Timeline for How $a+b$ can grow when $a!b! \mid n!$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 7, 2013 at 7:40 | history | edited | S. Carnahan♦ | CC BY-SA 3.0 |
Computation update
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| Jul 31, 2013 at 11:46 | history | edited | S. Carnahan♦ | CC BY-SA 3.0 |
corrections, updates.
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| Jul 30, 2013 at 19:32 | comment | added | Noam D. Elkies | ... and no example of $v > 22$ up to $2.25 \cdot 10^6$ (which exceeds $2^{20}$). | |
| Jul 30, 2013 at 15:10 | comment | added | Noam D. Elkies | Almost all the saving is in just the stored $2$-valuation. I'm also precomputing prime factorizations (Eratosthenes). | |
| Jul 30, 2013 at 14:58 | comment | added | S. Carnahan♦ | @NoamD.Elkies Okay, working in C and precomputing an array of valuations allowed me to work up to 500000 in 150 seconds. I'm getting a weird allocation error when I go above $10^6$, though. | |
| Jul 30, 2013 at 14:47 | comment | added | S. Carnahan♦ | Great! I was just thinking that I waste too much time recomputing valuations, so I will try to make a big array of $p$-valuations of $n!$ for small $p$, and do subtractions from that. | |
| Jul 30, 2013 at 14:14 | comment | added | Noam D. Elkies | Update: about 100 times faster... $v=21$ and $v=22$ first appear just a bit after $2^{19}$: $(59039, 465398, 524416)$, $(230111, 294839, 524928)$. | |
| Jul 30, 2013 at 13:36 | comment | added | Noam D. Elkies | C code is about 10 times faster. It took my laptop about 4 hours to reach $2^{18} = 262144$, which is the first time that $v=19$ and $v=20$ appear: $(34719, 227444, 262144)$, $(109237, 152927, 262144)$. I think it should be possible to save another factor of $10$ or so to at least reach $2^{21}$; watch this space (unless somebody else does it first)... | |
| Jul 30, 2013 at 0:41 | history | answered | S. Carnahan♦ | CC BY-SA 3.0 |