Timeline for Are there any Fibonacci numbers that are sandwiched between twin primes?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jan 1, 2023 at 4:05 | comment | added | Robbie Goodwin | Why, please, are you Asking that without Posting helpful research? After which number did you give up your own search? | |
| Dec 31, 2022 at 19:02 | history | edited | YCor | CC BY-SA 4.0 |
made title more specific
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| Dec 31, 2022 at 18:48 | vote | accept | Nandakumar R | ||
| Dec 31, 2022 at 18:47 | comment | added | Nandakumar R | Sure. Moved qn 2 to another post | |
| Dec 31, 2022 at 18:45 | history | edited | Nandakumar R | CC BY-SA 4.0 |
deleted 225 characters in body; edited title
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| Dec 31, 2022 at 16:53 | history | became hot network question | |||
| Dec 31, 2022 at 14:48 | comment | added | GH from MO | Please restrict to one question per post. This is standard policy on this website. | |
| Dec 31, 2022 at 12:57 | history | edited | Martin Sleziak |
edited tags
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| Dec 31, 2022 at 12:53 | answer | added | Ofir Gorodetsky | timeline score: 47 | |
| Dec 31, 2022 at 11:38 | comment | added | Ofir Gorodetsky | Heuristically, $F_{n}\pm 1$ are simultaneously primes with probability $\asymp 1/n^2$ since $F_n$ grows exponentially and the density of primes is $1/\log x$. The convergence of $1/n^2$ suggests a finite number of such sandwiched Fibonaccis. Twin primes $(p,p+2)$ must satisfy $p\equiv -1 \bmod 6$, so a sandwiched Fibonacci number must be divisible by $6$. Since $F_n$ is periodic modulo $6$, a short computation shows $F_n \equiv 0 \bmod 6$ if and only if $n \equiv 0 \bmod 12$. I couldn't even find $n$ for which not both $F_{12n}-1,F_{12n}+1$ are composite. | |
| Dec 31, 2022 at 11:37 | comment | added | Ofir Gorodetsky | Can you find a Fibonacci number $F_n>10$ for which $F_{n}+1$ is a prime? | |
| Dec 31, 2022 at 8:49 | history | asked | Nandakumar R | CC BY-SA 4.0 |