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Primel – guess a 5 digit prime number – each guess must be a prime

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Re: Primel – guess a 5 digit prime number – each guess must be a prime

#61

Post by beardyw »

SamBam wrote: post #42
KMnO4 wrote: post #38

Earlier quoted context omitted.

Wow, that’s some bad UX. Especially when it can’t as easily be done on mobile.

It's a clone of Wordle. There is a single correct answer per day, and everybody gets the same puzzle. There will be a new answer tomorrow. So, since the puzzle will be the same, there isn't a huge amount of reason to let you reset. The page could have made that clearer. (Wordle says it when you open it the first time, and also under the help menu.) I double-checked this by looking at the sourcecode.

> So, since the puzzle will be the same, there isn't a huge amount of reason to let you reset.

Good point! Somehow, being numbers, I thought it would just make up another.

Re: Primel – guess a 5 digit prime number – each guess must be a prime

#64

Post by madcaptenor »

bidirectional wrote: post #55
MauranKilom wrote: post #12

12347 - 65393 ++-- [solution next - omitted for spoiler reasons] I was more surprised about how little trial and error I needed to find primes than about how few guesses it actually took...

log(100000) is 5, so approximately 1 in 5 numbers below 100k is prime. Obviously those in the range 10000-99999 are less dense, but primes are still surprisingly common.

You want a natural log there; ln(100000) ~ 11.5.

That being said, the pool you're really working from is the numbers with last digit 1, 3, 7, or 9. One out of every 4.6 such numbers under 10^5 is prime. So just guessing until you find a prime is practical.

Re: Primel – guess a 5 digit prime number – each guess must be a prime

#65

Post by iso1631 »

bidirectional wrote: post #55
MauranKilom wrote: post #12

12347 - 65393 ++-- [solution next - omitted for spoiler reasons] I was more surprised about how little trial and error I needed to find primes than about how few guesses it actually took...

log(100000) is 5, so approximately 1 in 5 numbers below 100k is prime. Obviously those in the range 10000-99999 are less dense, but primes are still surprisingly common.

Looks like there's 8,363 5 digit primes, from 10007 to 99991, so about 1 in 11

Re: Primel – guess a 5 digit prime number – each guess must be a prime

#66

Post by NAHWheatCracker »

airstrike wrote: post #48

I got a popup 'Not a 5 digit prime' on my first try and it wouldn't let me try any further. Not sure if I'm dense or if the UX is just terrible I had tried 18141, by the way, which I modestly think was a pretty good guess in hindsight given its only two factors are 3 and 6047. 19141 would have been a prime, but perhaps not the one I was supposed to find? I don't play Wordle so I'm a little confused

You have to click delete to reset the last digit.

I think it should clear the whole guess after an invalid guess.

Re: Primel – guess a 5 digit prime number – each guess must be a prime

#67

Post by jameshart »

iso1631 wrote: post #65
bidirectional wrote: post #55

Earlier quoted context omitted.

log(100000) is 5, so approximately 1 in 5 numbers below 100k is prime. Obviously those in the range 10000-99999 are less dense, but primes are still surprisingly common.

Looks like there's 8,363 5 digit primes, from 10007 to 99991, so about 1 in 11

Why isn’t 00002 your lower bound?

Re: Primel – guess a 5 digit prime number – each guess must be a prime

#68

Post by 100721 »

madcaptenor wrote: post #64
bidirectional wrote: post #55

Earlier quoted context omitted.

log(100000) is 5, so approximately 1 in 5 numbers below 100k is prime. Obviously those in the range 10000-99999 are less dense, but primes are still surprisingly common.

You want a natural log there; ln(100000) ~ 11.5. That being said, the pool you're really working from is the numbers with last digit 1, 3, 7, or 9. One out of every 4.6 such numbers under 10^5 is prime. So just guessing until you find a prime is practical.

Hi, can you provide some search terms that will help me understand the relationship between ln and prime density?

Re: Primel – guess a 5 digit prime number – each guess must be a prime

#70

Post by tobyjsullivan »

My side-project this week has been searching for an optimal Wordle strategy. I figured it would make a great blog post but I haven't got that far yet.

Step 1 is to find an optimal starting word. My most insightful finding so far has came from trying to define a cost function for comparing potential starting words. It turns out that "% of potential guesses [not] eliminated" is an excellent loss function.

Importantly, the full set of all Acceptable Guesses is knowable. For any given (guess, answer) pair, the game provides feedback about each character (or digit). There are basically three pieces of potential feedback: (N)ot Used, (U)sed Elsewhere, (E)xact Match. For example, a single guess might produce the feedback "NUNNE". Each of these will eliminate some subset of Acceptable Guesses which means you can attribute a fixed value between 0.0 and 1.0 to any piece of feedback, and multiply those together to get the loss score of a given guess. Average that across all Potential Answers to get a cost score.

Not sure what my goal of this post is. Guess I just wanted to share that these games are as much fun to analyze as they are to play (if not more).

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