Largest Known Prime

1. Sep 17, 2013

MostlyHarmless

This news is a little dated, but I still found it interesting and wanted to see what everyone else thought about this years discovery of a new "largest" prime: $2^{(57,885,161)}-1$ its 17,425,170 digits long and would span all 7 harry potter books twice. Written out in plain text it would take up 22.5mb!

Is the size of primes we find only going to be limited by our computing power? Is there any other way of finding mega primes that aren't Mersenne primes($2^p-1$)?

(Fun facts credited to Adam Spencer from his fascinating TED talk which can be found here: Adam Spencer: Why I fell in love with monster prime numbers #TED : http://on.ted.com/gmnG)

2. Sep 17, 2013

Staff: Mentor

And not 17.5 MB?

3. Sep 17, 2013

Greg Bernhardt

4. Sep 17, 2013

AlephZero

You forgot about the commas after every three digits

5. Sep 17, 2013

Staff: Mentor

$$\frac 4 3 \times 17425170 = 23233560$$

Now 22.5 MB is 0.7 MB short.

6. Sep 17, 2013

MostlyHarmless

Hey, I was just posting what I read and learned from that talk, lol.

7. Sep 17, 2013

MrAnchovy

FAIL $\frac{223233560}{2^{20}} = 22.5$

8. Sep 17, 2013

MrAnchovy

Interestingly, its exactly 22.5 MB.

9. Sep 17, 2013

Staff: Mentor

Depends on the MB. But OK, if you select two arbitrary conventions, you can get this result.

I guess with two arbitrary conventions you can get ANY result :tongue2:

10. Sep 17, 2013

jackmell

Enjoyed video. Thanks. Looks like they are limited by our computing power and although there are methods to finding other primes, Mersenne primes take less effort to do so. You can google Primes, Mersennine primes, and the Lucas-Lehmer primiality test if you wish to learn more about it.

11. Sep 17, 2013

MrAnchovy

Save time googling, start here.

12. Sep 17, 2013

jackmell

I got a better idea. Since Jesse brought it up, how about he implement the Lucas-Lehmer algorithm in say Mathematica, on a number $2^p-1$ that he believes can be tested for primality in 9 hours, set it running before bed time say 10:00p, run it all night till 6:00a, and then report the results for us here.

Ok, little more work for you Jesse. Got time? Say do this for a group of (small) mersennine primes, record how long it takes to determine primality with your software/hardware setup, plot the points, then extrapolate how long it should take to compute the other known ones, see if they agree with known times, then suggest how long it would take for newer ones.

Last edited: Sep 17, 2013
13. Sep 17, 2013

MostlyHarmless

That doesn't sound completely "not-fun" but alas I don't have an over abundance a time And while I did get a free Mathematica license from my school I haven't installed it yet because my computer is well.. sub-par. :) maybe this summer..

14. Sep 17, 2013

lendav_rott

Wasn't it proven that there is no function that returns a prime for every integer? Aside the wow factor, is there an application for such discovery? :D

15. Sep 17, 2013

MostlyHarmless

Whether it was proven that one cannot exist I'm not entirely sure, but as fas as application, there is a foundation offering a substantial sum of money to find one, 1 million dollars I think? :)

16. Sep 17, 2013

Staff: Mentor

Unless I misunderstand what you mean, implementing function that will take n as a parameter and will return n-th prime, is trivial. Actually it was already done, many times. See for example this thread.

I can't guarantee these functions will work fast, nor can I guarantee your computer will have enough memory to run them for every n, but these are technical details.

17. Sep 17, 2013

MostlyHarmless

Yeah, I think the problem is you can't possibly test all values for n. But if you are asking about the expression I posted in the op, that doesn't always work and simply describes the form of a specific type of prime number.

18. Sep 17, 2013

Staff: Mentor

ROFL, I am just working on a program, so when I saw "function" I thought in terms of a program function, not a mathematical one.

19. Sep 17, 2013

MrAnchovy

Does the target hardware work in native decimal or is it arbitrarily implemented in binary? :tongue2:

20. Sep 18, 2013

lendav_rott

By the time someone Manages to find one and prove it works in a domain of ℝ the inflation will have made 1m dollars worth a sizeable 7 course lunch.