21–30 of 36 posts
Given that we know that there are infinitely many primes, why are we interested in knowing ever larger ones? It's somewhat like asking, what is the largest known natural number?
If nothing else, "what's the largest prime number you've found?" would be a fun question to ask another intelligent civilization, should we make contact with one.
>"Anyone can download the software free. So you, too, could discover a record-breaking prime number — if you have enough patience." Maybe mining zcash is lucrative, but finding a new big prime number sounds pretty nice
I wish we can collectively "mine" solutions for questions that are currently un-solved. Like Larger prime number, or create a hive mind that acts as an AI.
I have two questions: 1: How do we know it's the largest known prime number? What qualifies as a 'known' prime number? Is there an official registry somewhere? 2: Are all prime numbers smaller then this one also known? Or could somebody still come up with an unknown 'not very large prime number'?
1. Essentially, yes there's a list. Since there doesn't exist a higher level formula to identify primes it's been verified by some variation of a brute force method. 2. That all smaller primes are known can't be verified. Primes of this size are usually found by a number of formulas that find "likely" primes and then verified by brute force (afaik). Because of that fuzzy match to start there might be smaller primes t…
For example, there is at least one prime between 2^77,232,915 and 2^77,232,916 that we don’t know (https://en.wikipedia.org/wiki/Bertrand%27s_postulate)
(That’s a very loose bound. I think that, for any N > 2, there are more primes than squares of integers less than it)
Quote from the Article: """The figure is calculated by multiplying 2 by itself 77,232,917 times and then subtracting 1.""" Would HN agree that multiplying 2 by itself once is 2⨯2 = pow(2,2), twice is 2⨯2⨯2 = pow(2,3) and N times yields pow(2,N+1)? The Mersenne Prime found is pow(2,77232917) − 1, hence the article got the number wrong?
If you're going that way, you can also interpret it - pardon my programming - as the following: int result; for (int i = 0; i ... which obviously results in 3. Also a (mersienne) prime, but not quite as big as you'd expect, and certainly not millions of digits long.
Given that we know that there are infinitely many primes, why are we interested in knowing ever larger ones? It's somewhat like asking, what is the largest known natural number?
Quote from the Article: """The figure is calculated by multiplying 2 by itself 77,232,917 times and then subtracting 1.""" Would HN agree that multiplying 2 by itself once is 2⨯2 = pow(2,2), twice is 2⨯2⨯2 = pow(2,3) and N times yields pow(2,N+1)? The Mersenne Prime found is pow(2,77232917) − 1, hence the article got the number wrong?
If you're going that way, you can also interpret it - pardon my programming - as the following: int result; for (int i = 0; i ... which obviously results in 3. Also a (mersienne) prime, but not quite as big as you'd expect, and certainly not millions of digits long.
Earlier quoted context omitted.
1. Essentially, yes there's a list. Since there doesn't exist a higher level formula to identify primes it's been verified by some variation of a brute force method. 2. That all smaller primes are known can't be verified. Primes of this size are usually found by a number of formulas that find "likely" primes and then verified by brute force (afaik). Because of that fuzzy match to start there might be smaller primes t…
We know for sure that we don’t know all smaller primes. For example, there is at least one prime between 2^77,232,915 and 2^77,232,916 that we don’t know ( https://en.wikipedia.org/wiki/Bertrand%27s_postulate ) (That’s a very loose bound. I think that, for any N > 2, there are more primes than squares of integers less than it)
Earlier quoted context omitted.
1. Essentially, yes there's a list. Since there doesn't exist a higher level formula to identify primes it's been verified by some variation of a brute force method. 2. That all smaller primes are known can't be verified. Primes of this size are usually found by a number of formulas that find "likely" primes and then verified by brute force (afaik). Because of that fuzzy match to start there might be smaller primes t…
Calling it brute force isn't quite right. There is an efficient algorithm for prime determination (Lucas-Lehmer primality test) on Mersenne Primes (numbers of the form 2^p-1). https://en.wikipedia.org/wiki/Lucas–Lehmer_primality_test