# It's Prime factor!

The previous idea to find number of prime factors have failed due to my mismanagement. So now I am deciding to re-launch a new version of it with some major changes listed below:

• Now there will be nothing like "participation" or "member", etc.

• This time it will be open to all, there shall be no schedule, when to do what, etc.

• Those who shall be sharing there outputs, I will be plotting graph regarding it here.

$\large{What \space to \space do ?}$

This time, everyone is free of their choices to run or make their own program in whatever language, range they wish. But if you want to share your output better to do it in this format:

• Write in a sequence for e.g.: $a_0,a_1...$ where $\forall n\in\mathbb{W}\space a_n$ denotes number's having $n$ number of prime factors in the given range, example of the sequence for numbers from 0 to 10:[0,4,4,1] (not including 0,1)

This format is not necessary but it will help me to build the graph more easily.

You can either built you own program or use the old one, and if you think that your program is better than you can write in the comments too.

$\Large{Graphs:}$

$(From\space 1\space to\space 10^6):$

$(From\space 1\space to\space 10^7):$

$(From \space 1\space to\space 10^7 + 3\times 10^4)$

$(All\space Graphs\space At\space A\space Glance):$

• In the above graphs x-axis shows the number of prime factors, y-axis shows the percentage of those numbers having the corresponding number of prime factors.

Note :

• See On Most common number of prime factor! for more information

• Previous data are scrambled so we need to start form $1$ again :( but you can start from wherever you want.

• A request to RadMath to add this in the "Late events"

• The event starts from today!

• I shall be posting graph on daily basis, also you can write your conjectures (after observing the graphs obviously) in the comments!

• If any confusion is their in your mind related to this event then clear it quickly here

• Any suggestions can be given in the comments below.

• Hope we will explore something interesting and new!

Note by Zakir Husain
4 months, 1 week ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
• Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

## Comments

Sort by:

Top Newest

Could you give an example sequence?

- 4 months, 1 week ago

Log in to reply

For example for numbers from 0 to 10:[0,4,4,1] (not including 0,1)

- 4 months, 1 week ago

Log in to reply

Oh, I see what you mean. Thanks!

- 4 months, 1 week ago

Log in to reply

I guess I'll start. :)

From $1$ to $1,000,000$:

[0, 78498, 210035, 250853, 198062, 124465, 68963, 35585, 17572, 8491, 4016, 1878, 865, 400, 179, 79, 35, 14, 7, 2]

- 4 months, 1 week ago

Log in to reply

I used your old code, but I modified the "percentage done" section to act more like a status bar. :)

Substituted this for lines 18-20:

 1 2 3 4 print(f"Processing...\n{'_'*100}") for a in range(l, m): if round(m-a) % round((m-l)/100) == 0: print("\u2588", end="", flush=True) 

- 4 months, 1 week ago

Log in to reply

Added

- 4 months, 1 week ago

Log in to reply

$10^6 + 1$ to $10^7$:

[0, 664562, 1904303, 2444347, 2050689, 1349777, 774078, 409849, 207207, 101787, 49163, 23448, 11068, 5210, 2406, 1124, 510, 233, 102, 45, 21, 7, 3, 1]

- 4 months, 1 week ago

Log in to reply

Sorry, I have a slight correction to make for this interval:

[0, 586081, 1694289, 2193506, 1852634, 1225314, 705115, 374264, 189635, 93296, 45147, 21570, 10203, 4810, 2227, 1045, 475, 219, 95, 43, 21, 7, 3, 1]

I realized I had mistyped the starting number.

- 4 months ago

Log in to reply

10000001 to 10010000:

0,614,1832,2424,2059,1387,826,431,223,101,53,28,11,5,3,1,1,0,0,0,0,0,0,0


- 2 months, 2 weeks ago

Log in to reply

10010001 to 10020000:

0,628,1827,2409,2088,1354,833,421,231,114,48,22,12,7,2,2,1,0,0,0,0,0,0,0


- 2 months, 2 weeks ago

Log in to reply

10020001 to 10030000:

0,630,1813,2392,2091,1411,815,413,222,109,51,32,13,3,2,1,0,0,0,1,0,0,0,0


- 2 months, 2 weeks ago

Log in to reply

Added all three in one graph

- 2 months, 2 weeks ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...