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.

What to do?\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.: a0,a1...a_0,a_1... where nW an\forall n\in\mathbb{W}\space a_n denotes number's having nn 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.

Graphs:\Large{Graphs:}

(From 1 to 106):(From\space 1\space to\space 10^6):

(From 1 to 107):(From\space 1\space to\space 10^7):

(All Graphs At A Glance):(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 11 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
3 weeks, 3 days ago

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  Easy Math Editor

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Could you give an example sequence?

David Stiff - 3 weeks, 2 days ago

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

Zakir Husain - 3 weeks, 2 days ago

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Oh, I see what you mean. Thanks!

David Stiff - 3 weeks, 2 days ago

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I guess I'll start. :)

From 11 to 1,000,0001,000,000:

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

David Stiff - 3 weeks, 1 day ago

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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)

David Stiff - 3 weeks, 1 day ago

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Added

Zakir Husain - 3 weeks, 1 day ago

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106+110^6 + 1 to 10710^7:

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

David Stiff - 3 weeks, 1 day ago

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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.

David Stiff - 3 weeks, 1 day ago

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