Mathematicians Find Biggest Prime Number Ever

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Not only is this the biggest prime number ever, it smashes the previous record by five million digits. :eek:

This mathematical monster was discovered by Curtis Cooper at the University of Central Missouri in Warrensburg as part of the Great Internet Mersenne Prime Search (GIMPS), a collaborative effort to find new primes by pooling computing power online. It has 22,338,618 digits in total.
 
The prime numbers are infinite, and there is little practical use in discovering one, but the search is a good way to put computing hardware through its paces.
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Curious how they check if a number is prime, do they simply brute force divide it by every number up to n/2 to see if the answer is an integer?
 
sfsuphysics said:
Curious how they check if a number is prime, do they simply brute force divide it by every number up to n/2 to see if the answer is an integer?
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That is a good question. Once you try the first few numbers you can immediately throw out a significant portion.
If it isn't divisible by:
  • 2 - Throw out any even numbers and all numbers between n/2 and n/3
  • 3 - Throw out any number with digits that sum to a multiple of 3 and all numbers between n/3 and n/5
  • 5 - Throw out any number ending in 0 or 5 and all numbers between n/5 and n/7

I'm sure they have many more rules like these to reduce the workload.

Come to think of it, they probably just divide it by all known primes smaller than the number.:p
 
sfsuphysics said:
Curious how they check if a number is prime, do they simply brute force divide it by every number up to n/2 to see if the answer is an integer?
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sqrt(n), but I'd assume something like that with the various optimizations (e.g. look for a 5, sum the number's digits mod 3 and check for zero, check last three digits for divisibility by 8, subtract the sums of odd and even digits and look for 0 or 11, etc).
 
They kinda lost me when they admit the number is functionally useless...
 
All that number crunching could have been used to find cures for diseases. Oh well, at least we have a new useless prime number. That's almost as good. :rolleyes:
 
viscountalpha said:
The full number. All the digits. Much like the bacon, give me all the digits you have.
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Interestingly the truncated version of the number gives the following errors
windows calculator: Invalid input on any number beyond 4 digits after the power of sign
android 6.0: simply reports the infinity symbol for the result.

also the number locks up my pc when i copy it to the window... you can download the text file here http://www.mersenne.org/primes/?press=M74207281 it is 10Mb and used 95 MB of ram when open...
 
It really IS the biggest prime number...until the next bigger one is calculated, and then that will be the biggest ever, for a while. :)
 
I'd be curious what the practical application of this knowledge might be, or is it more of a "just because we are mathematicians and we are curious" type of perspective?
 
Zarathustra[H];1042094689 said:
I'd be curious what the practical application of this knowledge might be, or is it more of a "just because we are mathematicians and we are curious" type of perspective?
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Cryptography is probably the most common practical application.

There are more esoteric uses in other encoding and completeness (boundary problems) that I don't really understand, but have briefly encountered. :p
 
Interesting.

How often does one of these get discovered? Wonder how long the last "champ" was in place.
 
Arg. No editing on front page. Article answered my question:

Cooper also discovered the previous record holder in February 2013, which was 2^57,885,161 -1, a number with more than 17 million digits, along with two other older records. He has received a $3000 price from GIMPS for each discovery.
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And there's your practical application too! Winning $3000! :p
 
sfsuphysics said:
Curious how they check if a number is prime, do they simply brute force divide it by every number up to n/2 to see if the answer is an integer?
Click to expand...

Last time I tried to check prime numbers, The Sieve of Eratosthenes was the fastest algorithm by a wide measure. Not sure that algorithm works too well with numbers of this size though.
 
How do such large numbers get computed, are they basically just strings using math algorthms? You obviously can't do something like "int a = [huge number]" as there is a limit to how big a number can be.
 
Red Squirrel said:
How do such large numbers get computed, are they basically just strings using math algorthms? You obviously can't do something like "int a = [huge number]" as there is a limit to how big a number can be.
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The only limiting factor on how big a number can be is a matter of software hardware and memory... If a computer did not have set limits the number can be of any size.
 
Zarathustra[H];1042094689 said:
I'd be curious what the practical application of this knowledge might be, or is it more of a "just because we are mathematicians and we are curious" type of perspective?
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To be fair, the entire foundation of our scientific and mathematical understanding were born out of pure curiosity alone. Scientist are not people who study stuff because they thought it would be useful someday. They do what they do just because they were curious about the workings of nature.

It's the combination of our intellectual capabilities and our curiosity that got us to where we are today, and so it's important that we continue to pursue our curiosity. Scientist and mathematicians are not the ones who decide what's useful, they are there to discovery everything there is to be discover. The engineers are the one who will then decide what knowledge can be made useful.
 
Hornet said:
To be fair, the entire foundation of our scientific and mathematical understanding were born out of pure curiosity alone. Scientist are not people who study stuff because they thought it would be useful someday. They do what they do just because they were curious about the workings of nature.
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That's a fantasy. Scientists gotta eat. The offshoot of their efforts give something of value to someone, so there are people willing to pay them. Scientists doing science that doesn't have an immediate offshoot for making money, are either getting a paycheck to boost an organization's Prestige or Celebrity (which translates to money) or shoring up some Political position (which translates to money or favors).
 
That is old news.
I calculated a Prime number with 42 billion digits, I'd post it here but it may crash the forum.
 
jpm100 said:
That's a fantasy. Scientists gotta eat. The offshoot of their efforts give something of value to someone, so there are people willing to pay them. Scientists doing science that doesn't have an immediate offshoot for making money, are either getting a paycheck to boost an organization's Prestige or Celebrity (which translates to money) or shoring up some Political position (which translates to money or favors).
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Which is why researches at the frontier are funded by government rather than corporate. It's impossible to make a business model with a return of investment when you are researching stuff that may benefit us in 60 years time, or not at all. A good example would be quantum mechanics, it was nothing more than a curiosity driven research during it's infancy, no one could have predicted that it would play a vital role in today's technology.

Likewise, today we are doing many researches that are done simply with the objective of understanding nature, irrespective of whether those information are valuable or not. Stuff like finding Higgs boson or taking pictures of galaxies 13 billion light years away have no any practical use for us in the near future. But we still do them anyway, and we have to.
 
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