Timeline for How to explain this prime gap bias around last digits?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 23, 2020 at 19:51 | comment | added | Thierry Boulord | My 2.1 plot is finally exactly what is computed page 2, which is an evidence. With data from page 2, we have: $\begin{array}{c|cc} a & \text{Sum} & \text{Percent of total} \\ \hline 1 & 4623042 & 25.50 \\ 3 & 4442562 & 24.50 \\ 7 & 4439355 & 24.48 \\ 9 & 4622916 & 25.50 \\ \end{array}$ While my data gives : $\begin{array}{c|cc} a & \text{Sum} & \text{Percent of total} \\ \hline 1 & 11726 & 28.33 \\ 3 & 8969 & 21.67 \\ 7 & 9023 & 21.8 \\ 9 & 11666 & 28.19 \\ \end{array}$ Biases clearly follow the same pattern but diminish on larger $x$ due to $\log \log x/\log x$ term i guess | |
| Apr 23, 2020 at 18:09 | comment | added | vivian | For counting gaps of size exactly 10, I'd still expect a $\log \log x/\log x$ term. Here you wouldn't see an averaging effect, since you care about the values (mod 10) of the prime before and the prime after the gap. So, it does make sense that these gaps would be bigger. An analogous "crude experiment" would be to assume that $\pi(x_0; 10,(1,1))$, for example, on page 2, counts only pairs of primes with gaps equal to 10, instead of all that are 0 mod 10. Then you could take their values of $\pi(x_0;10,(a,a))$ for $a = 1,3,7,9$ and compare to your data. | |
| Apr 23, 2020 at 10:53 | comment | added | Thierry Boulord | And I would be really confused to learn that the discrepancy visible on my 2.1 data (occurence of gaps size of 10 after last digits) is a unique result of $1/\log x$ term. Does this experimental research on the prime gaps around the last digits make sense to you? Does it need to be further investigated? | |
| Apr 23, 2020 at 10:40 | comment | added | Thierry Boulord | First of all, I would like to thank you Vivian for your answer which allows me to understand more deeply the distinction to be made among the "full" bias. Your crude experiment with "virtual" deviations is very interesting. I now assume that my data displayed as a bar takes into account the full bias because of the averaging effect of summing over all values. Finally, the observed pattern of your sum calculated from the data on page 2 is not very far from my results in terms of occurrences between the last digits. | |
| Apr 21, 2020 at 16:04 | vote | accept | Thierry Boulord | ||
| Apr 20, 2020 at 23:56 | review | First posts | |||
| Apr 21, 2020 at 2:15 | |||||
| Apr 20, 2020 at 23:51 | history | answered | vivian | CC BY-SA 4.0 |