Most common number of prime factors

I wrote some Python code to check what the most common number of prime factors is for all numbers between 11 and 1,000,0001,000,000 (it took a while!). For example, 1010 has two prime factors, 22 and 55, and 220220 has four: 22, 22, 55, and 1111. Here's what I got:

(Please forgive the odd x-axis scale. I forgot to set this before I ran the program.)

At first I checked numbers between 11 and 10,00010,000, and then 11 and 100,000100,000, and when I did this, it appeared that it was most common for a number to have 22 prime factors. But as I increased the upper bound, 33 prime factors became the most frequent.

I'm not sure if this would change once again with an even larger upper bound, because my laptop took about 20 minutes to do up to 1,000,0001,000,000. Does anyone have anything to add?

Note by David Stiff
1 year, 1 month ago

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You could ask @Zakir Husain, @David Stiff.

Yajat Shamji - 1 year, 1 month ago

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@David Stiff - I have organised a discussion in which a code is share, we will execute it but by breaking into pieces (together) as it will take much longer time if executed by me alone. For more information click here, hope we will go beyond 10910^9!

Zakir Husain - 1 year ago

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