Timeline for Are there infinitely many primes that can be written as a sum of $k$ fibonacci numbers
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| May 2, 2023 at 0:00 | answer | added | Christian Elsholtz | timeline score: 3 | |
| May 1, 2023 at 2:55 | comment | added | Wojowu | On the other hand, I think it might be known that for all sufficiently large $k$, there is some prime that can be written as a sum of $k$ (positive) Fibonacci numbers. It feels analogous to the question of Are there primes of every Hamming weight?. | |
| May 1, 2023 at 0:10 | comment | added | Stanley Yao Xiao | This is a natural question but likely extremely hard: the Fibonacci numbers $F_m$ satisfying $F_m \leq x$ has density $O(\log x)$, and for any fixed $k$, the numbers expressible as a sum of at most $k$ Fibonacci numbers has density $O((\log x)^k)$. This is still far too thin for modern techniques to detect primes; this sequence has log density $0$. In fact several open problems involve detecting primes in sequences of log density strictly less than one but still positive, and some even involve sets with full log density! | |
| Apr 30, 2023 at 22:44 | history | asked | Benjamin L. Warren | CC BY-SA 4.0 |