https://www.mersenne.org/primes/?press=M136279841

The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 2

^{136,279,841}-1, having 41,024,320 decimal digits. Luke Durant, from San Jose, California, found the prime on October 12th.The new prime number, also known as M136279841, is calculated by multiplying together 136,279,841 twos, and then subtracting 1. It is over 16 million digits larger than the previous record prime number, in a special class of extremely rare prime numbers known as Mersenne primes. It is only the 52nd known Mersenne prime ever discovered, each increasingly more difficult to find. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. GIMPS, founded in 1996, has discovered the last 18 Mersenne primes. Volunteers download a free program to search for these primes, with a $3000 award offered to anyone lucky enough to find a new prime. Prof. Chris Caldwell founded an authoritative web site on the largest known primes which is now maintained by volunteers, and has an excellent history of Mersenne primes.

**The Fine Print:**The following comments are owned by whoever posted them. We are not responsible for them in any way.

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## (Score: 2) by coolgopher on Wednesday October 23, @09:40PM (10 children)

Surely 2136,279,841-1 should be 2^136,279,841-1? The former is certainly not prime...

## (Score: 3, Interesting) by looorg on Wednesday October 23, @09:48PM (9 children)

That does indeed seem to have gotten lost in the quote, it's from the first paragraph of the link. I see now that it got lost in my copy-paste of the submission to.

Also why are there negative signs in the dept line? Negative prime numbers are not really a thing. Was that added as some kind of space filler cause I did not add those in there.

Parent## (Score: 1) by pTamok on Wednesday October 23, @11:01PM (6 children)

The text needs ❬sup❭❬/sup❭ tags.

2❬sup❭136,279,841❬/sup❭-1 renders as

2

^{136,279,841}-1( I have used Unicode characters U+276C and U+276D to show the angle brackets/less-than & greater-than signs used in tags. They will not work by copy and pasting the text. )

Parent## (Score: 3, Interesting) by hubie on Thursday October 24, @12:25AM (1 child)

Fixed. Thank you all.

Parent## (Score: 2, Funny) by pTamok on Thursday October 24, @07:17AM

Thank you for making the necessary changes to the original article.

For someone with self-diagnosed minor OCD, me seeing something that can be put right without being able to do it myself is a niggle.

Yes, I straighten pictures, too.

Parent## (Score: 1, Insightful) by Anonymous Coward on Thursday October 24, @11:12AM

> for > and < for < also work. No need to go unicode. :)

Parent## (Score: 2) by DannyB on Thursday October 24, @07:37PM (2 children)

I can use < angle brackets > in the text just fine.

To write a less than symbol (<) write: <

To write a greater than symbol (>) write: >

To write an ampersand character that does NOT have any other significant meaning, write: &

It is left as an exercise for the reader how I wrote this post.

Poverty exists not because we cannot feed the poor, but because we cannot satisfy the rich.

Parent## (Score: 2, Interesting) by pTamok on Friday October 25, @10:16AM (1 child)

The problem comes when you want to copy and paste text in comments, if, for example, you want to quote something,

In order to quote you, I had to go back and edit the quote. If I hadn't, it would have looked quite different on publication (you can check with 'Preview', as the system then interprets the characters. Using Unicode lookalikes allows you to quote without needing to go back and edit.

Here is what your text looks like when copied and pasted into a quote without re-editing. Do you see the problems it generates?

But thank-you for the comment.

When

Parent## (Score: 2) by DannyB on Friday October 25, @01:37PM

You do identify a real problem. With my approach, copy-pasta characters seem to disappear into nothingness. In reality they seep into the groundwater and surrounding environment. Using Unicode characters would avoid that problem.

Poverty exists not because we cannot feed the poor, but because we cannot satisfy the rich.

Parent## (Score: 2) by hubie on Thursday October 24, @12:41AM (1 child)

The software replaces spaces with dashes for what is in the Department field. It is so that a name can be created for the department out of a short (hopefully sometimes funny or insightful) sentence. Perhaps one should capitalize the first letters in each word to do it properly, or enclose it in parentheses, but dashes also work, and perhaps was easier to code? So if one put "department of redundancy" in the Department field, you'd get in Slashcode

from the department-of-redundancy dept., though perhaps one would rather havefrom the Department of Redundancy Departmentorfrom the "department of redundancy" dept.It is problematic if one puts punctuation there, such as commas. I have found that you can put in HTML spaces and they won't get replaced by dashes the first time they render, but the HTML turns into regular spaces when the story is submitted. When an editor goes in later and reviews the submission and posts it, that HTML code isn't there and those spaces then get replaced by dashes.

Parent## (Score: 2) by hubie on Thursday October 24, @12:43AM

I forgot to add that I removed the commas so at least it looks like a sequence of positive integers again.

Parent## (Score: 1) by pTamok on Wednesday October 23, @11:04PM (4 children)

I'm trying to work out how many pages of A4 filled with FFFFFFFF....FFF it would take to print the number in hexadecimal.

## (Score: 1, Informative) by Anonymous Coward on Thursday October 24, @01:19AM (3 children)

Whew, probably only one or two, if that.

I mean, if we consider an A4 page holding 125 columns by 50 rows? then that's 6000 characters. Imagine 48 000 base-2 digits all being set to 1, in a row? That's quite a lot. But maybe in a string of 411mm digits it could happen, law of large numbers and all. Probably not many times though.

;-)

Parent## (Score: 3, Informative) by bzipitidoo on Thursday October 24, @03:11AM (2 children)

Much more than 2 pages. The number has roughly 136 million digits in base 2. Divide by 4 and that's still 34 million. At 6000 hexadecimal digits per page, that's a bit more than 5667 pages.

Like all but the first few entries of the Ackermann function, it's in the class of numbers that are so large they're not worth writing out. Much bigger numbers than a piddly googol. Always better to represent them with a short formula, if possible. Can reach such large numbers that a formula is the only practical way to represent them. It can be astonishing how quickly work that produces numbers that take thousand of pages to write out can grow in size until there aren't enough atoms in the entire observable universe to print the numbers.

Parent## (Score: 0) by Anonymous Coward on Thursday October 24, @05:25AM

Ohhh damn, you're right.

I was thinking about it in terms of a "random" prime, but it's 1000000-1 == 1111111. :-/ So *all* of them are FFF....

Whoops.

Parent## (Score: 2) by DannyB on Thursday October 24, @07:39PM

That's a lot more ink than printing thousands of pages of colons or semicolons.

Poverty exists not because we cannot feed the poor, but because we cannot satisfy the rich.

Parent## (Score: 2) by EJ on Thursday October 24, @02:01AM (10 children)

How is this useful? Can you even do anything meaningful with such a large number? Aside from simple curiosity, is there any value in knowing this, like knowing the quadrillionth digit of pi.

## (Score: 1, Funny) by Anonymous Coward on Thursday October 24, @02:56AM (2 children)

> How is this useful?

"Utility" is a funny concept with widely varying definitions among people. I'm guessing that "math bragging rights" might have something to do with it. But then there is the cash too--from tfs,

> Volunteers download a free program to search for these primes, with a $3000 award offered to anyone lucky enough to find a new prime.

Parent## (Score: 2) by EJ on Thursday October 24, @03:32AM

Well, yeah. I'm just thinking in terms of something like, "if only we could find a large enough prime, encryption would be unbreakable or we might understand how black holes work."

Parent## (Score: 4, Touché) by davidjohnpaul on Thursday October 24, @05:00AM

The guy who discovered it is "pretty sure" he spent less than $2 million on computing resources to find this one, so I don't think the $3000 was much of a motivator in this case.

Parent## (Score: 1, Informative) by Anonymous Coward on Thursday October 24, @04:10AM (1 child)

Large primes are used for data encryption and the like.

Parent## (Score: 3, Funny) by DannyB on Thursday October 24, @07:42PM

"That is true!" explained the senator. "We have now devised a ROT17 encryption which requires a different operation to decrypt than ROT13."

"Furthermore", explained the senator, "we chose 17 because it is a prime number, unlike 13."

Poverty exists not because we cannot feed the poor, but because we cannot satisfy the rich.

Parent## (Score: 3, Insightful) by pTamok on Thursday October 24, @07:41AM (1 child)

It allows you to determine another

perfectnumber.https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Elementary_Number_Theory_(Barrus_and_Clark)/01%3A_Chapters/1.16%3A_Perfect_Numbers_and_Mersenne_Primes [libretexts.org]

There is also a proposed 'post-Quantum' cryptosystem based upon the use of Mersenne primes: Mersenne-756839 (PDF) [nist.gov]

It has already been 'successfully' attacked. Exploiting Decryption Failures in Mersenne Number Cryptosystems [kuleuven.be], success being defined as:

But the thing to remember is that attacks tend to get better over time.

Parent## (Score: 2) by DannyB on Thursday October 24, @07:47PM

There are perfect numbers. But there are no perfect prime ministers.

A perfect prime minister would be one whose length of tenure was equal to the sum of its proper divisors. But since the minister is prime it doesn't have any proper divisors other than one. Thus there are no perfect prime ministers.

Poverty exists not because we cannot feed the poor, but because we cannot satisfy the rich.

Parent## (Score: 3, Troll) by ledow on Thursday October 24, @09:09AM (2 children)

If you're sitting on an secured TLS/SSL website and asking how discovering new large prime numbers can be "useful", you really need to go read even the most basic textbook on cryptography.

Parent## (Score: 3, Touché) by EJ on Thursday October 24, @03:09PM

I neither need nor want to be an expert in everything. Simply saying "cryptography" was good enough to satisfy my question.

Parent## (Score: 1) by pTamok on Friday October 25, @12:44PM

Not really: Mersenne primes are not used in the encryption methods in TLS/SSL unless it is by accident. They are far too well known, there are not many of them, and it would be easy to check a list of them, because it would be short. They are also too big for RSA - e.g. 1024-bit RSA requires two primes that are roughly 512 bits long (the two primes should be roughly the same size); RSA-2048 two primes of roughly 1024 bits, and RSA-4096 two primes of roughly 2048 bits. The newly found Mersenne prime has 100s of thousands of bits. Too big.

However, RSA does use primes. The prime number theorem states that the probability that an integer chosen at random, k, is prime is approximately 1/ln(k). Theis means that for numbers in the range of 2048 bits, about 1 in 1400 numbers are likely to be prime*. So you get a good random number generator, and get it to generate about that many numbers of 2048 bits, and start testing them to see if they are prime. For this, you use the Miller-Rabin primality test algortirm, which gives you a probabilistic answer as it would take far too long to factor the number to see if it were prime.

More details in this blog: How to find large prime numbers for RSA with the Miller-Rabin Primality Test [incolumitas.com]. They main bit is in the section headed: "Generating large prime numbers

pandqfor RSA"RSA encryption uses prime numbers of about 512, 1024, and 2048 bits. It doesn't need numbers larger than about 2048 bits, so generating new primes with 100s of thousands of bits doesn't help.

* a 2048-bit number is of the order of 2

^{2048}. The natural logarithm of 2^{2048}is 2048 x ln(2), which is 2048 x 0.693 = 1420 or 'about' 1400.Parent## (Score: 3, Interesting) by bzipitidoo on Thursday October 24, @03:06PM

This is great. I was guessing the next Mersenne prime would be in the 2^150m vicinity. The previous record holder for largest known prime was the last Mersenne Prime GIMPS found, ~2^82m.

When I was living in an apartment that had electric heat, I'd run GIMPS on my PCs instead of using the furnace. Checked a few dozen candidates, and all were not prime, no surprise given how rare they are.

It's not so free to run GIMPS any more, since computers have become much better at using less power when idle.