Interesting procedure

I have played with several numbers with the following rules:

Take a number. (Example 10)
Find the prime factors of the number (if it have) . ( Example 10 have prime factors 2 and 5)
Make a number using those prime factors in ascending order. (Example for 10 it will be 25 as prime factors are 2 and 5)
Now continue the process with the new number you have got. Continue this process until you get a prime number as it will not have any prime factors

Applying the whole process on 10 :

10 => 25 => 55 => 511 => 773

I have applied this procedure on many numbers. And I concluded a statement:

All numbers will eventually fall to a prime through the process

For 8 it was a quiet big task:

8 => 222 => 2337 => 31941 => 33371313 => 311123771 => 7149317941 => 22931219729 => 112084656339 => 3347911118189 => 11613496501723 => 97130517917327 => 531832651281459 => 3331113965338635107

Another incredible number was 20 and I am unable to obtain a prime yet. You can try it yourself.

You should also try out if you can find any number not falling to a prime, or if you can prove or disprove my statement.

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

This is quite intriguing Sahar! I immediately decided to try writing a program which would go through this process, but quickly realized that finding the prime factorization of numbers larger than $100,000,000$ is quite taxing on a laptop! It took mine about a minute just to get to the fifth iteration for 8!

However, here is something I observed. When I set a cutoff in my program which ended the process when it hit numbers larger than $20,000,000$ , here are the numbers which were ended between 2 and 200:

8, 16, 20, 40, 44, 48, 49, 64, 65, 77, 78, 80, 81, 86, 87, 91, 96, 104, 105, 112, 116, 120, 123, 124, 126, 128, 129, 130, 132, 135, 136, 144, 146, 150, 160, 161, 164, 168, 169, 170, 176, 178, 180, 184, 185, 186, 188, 190, 192, 195, 196

Interestingly, many of these numbers come in consecutive pairs (for instance 77 and 78). This could easily change for higher cutoff values of course.

Hopefully someone else has some more insight!

David Stiff - 1 year, 2 months 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}`	$\boxed{123}$