41-million-digit prime crunched by datacenter GPUs A former Nvidia engineer has found the largest known prime number – a whopping 41 million digits long – using an A100 GPU made by his previous workplace to do the grunt work. This wasn't the CPU-heavy hunt for primes that we've typically seen. No, this time GPUs, ones more widely used for the datacenter, did all of the heavy …
Mersenne primes have a special form. There are primality tests that work well if you have the complete factorisation of n + 1. And for Mersenne primes, we know the complete factorisation of n + 1, because (2^k-1) + 1 is just a power of two. Proving that a general number is a prime is much much much harder.
I doubt anyone searching for Mersenne primes does it because they think it will be useful. This has more to do with proving you can meet the challenge, and bragging rights. Much pure maths has been created with little to no expectation of usefulness, although a surprising amount has subsequently turned out to have serious importance, once the physicists, cryptologists et.al. got involved.
Much pure maths has been created with little to no expectation of usefulness
As a PhD pure mathematician, I'd say a great deal, probably most pure maths was created / discovered* with little to no expectation of usefulness. G H Hardy, I believe, claimed that what he had done was of no practical use whatsoever (little did he know that less than a century later, it would actually prove useful). My own thesis was on countable infinite ordinals, and useful only to other people studying them. But, the discipline of a rigorous approach, and proving things completely are useful transferrable skills, and you cannot do particle physics without learning some proper group theory, so algebra is useful too.
*There is philosophical discussion about whether mathematics is 'created' or 'discovered. I intend to avoid this as it is beyond my knowledge and skills, although I will say, that whichever is the case, mathematical notation is created, as are the rules for manipulation. Feel free to comment on your personal perspective or not, as the case maybe.
> Based on some of my experiences with the truthiness of "AI", I wouldn't be surprised if it spit out a number ending with "2".
There's only one 2 trlilion digit number ending with 2. All but the last digit are zero. Bravo AI.
Taking the bait so I can ask the 'Obvious' question(s):
Prove it !!! [Any 2 out of the following 2 will do !!!]
a) Prove your 2 trillion digit prime is a 'prime' !!!
b) Prove AI is 'Better' & 'Faster' than everything !!!
P.S. Yes ... I did ignore the 'Whooshing' sound !!!
:)
Or:
"Richard P. Feynman’s speech at the Nobel Banquet in Stockholm, December 10, 1965
Your Majesty, Your Royal Highnesses, Ladies and Gentlemen.
The work I have done has, already, been adequately rewarded and recognized.
Imagination reaches out repeatedly trying to achieve some higher level of understanding, until suddenly I find myself momentarily alone before one new corner of nature’s pattern of beauty and true majesty revealed. That was my reward.
Then, having fashioned tools to make access easier to the new level, I see these tools used by other men straining their imaginations against further mysteries beyond. There, are my votes of recognition.
..."
https://www.nobelprize.org/prizes/physics/1965/feynman/speech/#:~:text=I%20saw%20in%20each%2C%20joy,to%20learn%20about%2C%20their%20feelings.
This doesn't surprise me at all.
With domestic and business energy prices at a very high level, renting a server with plenty of GPU "grunt" can be quite a benefit if someone wants to make a computing-focussed donation to a project, such as GIMPS.
And there are many hobbyists who still contribute CPU and/or GPU cycles to various BOINC projects, such as GPUGrid, PrimeGrid, etc either via their small farm of computer hosts, or by buying computing time on various cloud services, such as AWS and others.
https://www.boincstats.com/stats/projectStatsInfo
But if the number of Mersenne primes is unbounded, then presumably for any fixed choice of "large", there will be more "large" Mersenne primes than small ones, and, further, infinitely more large than non-large. Which might make it at least more-or-less reasonable to say that Mersenne primes "are large". :-)
But perhaps what was meant that if considering all discovered "large" primes, you will notice that more of them are Mersenne than of any other type? (or some similar statement).
Mathematician:
"3 is prime; 5 is prime; 7 is prime...By induction it is clear that all odd numbers are prime."
Applied physicist:
"3 is prime; 5 is prime; 7 is prime; 9 is pr...oops; experimental error...11 is prime; 13 is prime... Obviously, all odd numbers are prime."
Engineer:
"1 is prime; 3 is prime; 5 is prime; 7 is prime; 9 is prime; 11 is prime; 13 is prime; 15 is prime; 17 is pri..."
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