Timeline for Perfect Runs of Consecutive Integers
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 27, 2019 at 12:35 | comment | added | Freddy Barrera | @FrançoisBrunault: I can confirm that there are no other perfect 2-runs and 3-runs below $1.8\times 10^{10}$, nor any perfect 4-runs. The closest for the latter is the run beginning at 113393279 that falls short by 4 of being perfect. | |
| Apr 25, 2019 at 19:53 | comment | added | François Brunault | My computer checked that there is no other perfect 2-run below $10^{10}$. An observation: in all the known perfect runs, the largest number is a large prime times some small prime factors. I don't know if this could help to find more runs. | |
| Apr 25, 2019 at 16:15 | comment | added | Sylvain JULIEN | Probably coincidental but your examples all fulfill $\tau(n)=2^m.d$ with $d$ a divisor of a prime. | |
| Apr 25, 2019 at 14:09 | history | edited | Freddy Barrera | CC BY-SA 4.0 |
New results.
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| Apr 24, 2019 at 19:28 | comment | added | Freddy Barrera | @GerhardPaseman: Yes, the above two examples, together with OP's (672, 673), are the only 2 and 3-runs below $10^8$. | |
| Apr 24, 2019 at 18:24 | comment | added | Gerhard Paseman | Are these the only examples below 6 million? Gerhard "Is Keeper Of Imperfect Information" Paseman, 2019.04.24. | |
| Apr 24, 2019 at 17:49 | history | answered | Freddy Barrera | CC BY-SA 4.0 |