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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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# Why Do We Need a 23 Million Digit Prime Number?

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joey joey に公開 2021 年 04 月 17 日