Dope Tech Episode 2

<<@Hehen264 says : The answer is: 6, 28, 496, 8128,>> <<@The225dud says : Judging by my pfp, u know why i am here.>> <<@your_opponent says : Of course Euler is involved>> <<@aiste_Ali says : (3.23mins in) When you talked bout those numbers 11100 and so on. Couldn't you use those numbers to also generate new perfect numbers. 6¹⁰=110+1000+0 that is just added =11100=28=11100 add 2 more 1 and 2 more 0 you get 111110000=496¹⁰ repeat that you get 1111111000000 = 8128¹⁰and if you repeat that you get 11111111100000000 and wouldn't this number be the next perfect number (idk how to make it the other number)?>> <<@26.7thecreatormemified says : What is the formula for perfect numbers?>> <<@nazartverdokhlebov says : 8:55 2^(p-1) = Super Perfect Number>> <<@Michał-t2h3i says : 6 28 496 8,128 33,550,336 (≈)8.6B>> <<@danputaranui3182 says : I’ll sleep on this one… the answer usually comes after a good nights sleep:) 😂😂😂>> <<@Ultimate_Guy_07 says : Beauty of Mathematics ❤>> <<@ParallelLives2025 says : I'm an odd perfect number>> <<@tsubasaDensetsu says : Me watching this because i am bored, and doesn't even understand how division works properly and yet understand how this thing works>> <<@gamingpompomdrybones says : Guys the answer was 8128>> <<@rasan-w2n says : There is a Numberblocks band because of this.>> <<@piruthvy_pawar says : Watch 20:48 , the largest mersenne prime of 2018 book shows that the perfect number is odd , yeah, it ends with 1 , I think no one saw it>> <<@Cutiegurl123 says : Me: Just use desmos>> <<@doanhcaokhac1735 says : This video was amazing, learned a lot.>> <<@shnailgirl says : Probably stupid but what about infinity? Feels like set theory might b a decent approach>> <<@eduxcwb says : 28 is perfect because it's a sum of 1 + 2 + 4 + 7 + 14 2:41>> <<@steinanderson says : the answer is no>> <<@fibetyjibets says : PERFECT NUMBERS MAKE PERFECT SQUARES OR RECTANGLES STARTING WITH 6 AND 28 THROUGH INFINITY. And every perfect number, including 28 and all perfect numbers upward ([28], [496], [8128], [33,550,336], [8,589,869,056]) can ALL be divided by four in to a whole number. They also can all be divided by four until them come to a mersenne prime. The number 7 is a mersenne prime number. The number 28 is a “perfect number”. 28 ÷ 4 = 7, a mersenne prime. The number 496 is a “perfect number”. 124 ÷ 4 = 31, a mersenne prime. The number 8128 is a “perfect number”. 8128 ÷ 4 = 2032. 2032 ÷ 4 = 508. 508 ÷ 4 = 127, a mersenne prime. The number 33,550,336 is a "perfect number". 33,550,336 ÷ 4 = 8,387,584. 8,387,584 ÷ 4 = 2,096,896. 2,096,896 ÷ 4 = 524,224. 524,224 ÷ 4 = 131,056. 131,056 ÷ 4 = 32,764 32,764 ÷ 4 = 8191, a mersenne prime. All perfect numbers are systemically full of sevens, as the number 28 is, as well as either the 6 or 1 parts of 7. All perfect numbers, except for the first two , 6 and 28, which are separately a pure, even 6 and a pure, even, multiple of 7, are a combination of an odd or even multiple of 7 , plus a 1 or 6, which makes the combo even and a perfect number. An example is 496. 496 is a perfect number. 496 is a combination of 490, which is an even multiple of 7, plus the even number 6. These two interior even numbers are in the perfect number 496. Another example is 8128, a perfect number. The odd multiple of 7, 8127, plus an odd number 1, combine inside 8128. The perfect number 33,550,336 is within a combination of the odd multiple of 7, and all the groups of each boxed subdivion of multiples of 7 within, plus the single and only added number 1 that makes 33,550,336 even, perfect, and logically consistent with all the elements of perfect numbers. This could be expressed as p for perfect number equals some odd(*~) or even(*-) multiple of 7, plus 1 or 6, where 1 attaches additionally to the odd multiple of 7, and 6 to the even multiple of 7. This makes all of these combined odd and even multiples of 7 and 6 or 1 into the perfect number they are. This is not building a perfect number from any multiple of 7, plus a 6 or 1. This is just recognizing the internal parts of perfect numbers. Perfect numbers are a ornaments on a chain of numbers. They are fruit on the number branch. They are charms on a number chain. Their fruit seeds are 1’s and 6’s attached to fruits of multiples of 7 that combine to make each perfect number fruit, and that they are always even and cannot be otherwise because of this structure that systematically forces even numbers. Perfect numbers all are forced to be even as all right angles are forced to be equal. They all want to be even. They all have the systemic “DNA” of the first “sewing stitches” of the properties of rectangular 6 and rectangular 28 , with it’s four mersenne primes of 7 expressed systemically and in some ways alternately and complementary in every fruit of propigated perfect numbers found in the number chain and linear branch of numbers at every perfect number along the way. All perfect numbers express the mersenne primes in dividing by 4 to a mersenne prime, like 28 divides by 4 to the mersenne prime of 7. They alternately express the first stitch of 6 attached to every internal multiple of 7, however astronomical the perfect number may be. I think it’s notable that the first perfect number, 6, if divided by 4, is 1.5, which is 1.4 plus .1, and that 1.4 is 2× .7. An internal .1 makes the 1.4 an even fourth of 6. The 1.4 +1 = 15, combines a fractional multiple of 7 with 1, and does it four times internally to make the 6. And I think it’s also worth noting that the four 7’s in the perfect number 28, interiorlly are 1+6. These interiors of the roots of perfect numbers keep expressing echos of themselves in every perfect number that materializes along the number chain as it’s tree grows ever larger, branching and bearing bigger perfect numbers like fruit. This is like Euclid’s axiom that all right angles are equal. All perfect numbers above 6, divide by 4, are able to be rectangular or square with whole numbers, are a whole number that is the number 1 combined with an odd multiple of 7, or the number 6 combined with an even multiple of 7, making all perfect numbers as reliably even as all right angles are reliably equal. FibetyJibets, May 26, 2026>> <<@laverdadescondida.366 says : ... 3790....>> <<@peacemakerq5385 says : 11.....eleven>> <<@Riyan-t6l says : That rules that guy wrote says everything ends in 6, and 8 but if that’s true then every perfect number is even>> <<@elainecristinadasilva3162 says : 6,28,496,8128,33556036.....>> <<@franzscheerer says : Doch etwas scheint noch nicht zu stimmen. Grok: Genau das ist der Punkt, an dem viele stolpern – und deine Frage ist hervorragend.Du hast vollkommen recht:2p2^p2^p hat nur die ungeraden Teiler 1. Es ist eine reine Zweierpotenz. Und trotzdem teilt 2p2^p2^p die Gruppenordnung Mp2−1=2p+1(2p−1−1)M_p^2 - 1 = 2^{p+1} (2^{p-1} - 1)M_p^2 - 1 = 2^{p+1} (2^{p-1} - 1) .Warum das kein Widerspruch istSchau dir die Zerlegung nochmal genau an:Mp2−1=2p+1⋅(2p−1−1)M_p^2 - 1 = 2^{p+1} \cdot (2^{p-1} - 1)M_p^2 - 1 = 2^{p+1} \cdot (2^{p-1} - 1) Der Faktor 2p+12^{p+1}2^{p+1} ist eine Zweierpotenz (sehr groß). Der Faktor 2p−1−12^{p-1} - 12^{p-1} - 1 ist ungerade (immer, für p≥2p \ge 2p \ge 2 ). Wenn du jetzt prüfst, ob 2p2^p2^p die ganze Zahl teilt, brauchst du nicht zu fordern, dass 2p2^p2^p den ungeraden Teil 2p−1−12^{p-1}-12^{p-1}-1 teilt. Das wäre tatsächlich unmöglich (außer für p=1p=1p=1 ).Stattdessen reicht es völlig aus, dass 2p2^p2^p den Zweierpotenz-Anteil 2p+12^{p+1}2^{p+1} teilt:2p+1⋅(2p−1−1)2p=21⋅(2p−1−1)=2(2p−1−1)\frac{2^{p+1} \cdot (2^{p-1} - 1)}{2^p} = 2^{1} \cdot (2^{p-1} - 1) = 2(2^{p-1} - 1)\frac{2^{p+1} \cdot (2^{p-1} - 1)}{2^p} = 2^{1} \cdot (2^{p-1} - 1) = 2(2^{p-1} - 1) Das Ergebnis ist eine ganze Zahl, weil 2p−1−12^{p-1} - 12^{p-1} - 1 eine ganze Zahl ist. Der ungerade Teil bleibt einfach stehen und wird mit der übrig gebliebenen 2 multipliziert.Beispiel zum Anfassen (p=5, M_5=31)Gruppenordnung: 312−1=96031^2 - 1 = 96031^2 - 1 = 960 Zerlegt: 960=26⋅15=64⋅15960 = 2^{6} \cdot 15 = 64 \cdot 15960 = 2^{6} \cdot 15 = 64 \cdot 15 Elementordnung von ω\omega\omega : 25=322^5 = 322^5 = 32 960÷32=30960 \div 32 = 30960 \div 32 = 30 , eine ganze Zahl. Funktioniert. 32 teilt 64 (den Zweieranteil), der Faktor 15 wird einfach "mitgenommen".Warum das für den Beweis entscheidend istGenau weil die Ordnung von ω\omega\omega eine reine Zweierpotenz 2p2^p2^p ist, passt sie perfekt in den 2-Sylow-Untergruppen der multiplikativen Gruppe. Und genau diese reine Zweierpotenz-Struktur macht den Widerspruchsbeweis so stark:Falls MpM_pM_p zusammengesetzt wäre, müsste ein kleiner Primfaktor (q) existieren, dessen Gruppenordnung q2−1q^2-1q^2-1 zu wenig Zweierpotenz-Faktoren hat, um eine Untergruppe der Ordnung 2p2^p2^p zu erlauben.Das ist die eigentliche Magie des Lucas-Lehmer-Tests: Er nutzt aus, dass die Ordnung von ω\omega\omega maximal im 2-Anteil ist.Verstehst du jetzt, warum deine Beobachtung ("2^p hat keine ungeraden Teiler") korrekt ist, aber trotzdem kein Problem darstellt? Die Zweierpotenz muss nur den Zweieranteil der Gruppenordnung "auffressen", nicht den ungeraden Teil.Möchtest du noch ein größeres Beispiel (z. B. p=7) oder die genaue 2-adische Valuation (wie viele Zweierfaktoren die Gruppenordnung genau hat) sehen?>> <<@MrLeast-ISO says : Acting like I understand a single word being said💔>> <<@FormerlyAVM says : Obviously>> <<@tarraknyc says : Is there a way to block private equity channels?>> <<@theGoldenknife_of_rivals says : the sigma funcation*>> <<@sundareshvenugopal6575 says : This channel is garbage.>> <<@decimusmaximus9978 says : This video just proves to me that I don't have a mathematical mind>> <<@Miguel-x2l says : The next perfect number is 8128. It's proper divisors (\(1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032,\) and \(4064\)) sum to exactly \(8128\) My favorite subject is calculus 😊>> <<@davidsilva-jf4fl says : I have the formula.>> <<@Roadrunner-hm5gw says : Wonderful video.>> <<@Vinxz_en says : We now know the formula to this 1. 6 2. 28 3. 496 4. 8128 5. 33,550,336 6. 8,589,869,056 7. 137,438,691,328 8. 2,305,843,008,139,952,128 9. 2,658,455,991,569,831,744,654,692,615,953,842,176 10. 19,144,557,081,991,206,112,108,643,000,318,418,580,314,11>> <<@LuanDSDK says : 8128>> <<@choen_ma says : P = 165,179,921.>> <<@LucasReyes-AerionBrightflame says : Lmao 6 7>> <<@AnotherFred-z8j says : Fun fact (like.. just fun little story): Between end of '83 and end of '87, I was employed in a company which had a 'scientific computer' departement. Just two persons maintening - and creating programs for - the big Norsk Data computer used by engineers to develop the product(s). When that news about the 'biggest prime number ever' came out (2^216091-1) came out, the one called Hubert wanted to print that number. So he set up that program and printed it. As it was impossible for that computer to handle big numbers (Fortran 77 IIRC), he converted digits to ascii, something like 0 being A, 1 is B etc.. and run that program. All happy he was showing the listing, several pages in 'accordeon' and it was impressive, till I pointed out that the last digit was (IIRC) 8.. He forgot to substart 1.. He printed that again. I still have that listing somewhere I think. Hubert is a legend to me.. also one of the first guys to get a McIntosh when it was available here.>> <<@KingLarbear says : i watched this again>> <<@James-ll3jb says : So what exactly is the "problem" here? There are truths that cannot be proven. (Gödel) That's the answer. The proof is the spoof.>> <<@sloth9494 says : It's 7>> <<@stevemarx1646 says : I'm quitting around 2:45 because 28 from your explanation should be 1,2,4,7,14. Not what you stated which is 1,2,3,4,5,6,7. Am I missing something?>> <<@plugsuit.bassist says : you look like the guy from viva la dirt league>> <<@dadosenigmáticos says : Bruh 10 isn't a perfect number? Or I dumb? 1+2+3+4= 10. Is not a perfect number? It Is my question>> <<@Keruux says : "unlikely to find another prime number anytime soon" *another gets discovered literally 6 months later*>> <<@romilsonalves6881 says : 6 28=2+8=10=1+0=1 496=4+9+6=19=1+9=10=1+0=1 8128=8+1+2+8=19=1+9=10=1+0=1 ...>> <<@Electron6967 says : Did Newton try to solve this problem? He would have absolutely solved the problem>> <<@JulyRodriguez-z6j says : Those are stupid questions they gave monkeys to stay destroying their own heads for years. Everyone needs the fundamentals>> <<@sanyochek496 says : 496 is like me>>