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# GIMPS crack whip on plucky processor to find largest prime number

The Great Internet Mersenne Prime Search (GIMPS) has announced the discovery of a new largest Mersenne prime number, 277,232,917 -1. The figure, viewable here (.zip file), was found by GIMPS' network of volunteer prime hunters, and is the 50th Mersenne prime discovered. It comprises 23,249,425 digits, and is 910,807 digits …

## COMMENTS

1. #### but has since been put to practical use in cryptography

So, how long before the FBI asks to ban prime numbers?

1. #### Re: but has since been put to practical use in cryptography

All numbers can be factored into primes. So the only way to be safe is [see icon]!

1. #### Re: but has since been put to practical use in cryptography

I suggest that mere mortals are required to use a non-decimal numbering system, possibly based on irrationals that would make finding primes much more interesting.

Or maybe requiring all CPUs to only deal with floating-point numbers (no integer calculations) which would kill the processing time and eradicate any exactitude. Of course, the powers-that-be would be allowed to do integer arithmetic.

2. #### Re: but has since been put to practical use in cryptography

You jest, but I suspect that at some point they might well try and pass a law to make the details of prime numbers a state secret.

That said, sillier laws have been passed in the past, and I suspect there will be in the future.

1. #### Re: but has since been put to practical use in cryptography

See: Indiana Pi Bill

Not passed but really stupid.

1. #### Re: but has since been put to practical use in cryptography

No more up votes .. 3 is enough.

3. #### Re: but has since been put to practical use in cryptography

Never mind the Fubby (FBI)... just don't tell Amber Fudd or she will get ideas way above her station (git central).

4. #### Re: but has since been put to practical use in cryptography

Not a joke

https://en.wikipedia.org/wiki/Illegal_number

2. Has anyone double checked to see if it can be divided by 3?

Whenever we had to find prime numbers at school the ones I 'found' were usually divisible by 3.

1. #### Just add the digits together....

If the resulting number is divisible by three then the original number was......

2. #### mod 3

Pretty easy to check --- all multiples of three, expressed in base 10, has a digit sum which is also a multiple of three (and can therefore be checked by the same rule).

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1. #### Re: mod 3

It goes up to eleven?

2. #### Re: mod 3

This simplifies to 3 divides 2^n-1 if and only if n is even, so we're good, it's not divisible by three. Phew.

3. "Whenever we had to find prime numbers at school the ones I 'found' were usually divisible by 3."

yeah too much busywork, doing all of those divisions. Imagine doing it WITHOUT an electronic calculator. That would be when _I_ was in school... through Jr. High anyway.

thinking of high school, I had a friend who came up with a really interesting way of calculating prime numbers. He proposed prime numbers "by addition", basically a set of 'for' loops that marked an array (you could use a bit array) for every value divisible by 'n' and then you just examine the array afterwards and print out anything with a zero in it. It would be significantly faster than dividing by every odd integer <= sqrt(number), but maybe not faster than dividing by "discovered prime numbers" <= sqrt(number). Anyway, for a value of this magnitude (re: article's number), I think you'd run out of RAM...

(then again it's only 2 ^ 77 million, so perhaps not?)

1. Known as the Sieve of Eratosthenes.

1. "Known as the Sieve of Eratosthenes."

thanks, I obviously hadn't heard of that one.

3. #### Thats my new password sorted

I'll just add 1 letter and symbol in random places and perhaps remove a few digits from the middle and I should be good to go!

1. #### Re: Thats my new password sorted

I'll just add 1 letter and symbol in random places and perhaps remove a few digits from the middle and I should be good to go!

Two letters surely - one uppercase and one lowercase?

1. #### Re: Thats my new password sorted

And some punctuation. shirley?

Won't someone think of the apostrophies?

1. #### Re: Thats my new password sorted

I had to change a password as it contained an asterisk. It was created on a Mac, but my Android phone must use a different ASCII code for asterisks or something and it simply would not work on that. Which was a pain. Here was me under the impression that ASCII was set in stone and should be the same across systems.

2. #### Re: Thats my new password sorted

Password Strength: Weak (needs mix of capital and lowercase letters, needs more than one special symbol, *IT Team: please insert another bullshit rule here, thanks, management*)

3. #### Re: Thats my new password sorted

My pin number is the last 4 digits of Pi .

1. #### Re: Last 4 Digits of Pi...

Well, IIRC some infinities are "even", and infinity can be defined as a fraction of -1/12 (note that is *minus* one).

So finding the "last" four digits might not be impossible in some aspects of mathematical analyses. It's the infinite set between two points that is more difficult. ;)

4. Do we really need it printed out? After all it's just 0b111..111.

5. #### A bloody good read actually

** Spoiler Alert **

My favourite part is:

"805527898274441538637314218125980674172584395778861841820859398697454646280030912007"

Didn't see it coming at all, genius.

1. #### Re: A bloody good read actually

It trailed off at the end to nothing. I wasn't expecting more though.

1. #### Re: A bloody good read actually

It trailed off at the end to nothing

That would have meant divisibility by 2, 5 and 10 at the very least.

2. #### Re: A bloody good read actually

Paid review!

3. #### Re: A bloody good read actually

I gave up after the first chapter, it was too formulaic.

6. #### Actually...

He wasn't the first to discover it - it was the Tr0tsk1 3lit3 haxors group running a meltdown trojan on his machine that did!

7. #### My favourite part...

...is where there are ten consecutive digits the same. Open the file and search for 9999999999 you'll find its there :)

1. #### Re: My favourite part...

Glad he didn't bail after seeing eight 9s in a row.

"Gladys, the prime generator's stuck again. Whack it on the side and restart it."

1. #### Re: My favourite part...

I'd be interested to know what the actual odds are of any specific ten consecutive digit number occurring in a truly random long digit sequence like this monster prime, I would hope its around 10^10 or one in ten billion? I searched for the same string sequence (9999999999) in the decimal digits of pi and couldn't find it in the first 200 million or so, perhaps finding it so much sooner in this sequence has a very low probability?

1. #### Re: My favourite part...

100% in a truly random number - any arrangement can appear, and will, which is what confounds peusdo-random number generators hard to prove if they really are random.

1. #### Infinite monkeys?

I think the ten digit statement above is only true for infinitely long random sequences and not for a specific sequence of a given length? If the probability of finding ten recurring digits in any randomly generated number sequence are less than one in the FIRST few billion digits then the odds of a specific ten digit sequence turning up far sooner (in say tens of millions of digits rather than billions) that should be much lower but perfectly acceptable, just less than 1% maybe? Isn't this how bitcoin miners use sha256 hash collisions for proof-of-work, as the odds of finding a really large (2^256) number with lots of recurring leading zeroes is extremely low for randomly generated inputs but every now and then someone in the pool gets lucky and guesses sooner than expected? You wouldn't expect to find the complete works of Shakespeare (or even the first page of Hamlet!) to ever be generated using monkeys on typewriters during the expected age of the universe due to the probability being 1 in 26 to the power thousands of characters?

https://en.wikipedia.org/wiki/Infinite_monkey_theorem#Probabilities

1. #### Re: Infinite monkeys?

Probabilities - wiki? load of bollocks. A truly random number has no probable outcome nor odds. Any sequence can appear in an infinite number: if it is probable then is is random? yes and no - the cat is dead or alive.

The probability of me winning the lottery is 50% - I either win it or don't.

1. #### Re: Infinite monkeys?

And the probability of me winning the lottery is 0% - I only bet on selected certainties - and making Camelot rich isn't one of them.

1. #### Re: Infinite monkeys?

That isn't probability - that is odds or chance.

2. #### Re: My favourite part...

Randomness isn't even, it's clumpy, like cosmic background microwave radiation. Anyone know of a really, really good random number generator?

1. #### Re: My favourite part...

There is structure in primes:

Mathematicians Discover Prime Conspiracy: A previously unnoticed property of prime numbers seems to violate a long-standing assumption about how they behave.

Among the first billion prime numbers, for instance, a prime ending in 9 is almost 65 percent more likely to be followed by a prime ending in 1 than another prime ending in 9.

2. #### Re: My favourite part...

Anyone know of a really, really good random number generator?

Despite frequentists' conniptions, probabilities ARE ontological and Nature has very good generators with fixed values built-in: HotBits: Genuine random numbers, generated by radioactive decay.

1. #### Re: My favourite part...

Cheers dude that's epic! I was considering getting one of those USB key things with some sort of decay based generator built in but this is more expedient.

2. #### Re: My favourite part...

(Beware line breaks every 100 characters)

I was disappointed to find that 0118999 wasn't there - let alone the rest of it.

For Pi fans: 3141592 is there, but not 31415926.

There are 23,714,413 decimal digits; so an arbitrary sequence of 7 digits (of which there are 10 million combinations) has a reasonable chance of being there.

Looking at sequences of repeated digits, the largest ones are:

zeros - 7

ones - 7

twos - 8

threes - 8

fours - 7

fives - 7

sixes - 8

sevens - 6

eights - 7

nines - 10

So nine does seem to be a special case.

2. #### Re: My favourite part...

If you dialed that when being murdered, you might be lucky and get two copper's arrive fresh from the kebab shop 6 hours later.

3. #### Re: My favourite part...

If you reverse the nines is it still a prime number?

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9. #### As used by the accounting department

http://dilbert.com/strip/2001-10-25

10. #### Pedantic Grammar Nazi Inbound, 9 o'clock!

... comprised of ...

Should probably be "composed of" or "comprises".

1. #### Re: Pedantic Grammar Nazi Inbound, 9 o'clock!

So why didn't you complain about copper's, which is possessive and should have been coppers, plural or, if they had the kabobs with them coppers' (plural possessive) kabobs (plural, non-possessive)?

11. #### FAKE NEWS

The real 50th Mersenne prime is 2**77,232,917 -1

1. #### Re: FAKE NEWS

Well, maddddog, that changes everything.

12. #### Perfect

We also have the world's largest known perfect number:

277,232,916(277,232,917-1)

It's an open question whether there exist any odd perfect numbers, but any that do exist must be greater than 101500.

13. #### Appreciation pint

...for defining primes as "numbers only divisible by one and themselves".

Prost!

1. #### Re: Appreciation pint

Technically, a prime is an integer p such that 1) p is not a unit (i.e., 1 or -1), and 2) whenever p divides ab, then p divides a or p divides b (or both). What is described here are irreducibles, not primes. That primes and irreducibles are the same thing is the definition of a unique factorization domain. (All primes are irreducible, but not all irreducibles are prime.)

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15. #### 42

So we still don't know where Deep Thought got 42 from then?

1. #### Re: 42

Fortitude?

It may not be the answer to everything but it sure does help.

16. #### Let me save you all some trouble

"69" occurs 229,286 times (first instance: digit 255)

"420" occurs 22,948 times (first instance: digit 613)

"80085" occurs 217 times (first instance: digit 145943)

Interesting pattern to note: The frequency of each number decreases proportionally to the length of that number, almost exactly to the rate of one order of magnitude per additional digit. It's almost like... base 10 or something.

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17. Will there ever be an end to this? If so, will that number contain the number of digits that's a prime number?

Yeah... it's after beer o'clock and the mind wanders...

18. #### Off topic...

...but I do giggle to myself when I can read the intelligent, thought-inspiring comments on a Reg thread, swipe straight past anything that is headed with “bombastic bob” and see just a few milliseconds glimpse of his/hers downvotes before I read then next post.

Happy New Beers :)

19. #### 5318008

It's in there. Just the once though.

20. #### Yawn

Call me when they have the first for π(x) > li(x) (estimated about 10316).

21. #### Missed Opportunity

Look, tie Mersenne Prime search to a block chain, Einsteinium for example. Payout in EMC2 when a prime is found. You'll have so much computing power, new Primes will be popping like corn.

Although the finders likely won't be boffins, so it will deprive El Reg of its customary reporting style...

22. #### A Girl called Pi.

I once new a girl called Pi

She had the most infinite eyes.

I once tried to kiss her

but her fists moved much quicker

so all that I got was -- black eyes.

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