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Hello,
I wonder. What is the biggest number under which all possible primes have been discovered?
Cheers,
Olivier | |
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Hello,
I wonder. What is the biggest number under which all possible primes have been discovered?
Cheers,
Olivier
Hello Olivier
The biggest number under wich all possible primes have been discovered is:
infinity+1
This by itself also means, that such a "biggest" number does not excist, since there is a limitless (infinite) number of primes, so even if you find a prime with trillions of digits, there WILL ALWAYS be a prime that is bigger than that prime.
Take a look here and see if you can find what you are looking for: http://primes.utm.edu/infinity.html
Thanks for your question.
Take care
KEP | |
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Hello,
I wonder. What is the biggest number under which all possible primes have been discovered?
Cheers,
Olivier
Hello Olivier
The biggest number under wich all possible primes have been discovered is:
infinity+1
This by itself also means, that such a "biggest" number does not excist, since there is a limitless (infinite) number of primes, so even if you find a prime with trillions of digits, there WILL ALWAYS be a prime that is bigger than that prime.
Take a look here and see if you can find what you are looking for: http://primes.utm.edu/infinity.html
Thanks for your question.
Take care
KEP
I read that differently. I think he is asking for the smallest number which has not been proven prime or composite. But, yes, you have answered it correctly for the way he worded it. | |
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I do not think a particular number can be given.
As an example, 982,451,653 has the property that all primes under it have been discovered; see the list The first fifty million primes.
However, it is easy to find all primes up to a higher limit, typically with the sieve of Eratosthenes.
On Wikipedia the exact count of primes below 100,000,000,000,000,000,000,000,000 is given. This could be because someone found all primes below that limit.
Note that it is extremely fast to determine if numbers of these sizes are prime or not. So there is usually no need for having a list. You can just check for primality again each time you need it, instead for doing a look-up in a list.
/JeppeSN
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Me:
On Wikipedia the exact count of primes below 100,000,000,000,000,000,000,000,000 is given. This could be because someone found all primes below that limit.
No, that count was calculated with advanced methods. I guess, after thinking a bit, it is not practical to "discover" all primes under 10^26. Even if each candidate is very fast to check, as I wrote. So your number must be greater than 10^9 but less than 10^26.
/JeppeSN
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Hello,
Sorry for my English, I indeed wondered about the "smallest number which has not been proven prime or composite". I was curious if there was a number under which nobody was looking for primes anymore since all below numbers would be categegorized as prime or not.
Thank you for the Sieve of Eratosthenes, which I didn't know about. Note that this is different. With this sieve, anyone could take a given number and run the algorithm against it to find all the primes but that leads to the problem of resources to run such a venture.
And that is more the point of my question, with all the computer resources given to prime hunt, is there a number under which no primegrid (or other) algorithm is running since it knows it won'd discover anything new.
Thanks. | |
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I read that differently. I think he is asking for the smallest number which has not been proven prime or composite. But, yes, you have answered it correctly for the way he worded it.
You read it correct and I answered it correct, see that is interesting, because now we have a true Homer Simpson situation:
"You are both right"
as he stated to Bart and Lisa when they both sought confirmation that their point of stand was in fact correct. Sometimes fantasy just ain't as far from reality as one may think :) | |
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And that is more the point of my question, with all the computer resources given to prime hunt, is there a number under which no primegrid (or other) algorithm is running since it knows it won'd discover anything new.
Thanks.
Generally the large primes which these projects are looking for have no real use - they are so large that they are unwieldy for encryption, plus it would be easy to go through the list of those that have been discovered (and published) to crack an encryption key by trial division. It's really just (* flame shields on *) an exercise in one-upmanship. Not many people are hunting for primes below the Top5000. If that kind of work tickles your fancy, then try some of PrimeGrid's PRPNet projects in the Project Staging Area, or have a look around at (* gasp! *) No Prime Left Behind http://www.noprimeleftbehind.net | |
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While there is a component of "publicity" or "my prime is bigger than yours", I would point out that PrimeGrid is working to resolve a few different mathematical conjectures ("The Riesel Problem", for one). If you're not into pure number theory, okay, but many here would disagree with the "one-upmanship" characterization.
Primes used in common encryption schemes (e.g. RSA) are comparatively tiny... there's no need for a big distributed computing project to find them. They are "a dime a dozen".
--Gary
p.s. No need for "flame shields"... we're a remarkably civil group! :-) | |
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While there is a component of "publicity" or "my prime is bigger than yours", I would point out that PrimeGrid is working to resolve a few different mathematical conjectures ("The Riesel Problem", for one). If you're not into pure number theory, okay, but many here would disagree with the "one-upmanship" characterization.
But the real question: if proven / disproven, what would that imply? "X is the smallest number that has Y property".
Good. And? If there's no use.... | |
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While there is a component of "publicity" or "my prime is bigger than yours", I would point out that PrimeGrid is working to resolve a few different mathematical conjectures ("The Riesel Problem", for one). If you're not into pure number theory, okay, but many here would disagree with the "one-upmanship" characterization.
But the real question: if proven / disproven, what would that imply? "X is the smallest number that has Y property".
Good. And? If there's no use....
Back in the day, before computers. having your name beside a world record prime served as a calling card that meant you had something between your ears besides hair. Similarly having your name attached to a conjecture is akin to a dog scent-marking territory, a form of "I was here first and made something of it". So yes, there's a use, just not the mathematical kind. | |
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