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Old 2021-06-10, 17:01   #1
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

5×193 Posts
Thumbs up Today's Favorite Mega Number

A favorite mega number must be a whole number greater than one million.

If you want to go down this rabbit hole,

see Matt Parker and Brady Herron on YouTube

Search YouTube.com for "Stand Up Maths" or "Singing Banana.


easy click - https://www.youtube.com/results?sear...stand+up+maths

So today, we have 1,754,847. Chosen for an arbitrary reason. It ends in 7 so it is not divisible by 2 or 5. It is less than two million, and to me,

17 is strong because it sounds like 'save a team'.

So, thanks to Maple - computer algebra system, we see that

This C7, that is seven digit composite number, namely 1,754,847 factors as

3 * 3 * 73 * 2671.

That is, a P1, another P1, a P2 and a P4 : -- )

Just count the digits.

Good Fun.

Regards,
Matt

Last fiddled with by MattcAnderson on 2021-06-12 at 21:39 Reason: added the word 'count'
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Old 2021-06-12, 06:20   #2
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Hi again all

My new favorite Mega number is

1,249,281

and, thankfully, due to Maple, computer algebra system, we see a prime factorization, so

ifactor(1,249,281) is 3*3*11*12619. Very Interesting

Cheers,

Matt
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Old 2021-06-12, 06:28   #3
MattcAnderson
 
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"Matthew Anderson"
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Oregon, USA

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And another one

due to factordb.com

changed one digit from the other one

it is true that

9249281 = 137 · 181 · 373

Regards,

Matt
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Old 2021-06-12, 07:47   #4
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Thumbs up

Matt here,

with another fun Mega number, starting with one

computer tool - Maple tells me that

ifactor(1,934,582);

is

(2) (13) (37) (2011)

Ah yess, 2011 a very good year for music.

We remember that Adele sang "Someone Like You"

Still Fun.

Matt
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Old 2021-06-12, 08:43   #5
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Smile

Starting from the middle and using year numbers

we have

2021 = 43*47

see Michael Penn discuss a Putnam exam question

https://www.youtube.com/watch?v=gn9ePie41xk

also

2019 = 3*673

and

2021*2019 = 4,080,399.

so

ifactor(4,080,399) is 3*43*47*673.


again Maple, the wonderful computer algebra system did all the heavy lifting, I mean factoring.

Fun for me, and you, fine reader.

Matt
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Old 2021-06-12, 12:51   #6
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Hi again all,

This is a new day, and we have a new number

Again, our tool of choice is Maple, a fully capable computer algebra system.

We see that

ifactor(2,295,147) = 3*23*29*31*37.

We have a fairly large Composite number that factors so some relatively small Prime numbers.

Specifically a C7 (seven digit composite number) - factors to a P1 and four P2.

We say that 2,295,147 is 37-smooth because 37 is the greatest prime divisor of our C7.

More fun every day.

Regards,

Matt
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Old 2021-06-12, 21:31   #7
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Hi again all

This is still a lot of fun for me.

As before, Maple - a super duper computer algebra system, was used.

We see that

ifactor(1826527) is 383* 251*19

so 1,832,527 is 383-smooth.

And, indeed, every positive integer is something-smooth.

Regards,
Matt
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Old 2021-06-12, 21:34   #8
Viliam Furik
 
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"Viliam Furík"
Jul 2018
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Quote:
Originally Posted by MattcAnderson View Post
see Matt Parker and Brady Herron on YouTube
His name is Brady Haran, FYI.
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Old 2021-06-12, 22:18   #9
Batalov
 
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"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

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Exclamation

Thank you Matt!

And thank you for the upcoming 8,999,994 more posts, that will surely follow (we have no doubts).
Please stick to your own rules and post no more than 1 of these "Today's" posts per day.
So far you have failed to uphold your own standard. We are disappointed.
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Old 2021-06-13, 02:18   #10
axn
 
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Jun 2003

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Brady is the producer of Numberphile (and many other ) channel.

Singing Banana is Prof. James Grime.

FYI.
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Old 2021-06-13, 04:34   #11
LaurV
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We love Zvezdelina! Our favorite teacher EVER!
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