I’m mostly posting this because i couldn’t find a graph of this when i searched for it myself, so i thought i would put it out there.
A function that approximates the data is 0.070 * log( 2.150 * 10^(-4) * x) + 3.322. (But i wouldn’t trust it too much)
**The backstory:**
I came across a sequence and messed around with it a bit. For fun i thought i would see how many prime factors the numbers in the sequence had. I was very surprised when large numbers in the sequence had seemingly few prime factors. So i thought i would check out if there was something weird going on. (spoiler: There wasn’t, I just overestimated the number of prime factors that numbers actually have. Who would have thought that (on average) a number around 10 000 000 has less than FOUR prime factors??)
**The sequence:**
I was tapping my fingers on the table, and was wondering how many ways i could put down all fingers on one hand. The answer is obviously 5! = 120. Or if you use both hands, the number is 10! = 3 268 800
But what if you can’t put down two neighbouring fingers one after the other? I made a sh***y python script and found out:
# of fingers – Possible ways to put them down
1 – 1
2 – 0
3 – 0
4 – 2
5 – 14
6 – 90
7 – 646
8 – 5 242
9 – 47 622
10 – 479 306
11 – 5 296 790
12 – 63 779 034
13 – Ran out of memory
Thanks for coming to my TED talk.
This is really interesting. I understand why you grouped the averages in buckets of 10k, but I’d also love to see an unaveraged plot of the number of prime factors for all nonprime numbers between 0 and 10,000,000, just to have laid my eyes on it.
And that’s why there are infinites larger than others.
The fact that we can casually count the number of primes between 0 and 10,000,000 is crazy to me. A computer is a fucking incredible invention.
Does this asymptote to anything or increase forever?
could have made the graph a bit nicer since the data is so cool..
Love to see that on a log scale!
Do we know what the limit is as x goes to infinity? Why does it look like 4ish, is it just because of the bounds of the data?
Drives me crazy when people don’t use commas in the number format (ie x axis).
![[OC] Average number of prime factors for numbers between 0 and 10 000 000](https://www.europesays.com/wp-content/uploads/2024/11/3s2pmo2srn2e1-1920x1024.png)
10 comments
I’m mostly posting this because i couldn’t find a graph of this when i searched for it myself, so i thought i would put it out there.
A function that approximates the data is 0.070 * log( 2.150 * 10^(-4) * x) + 3.322. (But i wouldn’t trust it too much)
**The backstory:**
I came across a sequence and messed around with it a bit. For fun i thought i would see how many prime factors the numbers in the sequence had. I was very surprised when large numbers in the sequence had seemingly few prime factors. So i thought i would check out if there was something weird going on. (spoiler: There wasn’t, I just overestimated the number of prime factors that numbers actually have. Who would have thought that (on average) a number around 10 000 000 has less than FOUR prime factors??)
**The sequence:**
I was tapping my fingers on the table, and was wondering how many ways i could put down all fingers on one hand. The answer is obviously 5! = 120. Or if you use both hands, the number is 10! = 3 268 800
But what if you can’t put down two neighbouring fingers one after the other? I made a sh***y python script and found out:
# of fingers – Possible ways to put them down
1 – 1
2 – 0
3 – 0
4 – 2
5 – 14
6 – 90
7 – 646
8 – 5 242
9 – 47 622
10 – 479 306
11 – 5 296 790
12 – 63 779 034
13 – Ran out of memory
Thanks for coming to my TED talk.
This is really interesting. I understand why you grouped the averages in buckets of 10k, but I’d also love to see an unaveraged plot of the number of prime factors for all nonprime numbers between 0 and 10,000,000, just to have laid my eyes on it.
And that’s why there are infinites larger than others.
The fact that we can casually count the number of primes between 0 and 10,000,000 is crazy to me. A computer is a fucking incredible invention.
Does this asymptote to anything or increase forever?
could have made the graph a bit nicer since the data is so cool..
Love to see that on a log scale!
Do we know what the limit is as x goes to infinity? Why does it look like 4ish, is it just because of the bounds of the data?
Drives me crazy when people don’t use commas in the number format (ie x axis).
Does it tend towards a limit?
Comments are closed.