Timeline for Primes in many variables polynomials form
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 10, 2021 at 17:26 | comment | added | Will Sawin | The easiest way to make a polynomial that represents all primes is to make a polynomial that represents all nonnegative numbers. This can be done with a one-variable polynomial, for instance. | |
| Feb 10, 2021 at 12:01 | comment | added | Gerry Myerson | There have been papers which reduce the number of variables from $26$, at the cost of incresing the degree of the polynomial. | |
| Feb 10, 2021 at 11:40 | review | Close votes | |||
| Feb 25, 2021 at 3:04 | |||||
| Feb 10, 2021 at 11:23 | comment | added | Jan-Christoph Schlage-Puchta | The existence of such a polynomial follows from the negative solution of Hilbert's tenth problem. Robinson and Matijasevic showed that every enumerable set is diophantine, that is, if for a set of integers $A$ there exists a computer program, that produces all elements of $A$, not necessarily in the correct order, then there exists a polynomial $P(x, y_1, \ldots, y_k)$, such that the equation $P(n, y_1, \ldots, y_k)=0$ is solvable in integers if and only if $n\in A$. The set of primes is enumerable, and from the polynomial $P$ it is easy to construct a prime producing polynomial. | |
| Feb 10, 2021 at 9:51 | comment | added | gmvh | Check e.g. primes.utm.edu/glossary/page.php?sort=MatijasevicPoly and references therein. | |
| Feb 10, 2021 at 9:50 | review | First posts | |||
| Feb 10, 2021 at 11:23 | |||||
| Feb 10, 2021 at 9:45 | history | asked | W. Wongcharoenbhorn | CC BY-SA 4.0 |