Timeline for Writing integers as determinants of matrices with prime entries.
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 24, 2017 at 13:02 | answer | added | Jan-Christoph Schlage-Puchta | timeline score: 1 | |
| Dec 23, 2017 at 19:46 | comment | added | Hailong Dao | So, is the answer to Question 1 yes, or still depending on some conjectures? | |
| Dec 23, 2017 at 19:13 | comment | added | Gerry Myerson | @Greg, shouldn't this be easier than twin primes? It just asks for gaps between semiprimes. arxiv.org/abs/math/0506067 may be useful. Products of two primes are tabulated at oeis.org/A001358 | |
| Dec 23, 2017 at 18:26 | comment | added | Greg Martin | Pretty much all such questions should follow from the generalized twin primes problem. Given any $n\times n$ matrix, fix $n^2-2$ of the entries to be any primes you want, leaving (say) two neighboring variables in the same row. It should be easy to arrange that the determinant of the resulting matrix will is a linear polynomial of the form $Ax-By$ in the two variables $x$ and $y$, where $A$ and $B$ are positive coprime integers. Then conjecturally, that linear polynomial evaluated at primes $x$ and $y$ should represent every integer $n$ of the correct parity infinitely often. | |
| Dec 23, 2017 at 16:23 | history | asked | Hailong Dao | CC BY-SA 3.0 |