January 22, 2016

Meet 274,207,281 − 1, the newly discovered prime number.

It's almost 5 million digits longer than 257,885,161 − 1 (which is about 17 million digits long, written out), which had before now been the longest prime number known.

The new prime number was discovered by machine No. 5, a computer at the University of Central Missouri, an otherwise nondescript desktop computer, which took the trouble to multiply 74,207,281 twos together and subtract 1 and then to check that it was not divisible by any positive integer other than 1 and itself.
This is the 15th prime number found by the Great Internet Mersenne Prime Search, or Gimps, for short, a volunteer project that has been running for 20 years. “I’ve always been interested in prime numbers,” said George Woltman, who founded Gimps after he had retired. “I had a lot of time on my hands,” he said.

31 comments:

PuertoRicoSpaceport.com said...

Wow! Lotta numbers.

If we assume 5 characters to the word, 17mm digits is the equivalent of 3.4mm words.

That's about 3 volumes of the Encyclopedia Britannica if printed out.

John Henry

Curious George said...

Meanwhile the Chinese are....

Original Mike said...

"The new prime number was discovered by machine No. 5"

Was number 4 down for maintenance?

mccullough said...

That number will be the federal debt after a Bernie Sanders presidency

Bob R said...

But it will cost 2^(57,885,161) − 1 for a cup of coffee, so it won't be so bad.

Patrick said...

A 22 million digit number is incomprehensible.

Dan Hossley said...

Encryption just got a little better.

Fernandinande said...

PuertoRicoSpaceport.com said...
If we assume 5 characters to the word, 17mm digits is the equivalent of 3.4mm words.


There are 22,338,618 digits in the new prime.

Original Mike said...

I would think machine number 5 is due for a promotion.

Levi Starks said...

I'm pretty sure machine #5 is benefiting from white privilege.

Blue Ox said...

Left unresolved:

Is it Numberwang!?

https://www.youtube.com/watch?v=qjOZtWZ56lc

mikee said...

One is the loneliest number, but this prime number comes pretty close.

MadisonMan said...

Was number 4 down for maintenance?

Machine Number 5 is prime. Machine number 4, not so prime.

Original Mike said...

"Machine Number 5 is prime. Machine number 4, not so prime."

Of course! {slaps palm to forehead.}

Michelle Dulak Thomson said...

I love the extremely simple proof that there is no largest prime. Suppose you think you have the largest prime. OK, now multiply every prime from 2 through your N and add 1. This number is either itself prime, or else has prime divisors greater than N, because any prime up to N, dividing it, leaves a remainder of 1.

rhhardin said...

Each machine costs about $2.50 a month to run, if you have it computing. Multiply that by the number of machines doing it. I get about $3 million a month in electricity cost.

Tank said...

Levi for the win !

George Grady said...

which took the trouble to multiply 74,207,281 twos together and subtract 1 and then to check that it was not divisible by any positive integer other than 1 and itself.

Just for the record, that's not actually how primality testing is done. In fact, if every atom in the universe had been checking, oh, say a trillion possible divisors every second since the beginning of the universe, they wouldn't have made a dent in the list of divisors to check. I mean, 2^74207281-1 is really, really big.

Gabriel said...

Our entire financial infrastructure depends on the knowledge of large primes and how hard it is to factor them.

It's easy to be dismissive of things which we had no idea were important.

You have no way to know what you might need to know, until the universe catches you not knowing it and punishes you.

Scott McGlasson said...

Grand Mufti Sheikh Abdulaziz Al-Sheikh called finding the new prime number “the work of Satan. It causes hostility and wastes time where it should not be spent.”

MikeR said...

It's not really a trick to make "the largest prime known". There are very efficient methods for checking if a number is prime, and a prime is expected about once in every (number of digits in the number). So if you start with a number that is a million digits long, you'd expect about one prime number in the next million numbers or so. It doesn't take long to check each one.
For coding, no one (yet) uses numbers that long, so no one bothers to make a bigger prime number. But there isn't much to it.
On the other hand, actually finding the divisors to a number that is _not_ prime is very difficult, and that difficulty is the basis for the most popular coding system. Find two very big prime numbers and multiply them together; no one knows a good way to find the two divisors from the product.

rehajm said...

University of Central Missouri Desktop Computer Discovers Large Prime Number and Helps University Researchers Discover They Haven't Accomplished All That Much In Their Lives

furious_a said...

The new prime number was discovered by machine No. 5, a computer at the University of Central Missouri...

Is that the machine that goes "PING!"?

Original Mike said...

"Is that the machine that goes "PING!"?"

No, #5 actually does work. We only turn on the machine that goes "PING!" when the Administrator stops by.

Roughcoat said...

Machine # 4 is busy working on the 9 billion names of God.

Kyzernick said...

Levi wins this one.

Mac McConnell said...

Machine #4 is working on winning Powerball numbers.

The Godfather said...

Don't mess with the 9 billion names of God. http://downlode.org/Etext/nine_billion_names_of_god.html

DanTheMan said...

Machine number 4 had its hands up, but the the Missouri police shot it anyway...

Fred Drinkwater said...

Ping? not Ping...

..The thing that goes "parp" went "parp".

robother said...

Good. I've been meaning to change my password to a harder one to guess.