How is 28 both perfect and happy?
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- čas přidán 8. 05. 2024
- We will discuss what makes the number 28 both perfect and happy.
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Steve, you made the first math error of your life when you calculated the "happy" number of 6, when you did 29: it should be 4 + 81, not 4 + 36. There's a first time for everything :)
Ah yes, thank you so much Steven for pointing that out.
@@bprpmathbasics i was going to point it out as well, but I also finished the sequence:
29
4 81
85
64 25
89
64 81
145
1 16 25
52
25 4
29
Ha! I spotted that too. He's blindly going into the unknown. Let's watch.
@@AspieGamer13 You made a mistake as well. 1+16+25 =42, not 52. To continue it, it becomes:
42
16+4
20
4+0
4
16
...
Urgh, probably NOT the first math error of his life. Also not the second, third, fourth, etc. The guy is great, doesn't need to be put in a pedestal like that. Doing that is just dumb af.
I made a program that determines if a number is happy and/or perfect
Up to 100000 the only perfect numbers are 6, 28, 496, and 8128. Of these 28, 496, and 8128 are also happy
There are only 51 known perfect numbers so *in theory* you could just check all 51 of them individually.
But of course, the perfect numbers get big really fast so it would be very infeasible to square each digit and add them for the larger ones.
@@Ninja20704 Even the next perfect number 33,550,336 would take a while to check.
This might help you find perfect numbers. 2^x-2^y where x=1,3,5,7... and y=0,1,2,3... Not all numbers produced by this formula are perfect but all perfect numbers (so far) fit this formula. x can equal 2y+1.
@@richardl6751 there a stricter formula for finding perfect numbers.
If p is prime and 2^p-1 is also prime, then (2^p-1)*2^(p-1) will generate a perfect number. Primes of the form 2^p-1 are called mersenne primes.
Furthermore, every even perfect number must have this form (We don’t know if any odd perfect numbers exist) meaning there is a 1-1 relation between Mersenne primes and even perfect numbers. So the key to finding perfect numbers is finding the p values where 2^p-1 is prime.
@@Ninja20704 Yes, I'm familiar with that formula, however it requires you find prime numbers first. My formula will produce a list of numbers that can be easily tested individually and non-perfect numbers can be rejected rather quickly.
I turned 28 this year, I am perfect and happy 🙏
Awesome! And next year you will be in a prime year!
cool
I was born in *28th* of June
I think you made a mistake on the “29”. Should be 85 and not 40
I agree - it is 9^2 and that is 81. 81+4+85.
I learnt about happy numbers in primary school (late 80s) and haven't heard of them since.
There is an error in the sequence. From 29, the next term should have been 4+81=85 and not 40.
The the sequence from there would be would be:
85, 89, 145, 42, 20, 4, 16, 37, 58, 89.
And from now it just repeats since we see 89 again.
On a side note, 496 is a number that is both perfect and happy as well.
Ah thank you!
@@bprpmathbasics It's nice to know you're human too:)
The timing of this video is impeccable. Synchroniticy. Let’s go 28!
This makes me sososo happy!
I have a BS in math, and I am always learning something new in math.
I guess I should feel happy for being 28.
28 is also a triangular number
Question: Can you please explain why π always appear in circular shapes? What is the function of π?
Because pi is the ratio between a circle's diameter and it's circumference. If you had a circle with diameter of length 1, then the ratio of the diameter to it's circumference would be 1 : π
Take for instance a square shape. It will have a perimeter equal to 4×s. Now if you were to find the perimeter of a circle more aptly called the circumference you would have a little challenge doing that. This is because Pi is the amounr of times the Radius wraps around to make the circumference.
Thanks
my "lucky" numbers were always 4 and 7, but now 28 is my reason why they are🗿
i noticed the error but doubted myself, came down to the comments to see that everyone else also noticed it, conclusion: I need more self confidence! lol
I wonder what it would have looked like without the error thought? because obviously it still gave the same result as expected which was repeating numbers, so that's interesting..
lastly, I almost thought 1 was perfect and happy, but then I realized its result for perfect is 0
6 is never happy when 4 + 81 = 40
Not 28 hours yet, can make video revision
I think you made a mistake in „happy“ sequence for 6…. 29
Is 85, not 40…..
Technically, 1 is a perfect and happy number. 1 is just 1*1, so take the one and 1=1. Perfect. Also, 1^2 is 1, so it's also happy.
Also, curious, I decided to look up a list of perfect numbers, and found there's actually a formula to find perfect numbers. 2^(p-1)(2^p-1). where p is a prime number. It also gave the first four perfect numbers as 6, 28, 496, and 8128.
496 is also perfect and happy, 1, 2, 4, 8, 16, 31, 62, 124, 248, 496. 1+2+4+8+16+31+62+124+248=496. Also 496 16+81+36=133 1+9+9=19 1+81=82 64+4=68 36+64=100 1+0+0=1
As is 8128. 1+2+4+8+16+32+64+127+254+508+1016+2032+4064=8128. 64+1+4+64=133 1+9+9=19 1+81=82 64+4=68 36+64=100 1+0+0=1
In fact, looking at the first 6 perfect numbers so far, it seems the first (6) and the sixth (33,550,336) are the only ones that aren't happy.
plugging p=11 into that formula gives 2096128 which isn't perfect (according to the program i made)
however other primes such as 2,3,5,7,13, and 17 do give perfect numbers when plugged in to that formula
According to wikipedia p and 2^p -1 both have to be prime to give a perfect number with that formula and 2^11 -1=2047 which isnt prime (2047=23*89)
1 is not perfect. Because 1 only has 1 as factors which is itself, we say 1 has no proper divisors (because proper divisors excludes the number itself). So the sum of all proper divisors is 0.
@@Ninja20704 I mainly said it as a joke, because you still include the 1 as the factors for every other perfect number.
@@Samir-zb3xk You're right, I hadn't bothered trying to calculate it out, just relying on the formula, but after calculating it out, it adds up to 2,295,392, not 2,096,128
@@AzureKyle did you calculate it out by hand? 😧😧
my computer calculated the sum of the factors of 2,096,128 to be 2,325,392
There's a Mathematician joke in there somewhere.
9x9=36 is crazy 💀
Factors work with binary so the perfect numbers will be perfect in binary. Are there any happy binary numbers?
I think that with the system he used every binary number would be happy. The process would keep giving you the number of ones in the number, which would always be less than the value of the number, and eventually it would decrease down to 1.
What about hexadecimal?
The next two perfect numbers are 496 and 8128. Spoiler gap follows...
:
:
:
496 and 8128 are both happy. After that, perfect numbers get very large, fairly quickly, so I used a computer. The next six are not happy. Then there's another happy one (it has 65 digits - possible on a whiteboard but I wouldn't recommend it!), five more not happy, another happy one (1373 digits), seven unhappy, then happy again (13086 digits) the next one is unhappy, but I decided to stop there.
Bz it is birthday date 28 .08
Bro while calculating happy number 6, you have made a mistake. after 2 9 it will 4+81=85
I want to be like 28
28s were rubbish, with their Co-Bo arrangement although 1 is still with us.
So why should we care about "The Perfect Number" and "The Happy Number"? What's the practical use of them?
Because math can be depressing
It is pure math versus applied math. It just is about finding interesting information about numbers, like in number theory.
BUT sometimes a practical applied use of pure math is found. A good example is the algorithms that are used in computers and other electronic devices for encryption and also data correction.
Who let you in?
This is a channel for people who like math regardless of their use. Would you say the same about literature?
Steve I unfortunately have to be that guy and say 6 is a perfect happy number. Unfortunately your miscalculation had lead you to believe that it wasn't however do check the problem again unless I am completly incorrect you should find after 16 steps you do get to a value of 1
Upon closer inspection my math was incorrect 6 is unhappy
I was wrong upon closer inspection I realized that 6 is not a happy value
9²≠36 😅😅😅 hqhqhaha
28 is an _odious_ number.
As a 40 year old, I can testify that being 28 was neither perfect nor happy. I was highly stressed and miserable at the time.
First comment and first like you can pin it?
You made so many mistakes in this video…
super don't care about silly properties of numbers.
I think you made a mistake on the “29”. Should be 85 and not 40