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!

Markdown

Appears as

*italics* or _italics_

italics

**bold** or __bold__

bold


- bulleted
- list

bulleted
list


1. numbered
2. list

numbered
list

Note: you must add a full line of space before and after lists for them to show up correctly

paragraph 1

paragraph 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"

Math

Appears 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}

Easy Math Editor

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.

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

Math	Appears 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

Could you give an example sequence?

David Stiff - 2 months, 3 weeks ago

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

Zakir Husain - 2 months, 3 weeks ago

Oh, I see what you mean. Thanks!

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]

David Stiff - 2 months, 2 weeks ago

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:

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)

Added

Zakir Husain - 2 months, 2 weeks ago

$10^6 + 1$ 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]

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.

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

Jeff Giff - 1 month ago

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

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

Added all three in one graph

Zakir Husain - 1 month ago

Math	Appears 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}`	$\boxed{123}$