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The largest known prime number has emerged. It has more than 23M digits

washingtonpost.com

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Re: The largest known prime number has emerged. It has more than 23M digits

#31

Post by nopacience »

mattashii wrote: post #9
cnvogel wrote: post #7

Quote from the Article: """The figure is calculated by multiplying 2 by itself 77,232,917 times and then subtracting 1.""" Would HN agree that multiplying 2 by itself once is 2⨯2 = pow(2,2), twice is 2⨯2⨯2 = pow(2,3) and N times yields pow(2,N+1)? The Mersenne Prime found is pow(2,77232917) − 1, hence the article got the number wrong?

If you're going that way, you can also interpret it - pardon my programming - as the following: int result; for (int i = 0; i ... which obviously results in 3. Also a (mersienne) prime, but not quite as big as you'd expect, and certainly not millions of digits long.

  int result; 
  for (int i = 0; i
so of course it will always be 3

Re: The largest known prime number has emerged. It has more than 23M digits

#32

Post by colanderman »

nopacience wrote: post #31
mattashii wrote: post #9

Earlier quoted context omitted.

If you're going that way, you can also interpret it - pardon my programming - as the following: int result; for (int i = 0; i ... which obviously results in 3. Also a (mersienne) prime, but not quite as big as you'd expect, and certainly not millions of digits long.

int result; for (int i = 0; i so of course it will always be 3

That is the joke.

Re: The largest known prime number has emerged. It has more than 23M digits

#33

Post by tzs »

TekMol wrote: post #4

I have two questions: 1: How do we know it's the largest known prime number? What qualifies as a 'known' prime number? Is there an official registry somewhere? 2: Are all prime numbers smaller then this one also known? Or could somebody still come up with an unknown 'not very large prime number'?

> Are all prime numbers smaller then this one also known?

No, and they will never all be known.

There are approximately n/log(n) primes less than n. In this case n is 2^77232917 - 1. n/log(n) is approximately 8.6 x 10^2317930.

If you gave every person on Earth a million million processors [1], running at 1000 GHz each, that could find a prime each clock cycle, and each person used a time machine to send their processors back to when the dinosaurs went extinct so they by now they have all been running 65 million years...we'd have found about 1.4 x 10^49 primes.

Heck, if every particle in the universe was somehow made to computer, each of which could produce a new prime in the time it takes light to travel the Planck length (the smallest meaningful length possible in the universe), and they had all been doing this since the beginning of the universe, they would have discovered by now about 10^147 primes.

That's a mere 0.000...00012 percent of the way there, where I've skipped more than 23000000 zeros.

Re: The largest known prime number has emerged. It has more than 23M digits

#34

Post by Someone »

throwacide wrote: post #29
Someone wrote: post #24

Earlier quoted context omitted.

We know for sure that we don’t know all smaller primes. For example, there is at least one prime between 2^77,232,915 and 2^77,232,916 that we don’t know ( https://en.wikipedia.org/wiki/Bertrand%27s_postulate ) (That’s a very loose bound. I think that, for any N > 2, there are more primes than squares of integers less than it)

What’s the significance of primes being one less than large powers of 2? Does this mean base-2 is the most natural base?

2 is the only integer n such that n-1 = 1.

That’s significant because (n^m) - 1 is divisible by n - 1.

So, for example, 125320078^35785332 - 1 is divisible by 125320077 and, hence, not a prime.

So, this problem has been solved for all n>2.

n^m + 1 is a more difficult problem. For example, for n=10, we get 2: prime, 11: prime, 101: prime, 1001: composite, 10001: composite, etc (at least the 8,000 following are composite. See https://math.stackexchange.com/questions/2108085/is-there-a-...)

Re: The largest known prime number has emerged. It has more than 23M digits

#35

Post by SketchySeaBeast »

pavel_lishin wrote: post #14
SketchySeaBeast wrote: post #6

Earlier quoted context omitted.

Isn't that the point of projects like folding@home? And hive mind AI is literally skynet.

The Borg would be a better analogy; Skynet was just an AI with a specific purpose, no hive-mind about it.

Well that's more reassuring.

Re: The largest known prime number has emerged. It has more than 23M digits

#36

Post by throwacide »

Someone wrote: post #34
throwacide wrote: post #29

Earlier quoted context omitted.

What’s the significance of primes being one less than large powers of 2? Does this mean base-2 is the most natural base?

2 is the only integer n such that n-1 = 1 . That’s significant because (n^m) - 1 is divisible by n - 1 . So, for example, 125320078^35785332 - 1 is divisible by 125320077 and, hence, not a prime. So, this problem has been solved for all n>2 . n^m + 1 is a more difficult problem. For example, for n=10 , we get 2: prime, 11: prime, 101: prime, 1001: composite, 10001: composite, etc (at least the 8,000 following are com…

Oh, neat. Thanks.
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