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  • 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.

You remember prime numbers right?

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B1 US prime prime number exponent digit encryption software

Why Do We Need a 23 Million Digit Prime Number?

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    joey joey posted on 2021/04/17
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