Analysis page (Most common Number of prime factors)

All the analysis made from the outputs of participants will be shown here.

Graph of Prime factor distribution from $0$ to $10^6$ :
Graph of Number of prime factors occurrence percentage (till $10^6$ ):
Graph of Prime factor distribution from $0$ to $10^8$ :

Note :

If you have another idea (rather than line graph) of representing the data then please share!
Thanks to Páll Márton to submit answer till $10^8$ .

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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

@Zakir Husain I think Pie chart will be better as it will help visualise more clearly.

Aryan Sanghi - 10 months, 3 weeks ago

Sure!

Zakir Husain - 10 months, 3 weeks ago

It seems that till $10^6$ numbers with number of prime factors - $2,3,4$ are most common. Also highly composite number are more rare than primes

Zakir Husain - 10 months, 3 weeks ago

Reminds me of $\dfrac{1}{(x-k)^n}$ ...

Jeff Giff - 10 months, 3 weeks ago

What? I didn't understood, what you meant?

Zakir Husain - 10 months, 3 weeks ago

x=number of prime factors, k & n are unknown constants, the output of the function is the number of number that have x prime factors.

Jeff Giff - 10 months, 3 weeks ago

Matches the graph

Jeff Giff - 10 months, 3 weeks ago

@Jeff Giff – Are you asking or telling???

Zakir Husain - 10 months, 3 weeks ago

@Jeff Giff – Except for $x < 2$ I guess?

David Stiff - 10 months, 3 weeks ago

Looking great @Zakir Husain ! Could you share the actual numbers as well?

David Stiff - 10 months, 3 weeks ago

$\Large{Announcement:}$ New plan is here, everything is nearly changed now

Zakir Husain - 2 months, 3 weeks 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}`	$\boxed{123}$