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Why Do We Need a 23 Million Digit Prime Number?

Why Do We Need a 23 Million Digit Prime Number?

You remember prime numbers right? Numbers that can only be evenly divided by
one and themselves? Well it turns out finding prime numbers is
not only useful for protecting data, but it could make you money! On December 26th, 2017, the largest prime
number ever discovered was found by Jonathan Pace of Germantown, Tennessee. The number is over 23 million digits long,
meaning I don’t really have time in this video or my entire life to list the whole
thing out, but it’s easier to call it by its nickname, M77232917. It gets this name because that’s the exponent
you raise 2 by to find it. Oh, and don’t forget to subtract one when
you’re done multiplying 77,232,917 twos together. Otherwise you just created a number you can
divide by two and you’ll have wasted all that time. Prime numbers found this way, by raising two
by a prime exponent and subtracting one, are called Mersenne primes, named for a 17th century
French friar, hence the capital “M” in the shorthand name. 3 is a Mersenne prime, since it’s two to
the second power minus one. Same for 7, which is two to the third power
minus one. But the exponent has to be prime. Two to the sixth power minus one is 63, which
is divisible by 3 so, not a prime. 9 of the 10 largest primes found to date are
Mersenne primes, not because they’re the most common — the Prime Number theorem tells
us there must be a simply huge number of undiscovered primes between this newly found one and the
next largest Mersenne prime — but we find them because that’s how we keep searching
for them. In fact you can be a part of the search for
the next one! You don’t even have to do the math yourself,
just some software provided by the Great Internet Mersenne Prime Search, or GIMPS! The software uses the idle processing power
of your CPU to run what’s called the Lucas-Lehmer test, where Mersenne numbers are checked against
a specific set of numbers. If the Mersenne number you’re checking divides
evenly into a certain number in that set, then it passes the test and is indeed a prime
number. Obviously it takes quite a bit of horsepower
to see if a 23 million digit number divides into an even bigger number, which is why the
project needs the public’s help. Almost 200,000 users are running the GIMPS
software and if their PC runs a number that passes the test, they could win money. Pace is eligible for a $3,000 prize, and whoever
finds a 100 million digit prime could win $150,000 dollars.It’s like cryptocurrency
mining for those of us that can’t afford to buy a dozen graphics cards. You may wonder why we bother searching for
primes at all? Why for the glory, of course! We’ve only found 50 Mersenne Primes and
next to almost every one of them is the finder’s name for all of nerdy eternity. Plus prime numbers play a crucial role in
keeping data secure. One standard, RSA encryption, relies on multiplying
two large prime numbers together to generate a key. Knowing the two primes that went into the
key is the secret to decrypting the data, but it takes an impractical amount of computational
power and time to suss out what those numbers are if you don’t already know them. So the key can be public and your data is
still secure. Of course since the Mersenne primes we’ve
been finding lately are tens of millions of digits long, these may not be the best candidates
for encryption. If you see a key that’s an absolutely huge
number, it won’t be hard to guess which Mersenne prime went into it. Gigantic primes won’t be useful until quantum
computing is used to break RSA encryption, and even then we may just use a different
method of protecting data. So there may not be much practical use in
searching for Mersenne primes, aside from winning that $150,000 for running a program
while you watch youtube. I gotta download that software when I get
home. Before you run off and download GIMPS, go
ahead and subscribe. And for more math, find out how ham sandwiches
are helping us understand the universe, here. The largest prime found by hand is M127, so
we’re obviously a bit past that by now. Until next time, I’m Julian, don’t forget
to share that sweet prize money with me when you win.

100 thoughts on “Why Do We Need a 23 Million Digit Prime Number?”

  1. When RSA gets broken by quantum computing, just adding larger primes isn't going to help in any way… So realistically, these primes will never be useful, according to Seeker at least.

  2. I thought there was no algorithm to prove a number was prime after X huge number of digits. You could only say probably it was prime?

  3. Your math is wrong bc the Universe is electric. If you take into account the flatness of the planet Earth, and the electricalness of the Universe, you will see any Prime you want. Even Amazon Prime, which f#cking sux.

  4. #seeker why not grab any insanely long digit that end in a 5, square it, and then add 1? wouldn't that give u access to whole range of primes?

  5. I only count using numbers that have their own nicknames: Uno, Deuce, Dozen, Baker's Dozen, Fitty, Gross, M77232917… (I skipped a few)

  6. Please don't download GIMPS if you didn't know what it is. Lucas-Lehmer formula is very CPU intensive, it will shorten lifespan of your device!

  7. Could decimals be prime numbers? Could fractions be prime numbers?
    Could a prime number have 1 googolplex digits?

  8. If you have processing power to spare on your computer I would suggest running [email protected] rather than GIMPS.

    "[email protected] (FAH or [email protected]) is a distributed computing project for disease research that simulates protein folding, computational drug design, and other types of molecular dynamics. As of today, the project is using the idle resources of personal computers owned by volunteers from all over the world. Thousands of people contribute to the success of this project."
    (From )

    No, you don't get 150 000 bucks. And yes, I love primes and could use 150 000 dollar.

  9. I’m not a fan of gimps, I had it on my computer and I realized my battery life was absolutely awful so I checked what was using power and it said 85% of battery usage was from gimps

  10. They're also used for (non-cryptographic) pseudo-random numbers. The Mersenne Twister is a generator that consists of an LFSR whose period is a Mersenne prime.

  11. Or download World Community Grid and help cure cancer, AIDs, malaria etc for no reward instead of chasing a prime number for cash.

  12. Its just number. We cannot use it or read it or write it . So what's the point of getting such huge number? I think you should talk technology behind it

  13. for(int i=0; i<∞; i++){
    if(prime == true){
    Log.d("log", list_of_primes.getText().toString());

    I just solved prime numbers with java, you're welcome humanity.

  14. Yeah, but if you have a notebook with some Intel CPU ending with Y or U, you can forget about running the program. Because you've bought piece of crap. 🙂
    And even if you have notebook in general, running this will make your CPU a air heater. And possibly shorten it's lifespan.
    Only on decenlty powerful desktops, with proper cooling (ideally water) you can do something like this.
    I really don't like the given definition of primes. Yeah, EVERY number is divisible by 1 or itself. It's obvious, we shouldn't even include it.
    Define primes using composites. That the number cannot be breaken down any further. Or…geometry. That the number cannot be any (n-dimentional) rectangle, but only straight line. I admit, it's little bit more abstract, but it also get's to the point.

  15. Just take a Mersenne prime, like this newly discovered 2.3 million digit prime.
    2^ Mersenne prime= bigger Mersenne prime
    2^bigger Mersenne prime= even bigger Mersenne prime
    Keep repeating till you have a 100 million digit prime

  16. Solves Riemann Hypothesis. Discovers 200 new prime numbers, collect prize money for primes, then reveal you have solved the Hypothesis for another million.

  17. So if I take 2 to the M77232917 power like the entire 23 million digit long number and subtract 1, is that a bigger prime number? Since the exponent is prime? Or am I thick.

  18. Don't you think, this software could be only out for public just to crack prime number, so then can break already encrypted data. Cheers

  19. 73819937748198747828837289376499168462886376386486387640079859837720984764829198736784991999384782910093772894672861977387367465245164165267307496296277386537627286375529539572662849638724735377386075836499477472982663753524166375285393$627286262727636379928387390109828377374783950509599584727819161541314152563847399287636718900029298287262625141413341526759506059477362627281816153738392827382892287

  20. Just like many others on this channel, this video was clickbait. I have gained zero knowledge. The question was "why do we look for primes?" and the only thing that you said was "if you find it, you get money". That's obviously just a motivation to get more people to join the search and doesn't tell at all, what the point of it is. And by the way, the chance of finding the prime is really really small, it's basically like a small lottery which you pay for with your prossesing power.

  21. Hi bro. I found out two fonctions can generate prime number under 100. But over that numbers alot of constraintes should be considerated… too I going to be famous 🙂

  22. The number 23 was always my favorite number. I never knew why. I always wondered why it was important. I would say 23. When asked why I would say I don’t know. As time went on I likes how 23 was lebron James number when I was into basketball. When I was into space and science I liked it cause the earth was on a 23 degree angle so perfectly that we have seasons and the earth has the ability to sustain life. As time went on I saw it more and more. Videos I watched where 23 mins long. My dad won 10k dollars from the loto from playing the number 23. It just creeps it’s way into my life. It’s so strange. Btw I am not born on the 23. But my dad mum am all 3 grandparents are.
    April 23
    August 23
    November 23
    December 23
    My dad won the loto on the 23 of November. It is so strange.
    And now a 23 million didgit prime number W H A T

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