AI: Can a robot find the largest prime number using a computer powered by an off-the-shelf Intel processor?
Dennis
Dennis Mazur
Such calculations depend mainly on the size of registers inside the processor. So, if you mean the largest known prime number (2^274,207,281), then it is NOT possible. But, the processor can do largest prime number calculations up to a number that is again limited by the size of registers.
Such calculations depend mainly on the size of registers inside the processor. So, if you mean the largest known prime number (2^274,207,281), then it is NOT possible. But, the processor can do largest prime number calculations up to a number that is again limited by the size of registers.
You mean this ? https://www.mersenne.org/primes/?press=M74207281
The discussion here seems to indicate other resource limits than register size: https://crypto.stackexchange.com/questions/48814/highest-prime-number-calculated-on-a-regular-pc
(think this is all done in software )
I will caveat this by saying "that depends on what else the robot is doing". If this robot has a dedicated off-the-shelf processor, plus supporting hardware and a reliable power source, then why not ? If the robot is involved in any other meanderings, then your mileage may vary. Your prefix is "AI:", which is intriguing. I'm not sure that finding prime numbers is a typical "AI" application. Depends on how much "AI" is there. The robot may complain.
As Euclid proved, there are infinitely many prime numbers, so the answer is no.
Yes, but Euclid never published Intel results for a robot. So the answer to the question is best addressed by a more contemporary view. No one said how long the robot would work on the problem, or what resources the robot might acquire as calculation proceeds. So the answer is yes.
I find this to be linked to your other question here on the site, if an AI could compute the largest prime or conclude it is a fool's errand.It depends of how much I is in that AI and the way it is designed. Intel or not , future, present or past, one cannot compute the infinity. Why the race for the largest prime? well I personally guess it has to do with robustness testing. You want fast, dependable machines, you also want to find a way to objectively rank them. For gaming rigs you have resource-demanding games and test renders . For scientific computing one such benchmark is .. computing primes. Who can get to the next prime faster, which machine has lowest number of failures or errors etc have nothing to do with the ..next prime but have everything to do with identifying objectively a capable stable computing platform- by running this test. Other tests are designed, maybe similarly difficult -computing extra decimal places for pi or e or terms in the Fibonacci series.A good testing algorithm for long-term testing is infinite, resource intensive, and verifiable step by step so errors can be identified and rooted out - or architectures disqualified for certain real,high importance scientific testing.
It is not a simple matter to select a good say, multiphysics simulation solution. If besides the software limitations or errors you also get hardware-related numeric errors tests such as this are important to avoid (future) possible disasters when results from simulations run on machines identical to the tested configurations are used in real-world applications.I do not think that anyone still thinks the largest prime is a finite computable number. It does not mean the search is meaningless- see reasons above. Yes, humans are complicated this way, we do meaningless stuff for a reason :)
The original question was likely tongue in cheek, as you point out. And my R2 unit just passed a second round of diagnostics, so things are great! Happy New Year to everyone!
sure but it might also be a jab at Intel that was found to have some "particularities" in the architecture that could potentially give erroneous computation results. Also it is not the first time I hear this.. at a numerical simulation lab back in my faculty years we were tasked with some homework but we were instructed to watch out for errors if we had the core 2 duo or some of the older second or third gen i-cores .Strangely enough newer strands of ARM core processors or other desktop processors and newer server -i ntel lineup (xeons ) do not suffer from this. Don't know if relevant for day-to -day computing tasks, but got me stuck to the competition since :).And I relegated my old core2duo rig to home entertainment/cinema/smart(er) tv duty.
Just to clarify: prime numbers are a subset of natural numbers, and there are infinitely many prime numbers. These two facts, taken together, mean that the ordered set of prime numbers has NO upper bound. So, there is NO largest prime number, hence no robot can find it.
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