The New Largest Prime Number Ever Discovered! (confirmed today)

[@Domotro]

Had to pause everything and make this video when I read that it had been confirmed today! Here's a link to the official press release from "G.I.M.P.S." with more info about the software and people involved in this discovery: www.mersenne.org/primes/?press=M136279841 Here's a link to a livestream I did last week when it was quietly announced that a new "probable prime" of this type was discovered. This livestream discusses some more things about Mersenne primes (which this new prime is the 52nd known one of): kzbin.infoSaRkK_wJbU8?feature=share Stay tuned for my Grade -2 finale episode coming out on my @ComboClass channel pretty soon. And make sure you've caught up on my previous main episodes from the grade here: kzbin.info/aero/PLsATqXCEHAbpDaoO9SCY3T9l4ak98kM2F

[@Ninja20704]

It has been so long since we found a new Mersenne prime and wow, the difference is size compared to the last one in just jawdropping

[@Domotro]

Yeah, almost 6 years, and the size of this one is larger than if you doubled the size of the last record-breaking one more than 50 million times!

[@acelm8437]

Yeah I almost thought they had stopped making progress. Guess they had never stopped checking and there just happened to be a huge gap.

[@bjorntorlarsson]

I found one of those free online calculators that finds all divisors of a number. I was impressed by how it listed them in real time as I was typing the digits (base 10). Until the 15th digit when it hesitated for a few seconds. And the 16th digit number it didn't want to calculate before Chrome said that the page is unresponsive. I don't think it is made for numbers with millions of digits. That's another sport.

[@bjorntorlarsson]

I typed that new prime on my pocket calculator, and divided it by 7 to test it. The answer is 3 (gotcha!) If one turns the calculator upside down. Otherwise it looks like E, but then the 7 looks like L. So... research ongoing!

[@bjorntorlarsson]

Only 52 Mersenne primes found out of 136,279,841 candidates. Although 4 primes are already among the 7 first candidates of 2^n-1. Hmm. How many straws does a haystack consist of?

[@tomkerruish2982]

There are fewer candidates than that. The exponent must itself be a prime. There are approximately 5.7m primes less than 10⁸, so the number of potential candidates would be in the neighborhood of 7.5m. There may be further restrictions on the exponent of which I am unaware.

[@jesusthroughmary]

​@tomkerruish2982 there are no further restrictions

[@EvanEscher]

(2^2)-1, (2^3)-1, (2^5)-1, (2^7)-1 are all primes. 2, 3, 5, and 7 are the first 4 primes too. (2^11)-1 is not prime though (11 is the 5th prime)

[@jesusthroughmary]

@@tomkerruish2982 there are no further restrictions

[@skiller.X]

i was using that prime as my password, time to change it now, thanks!

[@TymexComputing]

Same comment was on matts Parker channel...

[@TurdBoi666]

Too late. I have already logged in through your account

[@EvanEscher]

So what you're telling me, is that all mersenne primes are hyper elevens in binary

[@ker0356]

1, 1, 1, uhh, 1

[@jesusthroughmary]

I kept waiting for him to say this

[@Hacker1MC]

That's over 17MB of ones. Bigger than a short-term Minecraft world

[@815TypeSirius]

Domo, ありがと。Prime beef updates. Yum yum.

[@shutupimlearning]

normally I have no interest in number theory, but your enthusiasm is infectious!

[@jorgechavesfilho]

Great! I've watched some good videos on this discovery, but Domotro's is by far the best.

[@MrDowntemp0]

Do they always check that same prime +/- 2 and 6 to see if its a twin or sexy prime? Would be neat if the biggest prime has a feature like that. But maybe Mersene primes aren't as likely to do that. Do you think there's anything to be learned by searching for primes lower than the biggest, since there's big gaps between each record breaker?

[@jesusthroughmary]

We really got a new Mersenne prime before GTA 6

[@RobertBlair]

What other bases can we use to find primes of form 1111...111? In base 3, 111 = 13, and probably more

[@ophios]

two the power of some very large number.. aw man, if only one of the ones was a five

[@TymexComputing]

Your channel is the best for normal user :)

[@TRex-fu7bt]

Mersennes have that funny property of being very large in magnitude but very small to describe

[@threeholepunchmike3549]

if you want to see the number, stop by standupmaths matt parker of numberphile fame. he put 100k numbers per frame for 6+ minutes lol

[@Domotro]

I'm going to watch that later today. Matt Parker is great

[@kerrynewman1221]

I saw that earlier.

[@picrust314]

What is the largest non-Mersenne prime?

[@ra1nman_mashups]

I saw that a few mins ago lol

[@maynardtrendle820]

​@@DomotroI just watched it on .25 speed, so that I could absorb the sheer numerocity😂.

[@miroslavzderic3192]

father Pucci when someone chews gum in church:

[@gheffz]

Excellent!

[@jf3518]

So this number is roughly 14GB in size. Gonna make RSA pretty sercure though :D

[@jortor2932]

Waiting for u only your talk on this but even before u got greeted by that small creature

[@maynardtrendle820]

I read it. It was SUPER boring.😢

[@colinmaharaj]

awesome

[@colinmaharaj]

Whats the C code to test for this

[@juandesalgado]

There is pseudo code in the wikipedia page for the "Lucas-Lehmer primality test"... but you will have to use some arbitrary-precision arithmetic package, like openssl/bn.h, BigInt, or boost.multiprecision.

[@z0ru4_]

Je m'en rends seulement compte mais il a pris du poids un peu le pauvre

[@martian8987]

Still not big enough

[@seamusbolger5519]

Do we know what the last digit of this new prime is?

[@jesusthroughmary]

The exponent is 1 mod 4, so the last digit is 1

[@jesusthroughmary]

Mersenne primes can only end in 1 or 7

[@dan32767]

2

[@Hacker1MC]

@@jesusthroughmary (2^2) - 1 = 3

[@jesusthroughmary]

@@dan32767 so it's even?

[@baubobbi371]

oh.

[@gheffz]

Add 2 to it?

[@asheep7797]

It won’t be prime, as all primes of the form 2^n+1 have been proven to also be of the form 2^2^n+1.

[@MrDannyDetail]

@@asheep7797 If 'm' is a Mersenne prime then what you say wouldn't preclude m+2 from also being prime, because adding two to the Mersenne prime has already stopped it from being of the first form anyway, but it would make a number that was impossibly big to test, because most large numbers are far too big to be tested for primality, but there happens to be a shortcut of sorts for testing Mersenne numbers for primality which means we can test far larger numbers if they happen to be of that form.

[@gheffz]

@@asheep7797 Yes, unlikely - agree! (or likely at that massive scale?)... twas a joke. But I love this saying "2, the oddest of all the primes!"

[@jesusthroughmary]

@MrDannyDetail adding 2 to any Mersenne prime does in fact give you a number of the form (2^n)+1, which is only prime when n = 2^k

[@MrDannyDetail]

@@jesusthroughmary Oops sorry, for some reason I was getting confused and thinking the first form you gave was the Mersenne formula itself, when obviously that has a '-1' rather than a '+1'.

[@yanntal954]

Did whiteboards file a lawsuit against you? 😂

[@815TypeSirius]

BTW we have new infinite recursive programming languages coming out that can make almost any calculation infinitely scaleable. This is very big. I bet we see a new prime in less than 10 months, give or take.

[@anto_fire8534]

yeah no programming language wont change anything

[@815TypeSirius]

@anto_fire8534 how are people this confidently ignorant. Go learn about parallelism in compute and come back with an apology.

[@anto_fire8534]

@@815TypeSirius GIMPS (Great internet mersenne prime search) is the very definition of parralelism, it uses a large amount of personal computers to try to find mersenme primes. current programming languages can already let you handle stuff in parralel very well. having new languages wont change anything. furthermore, the ones who made the project have had decades to optimize their code to the limit, having a new programming language wont magically make everything faster by 10x. i owe you no apologies you're the one who seems clueless about what you are talking about

[@anto_fire8534]

in short they dont need new languages to handle doing stuff in parralel, they're already doing it.

[@815TypeSirius]

@anto_fire8534 good luck in life. Muting you, assuming you're not a bot.

[@darksaurian6410]

who cares

[@asheep7797]

I do!

[@adil0028]

I do