The largest Mersenne prime is 2^82589933-1....so far

[@Darkev77]

Best Math professor on KZbin hands down.

[@mkiiespi7078]

Breaking news! We found a new biggest Mersenne prime (and by extension, also the biggest prime we know): 2^(136,279,841)-1!

[@DrTrefor]

Glad I added the “so far!” To the title:D

[@singingbanana]

Great video

[@aashsyed1277]

hi james

[@omargaber3122]

Update: A larger number has been found, which is: (2^(136,279,841)-1)

[@namduonghoang6301]

The MERSENNE PRIMES formula is part of the following formula 1. Let a, b, n be natural numbers with a>b - {[a^(a-b)]-[b^(a-b)]}/[(a-b)^2] is always a natural number. If {[a^(a-b)]-[b^(a-b)]}/[(a-b)^2] is prime then a-b is prime. If a-b is composite, then {[a^(a-b)]-[b^(a-b)]}/[(a-b)^2] is composite. - If [(a^n)-(b^n)]/(a-b) is prime, then n is prime. If n is composite then [(a^n)-(b^n)]/(a-b) is composite. 2. Let a, b, n be natural numbers where n is odd - With a+b being odd, {[a^(a+b)]+[b^(a+b)]}/[(a+b)^2] is always a natural number. If {[a^(a+b)]+[b^(a+b)]}/[(a+b)^2] is prime then a+b is prime. If a+b is composite then {[a^(a+b)]+[b^(a+b)]}/[(a+b)^2] is composite. - If [(a^n)+(b^n)]/(a+b) is prime, then n is prime. If n is composite, then [(a^n)+(b^n)]/(a+b) is composite.

[@khalilmohammed2297]

could you make a playlist for the AXIOMS OF SET THEORY

[@ffggddss]

I gather it would have been way too involved to go into in this video, but this begs the question, "How does the Lucas-Lehmer test work for Mersenne numbers?" Anyone who's fiddled around with Mersenne candidates, M(p), where p is prime, has likely noticed that any prime divisors of M(p) are always of the form, 2kp + 1. But the Lucas-Lehmer test is apparently more streamlined than that. Fred

[@arnavbhavsar8567]

Is it possible there are prime numbers between any of the 7 largest prime numbers?

[@DrTrefor]

Definitely possible. For instance, there could be a non-Mersenne prime in between those. My understanding is that while Mersenne primes have been exhaustively searched (i.e. we know there isn't a Mersenne in between the 7) that undoubtably there are many non-Mersenne's in that range.

[@alephomega955]

@@DrTrefor I claim there are at least 100 primes in between the second largest prime number and the largest prime number. Now all everyone has to do is prove me wrong.

[@NURULISLAM-bq7br]

Great video. Thanks a lot!

[@zemoxian]

I’m not sure why, but I started wondering if Rayo’s number could be prime. Then I started to wonder whether or not any properties of such a number could be known given the description of the actual number is too large to be written using the matter in the observable universe. Then I wondered if the largest prime less than Rayo’s number might actually require more than a googol symbols to be described. Finally, I’m wondering if there’s a way to place a civilization/entity on the Kardechev scale that could actually make practical use of Rayo’s number. I’m guessing it has to be higher than 7. Can such a thing even exist?

[@DrTrefor]

It naively seems to me that adding additional requirements (like that it must be prime) would make it harder to express and thus require more symbols than without that condition, so I guess the largest prime number expressible in a google symbols from set theory is smaller than rayo's number.

[@أنس-ت1س]

@@DrTrefor I have discovered a new prime number for real

[@أنس-ت1س]

A new biggest one

[@أنس-ت1س]

@@DrTrefor I can tell you that number if you want to

[@أنس-ت1س]

@@DrTrefor it is (2*10^2^1000000038839738)-1

[@feynstein1004]

Hmm I'm probably being a dunce here but wouldn't it be easier to check for the factors of a candidate n -1 or n+1 and then use that information to check if n has any factors?

[@DrTrefor]

There are a whole basket of different types of tricks for testing primes...but each has a computational cost associated with them, so it is a question of using the more computationally efficient tricks.

[@feynstein1004]

@@DrTrefor Ah okay. I hadn't taken that into account. Thanks for the reply :)

[@penklislawnmowing4508]

I didn't realise that 82,589,993 is only a semi prime number 2239*36,887= 82,589,993

[@geoffseyon3264]

The number is 82,589,933 not …993

[@beneyal9264]

there is my new largest prime number, 2^93,786,361-1

[@GinoGiotto]

Well the result from a user on GIMPS says it's not prime. Here is the link: www.mersenne.org/report_exponent/?exp_lo=93786361&exp_hi=93786361&full=1 However sometimes computers make mistakes, so if you really believe your number is prime you can join gimps and test this number yourself. If your result is the same of the previous user, then I'm sorry but your number is definitely not prime. Is your result is different from him then it could still be prime, but frankly that's unlikely.

[@beneyal9264]

@@GinoGiotto it's a prime number for me, because there are no known factors

[@GinoGiotto]

@@beneyal9264 Did you read my comment? Do you know what GIMPS is or how it works? Saying "there are no known factors" means absolutely nothing. Right now it has been verified that your number has no factors smaller than 2^77 but of course it could still have bigger ones, so it's not a sufficient argument to say that's prime. And as I said your number is most likely NOT prime since the LL test gave a negative result. There is no such thing as "It's a prime number for me", it's either prime or isn't, it's math, not a matter of opinion.

[@beneyal9264]

@@GinoGiotto ok

[@GinoGiotto]

@@beneyal9264 Mh not sure if you understood, but anyway I have a little curiosity. It happened that your number is exactly the same as in this video kzbin.info/www/bejne/hqbYpKp3rdWtn7c, I think this is quite a funny coincidence, since the amount of possible prime exponents in this region is very large. Did you just saw the video and copied that number for no apparent reason? Or maybe you have two channels idk

[@VasanthKumar-cg1wo]

Please help. How to checking 2^82589933-1 coding??

[@KienVo1]

Mine is 2^7-1 and I memorized all digits

[@jahonysantiagoguerrero4463]

Lâu lắm rồi mới được nghe lại bài này. Hay lắm ạ 😘

[@Diamond_Hanz]

A million and one

[@DrTrefor]

Haha:D Actually I think someone on the playlist did a video on this number:D

[@ffggddss]

@@DrTrefor Yes, I saw it, though I can't recall who it was. Meanwhile, 1,000,001 = 101·9901 Fred

[@Michael-jt3lx]

Why do we care about large primes tho

[@DrTrefor]

The dominant application is encryption, was relies on the fact that it is very hard to factor extremely large numbers. If we were able to discover a method to find primes vastly more efficiently, this same method would end up undermining modern encryption.

[@Johnpatrickbrithon6109]

@@DrTrefor Hi professor, what if I would send a new simple formulae for computing such very large prime numbers?

[@SoI-]

@@DrTrefor And we like big numbers.

[@ToanPham-wr7xe]

😮