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51st Known Mersenne Prime Number Found (mersenne.org)
chalsall (Slashdot reader #185), writes:
The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 2^82,589,933-1, having 24,862,048 digits. A computer volunteered by Patrick Laroche from Ocala, Florida made the find on December 7, 2018.
GIMPS has been on amazing lucky streak, finding triple the expected number of new Mersenne primes -- a dozen in the last fifteen years.
"This anomaly is not necessarily evidence that existing theories on the distribution of Mersenne primes is incorrect," notes GIMPS. "However, if the trend continues it may be worth further investigation. " They also report that the newly-discovered prime number "is more than one and a half million digits larger than the previous record prime number" -- and it's one of just 51 known Mersenne prime numbers ever discovered. "GIMPS, founded in 1996, has discovered the last 17..."
Patrick Laroche is one of thousands of volunteers using GIMPS' free software to hunt for prime numbers -- and is now eligible for a $3,000 "research discovery award," the group writes at mersenne.org. "GIMPS' next major goal is to win the $150,000 award administered by the Electronic Frontier Foundation offered for finding a 100 million digit prime number" -- of which $50,000 will be awarded to the discoverer, with another $50,000 going to a 501(c)(3) mathematics-related charity selected by GIMPS, and $50,000 retained by GIMPS to cover expenses and fund other awards.
GIMPS has been on amazing lucky streak, finding triple the expected number of new Mersenne primes -- a dozen in the last fifteen years.
"This anomaly is not necessarily evidence that existing theories on the distribution of Mersenne primes is incorrect," notes GIMPS. "However, if the trend continues it may be worth further investigation. " They also report that the newly-discovered prime number "is more than one and a half million digits larger than the previous record prime number" -- and it's one of just 51 known Mersenne prime numbers ever discovered. "GIMPS, founded in 1996, has discovered the last 17..."
Patrick Laroche is one of thousands of volunteers using GIMPS' free software to hunt for prime numbers -- and is now eligible for a $3,000 "research discovery award," the group writes at mersenne.org. "GIMPS' next major goal is to win the $150,000 award administered by the Electronic Frontier Foundation offered for finding a 100 million digit prime number" -- of which $50,000 will be awarded to the discoverer, with another $50,000 going to a 501(c)(3) mathematics-related charity selected by GIMPS, and $50,000 retained by GIMPS to cover expenses and fund other awards.
A prime number can only be divided by one, itself, and Chuck Norris.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Might want to look for a bug in your code first, before going on to blame mathematical theory.
"First they came for the slanderers and i said nothing."
Thanks - I can use that as one of the primes in my 82 billion bit private key - lets see the NSA crack that!
try { do() || do_not(); } catch (JediException err) { yoda(err); }
And before anyone asks, no these large Mersenne are much too large to be used in practical cryptography. There is a random number generator called a Mersenne twister which does use a Mersenne prime, but that uses much smaller ones to be feasible, and in any event is not sufficiently random to be safe for serious cryptographic purposes.
The primary interest in these primes is two-fold: First they have a very efficient primality test, the Lucas-Lehmer test https://en.wikipedia.org/wiki/Lucas-Lehmer_primality_test and so if one is interested in simply finding very big primes, these are the ones to look for. For most of the last 100 years the largest known prime has beena Mersenne prime.
Second, there's a connection with perfect numbers. A number is said to be perfect if the sum of all its positive divisors which are less than the number add up to the number. For example, 6 is perfect because 1,2 and 3 divide 6 and 1+2+3=6. But 8 is not perfect because 1+2+4=7 which is not perfect. The two oldest unsolved problems in all of math are a) are there any odd numbers which are perfect and b) are there infinitely many even numbers which are perfect? About 2000 years ago, Euclid recorded a proof (which may or may not have been due to him) that every Mersenne prime allows you to construct an even perfect number. In the 1700s, Euler proved that any even perfect number must arise from Euler's construction. So if one cares about answering this question about even perfect numbers, then one wants to investigate Mersenne primes.
About 2000 years ago, Euclid recorded a proof (which may or may not have been due to him) that every Mersenne prime allows you to construct an even perfect number.
I "rediscovered" that proof as a teenager, and thought I was breaking new ground. Then I found it was actually discovered 2000+ years ago. Mathematics has a special way of putting your hubris in perspective.
Live today, because you never know what tomorrow brings
17 * 3 is not prime in the mathematical sense or in the free 2 business day shipping sense either.
What is practical application of this if not for cryptography
I do not believe in karma. "Funny"=-6. Do good and forbid evil. Yours, Oft-Offtopic Flamebaiting Troll.
No direct practical applications. But practical and interesting are not synonyms.
Did they use a computer for that?
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Sigh.
You can get past a googol (10^100) with factorials of a 3 digit number. Factorials are thus "using" such numbers. Calculate the odds of N things chosen out of M and the numbers explode quickly.
Just because a number isn't representative of a practical physical quantity doesn't mean it's useless. Want an example? Encryption. I doubt you will ever exprienve having 2^4096 "anythings"... but the fact such a number exists, can be proven to be prime, and for which the mathematics applies is still incredibly useful.
that would be overpriced in the rib sense too, even at a posh restaurant
With the price of crypto-currencies on what looks like a downward trend, this past week being an exception, could all that GPU and crypto-mining HW be put to use fishing for gimps?
The Russians have won. They have made the world a cesspool of distrust, greed, fear and hate.
Wait, so the GIMP photo editor all along was just a ploy to search for Prime Numbers !?
51 is a PRIME number
at Amazon?
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A number with 24 million digits
Funny how we can only express a number by its power (10^24), and as technology and computers make progress we'll have to find another way to talk about a number when even its power is too large to give the brain a hint on how big it is.
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The NSA and GCHQ always get a LOL as they wait for the outside world to catch up with their decryption math.
Domestic spying is now "Benign Information Gathering"
I "rediscovered" that proof as a teenager, ... Then I found it was actually discovered 2000+ years ago.
But did Euclid bother to register it with the corresponding Copyright/Patent Offices? No? Then IT'S STILL UP FOR GRABS, DO IT NOW. Add "ON A COMPUTER" and you're golden.
Or just say you identify as Euclid today and don't even bother. It didn't work for this guy but he was arguing about age, which is math. And we all know that "Math Is Hard" from that great sage: Barbie.
If the universe is someone's simulation -- does that mean the stars are just stuck pixels?
"GIMPS' next major goal is to win the $150,000 award administered by the Electronic Frontier Foundation offered for finding a 100 million digit prime number"
Wait a minute, why is a civil liberties group funding a contest to solve mathematical problems? Following the link, they make it pretty clear that their ordinary funding doesn't go toward this, and apparently one interested party gave them the funds for this specific purpose. Still doesn't answer why they approached the EFF instead of, say, CERN.
Corruption is convincing someone that the selfless ideal is the same as their selfish ideal.
How about (10^4899)^4899
Don Knuth came up with a way of representing really big integers. He observed that multiplication is repeated addition and exponentiation is repeated multiplication, and devised a way to represent repeated exponentiation.
Just another wannabe fantasy novelist...
That's nice thanks.
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I did a ballpark estimate of the odds of finding a new Mersenne prime. It's very roughly 1 in 100,000 that an untested number that has no small factors (less than 2^76) will be prime.
Just one Mersenne prime has been found between 2^44 million and 2^74 million, and then there are no less than 3 in the next 10 million powers of 2 (minus 1 of course)? That's a lot.
It adds to our knowledge. Maybe we can see more patterns, or figure out something else interesting. The more data we have...
Intellectual Property is a monopolistic, selfish, and defective concept. It is "tyranny over the mind of man"
It is for me. Life is too short to spend on personal amusement.
I do not believe in karma. "Funny"=-6. Do good and forbid evil. Yours, Oft-Offtopic Flamebaiting Troll.
About 2000 years ago, Euclid recorded a proof (which may or may not have been due to him) that every Mersenne prime allows you to construct an even perfect number.
I "rediscovered" that proof as a teenager, and thought I was breaking new ground. Then I found it was actually discovered 2000+ years ago. Mathematics has a special way of putting your hubris in perspective.
No need for the scare quotes. If you found it on your own then you legitimately rediscovered it.
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It is for me. Life is too short to spend on personal amusement.
... he says by posting on Slashdot.
Inheritance is the sincerest form of nepotism.