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is it trivial that the series of medians for the second prime factor of numbers up to N is a specific number? isn't it just as plausible that this median would
by 2-718-281-828 3y ago
is it trivial that the series of medians for the second prime factor of numbers up to N is a specific number? isn't it just as plausible that this median would increase?
- drexlspivey 3y agoThe median of the first prime factor is 2
- codetrotter 3y agoBut intuitively it’s weird that the median of the second prime factor is not 3, right?
- drexlspivey 3y agoOnly multiples of 6 (1 in 6 numbers) have 3 as their second prime factor so I wouldn’t expect the median to be 3
- deleted 3y ago[deleted]
- eru 3y agoI guess it depends on whether you count multiples of 4 to have 2 as both their second and first prime factor?
- deleted 3y ago[deleted]
- NikkiA 3y agoI'd expect the mode of the second prime factor to be 3, but not necessarily the median.
- deleted 3y ago[deleted]
- cmiller1 3y agoThe sequence of the medians of successive prime factors would be interesting
- deleted 3y ago[deleted]
- LanceH 3y ago> isn't it just as plausible that this median would increase? Every sixth number will have a factors 2 and 3. (so 3 is the second prime for 16.666% of numbers) Every 10th number will have factors 2 and 5. Every 15th number will have factors 3 and 5. Of course then you have to subtract out every 30th number which contains a 2, 3 and 5. They ignored duplicates and it would have been nice if they had defined "first" and "second" properly. Also note that a prime counts the 2nd factor as "infinite", adding one to the "above 37" bucket. Anyhow, you add those up and it's easy to at least see that in any range of numbers it very quickly approaches 50%. Keep going to write out the Venn diagram and it happens to come out at 37. It's low enough, I assume it could even be done by hand.