouldn’t be surprised that we don’t know this. | |
| Jan 19, 2023 at 13:51 | comment | added | Timothy Chow | For the closely related question of whether there are infinitely many primes of the form $d^2+1$, see the Wikipedia article on Landau's problems for some references. | |
| Jan 19, 2023 at 11:03 | comment | added | numberwat | Thanks for the information. This is surprising to me :) | |
| Jan 19, 2023 at 11:03 | vote | accept | numberwat | ||
| Jan 18, 2023 at 15:45 | history | answered | Stanley Yao Xiao | CC BY-SA 4.0 |