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Can humans say the largest prime number before we find the next one?

saytheprime.com

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Re: Can humans say the largest prime number before we find the next one?

#151

Post by TheRealPomax »

Dylan16807 wrote: post #138
TheRealPomax wrote: post #132

This title really needs "Mersenne" in it, because for just "primes" the answer is trivially "no".

They're not talking about the next time we find a prime, but they're also not talking about the next time we find a Mersenne prime. They're talking about the next time we find a largest known prime. Mersenne or not. So while the title could be clearer, adding the word "Mersenne" would imply the wrong thing. While it's true that the next record will probably be Mersenne, the next Mersenne might not be a record.

Or we can just, you know, read the page.

  Step 1: Claim your chunk of the fresh new Mersenne Prime
which sure seems to suggest we're talking specifically about Mersenne primes. And then we keep reading, and it ends with:

  None of us can do it alone, but together we can achieve pointless, nerdy things.

  That is, unless... the folks at Mersenne.org find a new, even bigger Mersenne prime before we can do this.
Which sure reinforces that this is about the Mersenne prime hunt, not just "any prime sequence". But why stop there? We could just watch the actual video.

Re: Can humans say the largest prime number before we find the next one?

#152

Post by Dylan16807 »

TheRealPomax wrote: post #151
Dylan16807 wrote: post #138

Earlier quoted context omitted.

They're not talking about the next time we find a prime, but they're also not talking about the next time we find a Mersenne prime. They're talking about the next time we find a largest known prime. Mersenne or not. So while the title could be clearer, adding the word "Mersenne" would imply the wrong thing. While it's true that the next record will probably be Mersenne, the next Mersenne might not be a record.

Or we can just, you know, read the page. Step 1: Claim your chunk of the fresh new Mersenne Prime which sure seems to suggest we're talking specifically about Mersenne primes. And then we keep reading, and it ends with: None of us can do it alone, but together we can achieve pointless, nerdy things. That is, unless... the folks at Mersenne.org find a new, even bigger Mersenne prime before we can do this. Which sure r…

> which sure seems to suggest we're talking specifically about Mersenne primes

Primes with an s? No, that sentence is about the single prime that was just found, which happens to be Mersenne.

> That is, unless... the folks at Mersenne.org find a new, even bigger Mersenne prime before we can do this.

Because that's by far the most likely source for the next time we find a biggest prime. If we found one another way, I don't think they'd treat it any differently.

And importantly they said "even bigger". We very likely have a lot of not-bigger Mersenne primes to find. But that wouldn't interrupt the project.

> Which sure reinforces that this is about the Mersenne prime hunt, not just "any prime sequence". But why stop there? We could just watch the actual video.

"Could humans say the largest prime number known to us before we find the next one?" sounds like exactly what I'm saying, not what you're saying.

Re: Can humans say the largest prime number before we find the next one?

#154

Post by Xcelerate »

aphantastic wrote: post #96
Xcelerate wrote: post #21

Ooh, let’s do this with the Busy Beaver function too. BB(5) is only 12,289 binary digits to say out loud. BB(6) and BB(7) can’t possibly take that much longer to say.

BB(5) is known to be 47,176,870, or 10110011111101110010100110 in base 2. https://wiki.bbchallenge.org/wiki/BB(5)

Yeah, that’s the shift function / number of steps. I’m talking about the length of the contents on the tape when the machine enters a halt state. The notation “BB” is a bit overloaded in the literature.

Re: Can humans say the largest prime number before we find the next one?

#155

Post by aphantastic »

Xcelerate wrote: post #154
aphantastic wrote: post #96

Earlier quoted context omitted.

BB(5) is known to be 47,176,870, or 10110011111101110010100110 in base 2. https://wiki.bbchallenge.org/wiki/BB(5)

Yeah, that’s the shift function / number of steps. I’m talking about the length of the contents on the tape when the machine enters a halt state. The notation “BB” is a bit overloaded in the literature.

The length of the contents of the tape of any halting TM will be less than or equal to the number of steps it takes to run. Quite trivially: you can’t consume tape without taking a step. For BB(5), 4098 1’s are written to the tape (this is referred to as Σ(5)). As for the length of the contents, I’m not sure, but again you can’t so sume tape without a step, and anecdotally the BBs are generally “back and forth”, at least the Collatz-like ones (which BB(5) is).

Re: Can humans say the largest prime number before we find the next one?

#156

Post by Xcelerate »

aphantastic wrote: post #155
Xcelerate wrote: post #154

Earlier quoted context omitted.

Yeah, that’s the shift function / number of steps. I’m talking about the length of the contents on the tape when the machine enters a halt state. The notation “BB” is a bit overloaded in the literature.

The length of the contents of the tape of any halting TM will be less than or equal to the number of steps it takes to run. Quite trivially: you can’t consume tape without taking a step. For BB(5), 4098 1’s are written to the tape (this is referred to as Σ(5)). As for the length of the contents, I’m not sure, but again you can’t so sume tape without a step, and anecdotally the BBs are generally “back and forth”, at l…

Sure, I’m just referring to the fact that there doesn’t seem to be a widespread standard on what “Busy Beaver” refers to in the literature. Scott Aaronson tends to reference the shift function, but older papers consider Σ as the “Busy Beaver function” or the “ones function” as you point out. My number came from running the machine itself and considering the largest contiguous section of output (since you typically start with a tape consisting of infinite zeros).

If we think of the nth prime as the output of a Turing machine that computes the prime numbers where n is on the input tape, then if people are saying the output aloud of such a machine, it would make sense to do so similarly here as well.

Ultimately, it doesn’t really matter. All these functions basically grow at the same rate asymptotically.

Re: Can humans say the largest prime number before we find the next one?

#158

Post by arjvik »

whoami_nr wrote: post #150
wslin wrote: post #48

Earlier quoted context omitted.

Every base is base 10 ;) https://www.reddit.com/r/ExplainTheJoke/comments/1czson4/eve...

Wouldn't 64 in base64 be represented as = ? (and not 10). Love the comic!

No, that’s 63 :)
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