4 ms·

So are people just really good with numbers? I don't know any 5 digit primes nor do I know a way to calculate them on the fly.

eganist 5y ago
I intuited a probably-inaccurate trick with exponentially raising a small prime (e.g 7*7*7etc), doubling the multiple (*2), and subtracting 1 (to get an odd number). That got me two substantially-different primes and narrowed my numbers a lot, which then became guesswork. My guesses in the end: -?--- ?---! ?-??! ?!??! !!!!!
- metalliqaz 5y ago
  lol this would not help me at all by the way am I supposed to take some meaning from the italicized '7' or was that just a typo?
  - ColinWright 5y ago
    He probably had 7x7x7, but with asterisks instead of the "x"s.
    - eganist 5y ago
      correct, thanks for the heads up. Fixed
- madcaptenor 5y ago
  The number you come up with in that way is at least guaranteed to not be divisible by 2 or 7. Obviously that doesn't mean it's prime but it definitely helps your odds.
  - naniwaduni 5y ago
    Also usefully, (2(a+1)^n-1) % a = (2a(a+1)^(n-1) + 2(a+1)^(n-1) - 1) % a = 1. So if you choose one of the 3k+1 primes, it's also guaranteed not divisible by 3.
NeoTar 5y ago
apparently 9.3% of all '5 digit' numbers are prime, so random guessing isn't a bad strategy - you'll find one in 10.75 totally randomly chosen numbers to be prime. Being a little smarter, prime number can only end in a 1, 3, 7 or 9 - (ending in 0, 2, 4, 6, 8 would be even, ending in 5 would be odd), so in fact it's more like 25% of 'likely' guesses.
- kadoban 5y ago
  IIRC, randomly guessing is _always_ a good strategy for "give me a prime in the range [a, b]" , in other words that's what's used for algorithms that need primes anyway. Either guess and check or guess and increase-by-2-until-prime. Does work _much_ better in this range than at crypto sizes though.
NikolaeVarius 5y ago
Its a weird thing where in smaller scales, primes numbers that LOOK prime are decent candidates of actually being prime.
- madcaptenor 5y ago
  All one- and two-digit numbers that look prime are prime, except 91. This assumes that you can easily identify - multiples of 2 and 5 (by their last digit) - multiples of 3 (the sum of their digits is divisible by 3) - multiples of 11 (for two-digit ones, they have both digits the same: 11, 22, 33, ..., 99) - squares So the first number that looks prime but isn't is the product of the two smallest primes that aren't "easy", which is 7*13 = 91.
emaro 5y ago
I thought the same, but it rejects guesses that are not valid prime numbers. So you'll find some with trial and error. With that it took me only three guesses.
Maursault 5y ago
You can guess a prime relatively easily given a few attempts, as besides 2 and 5, all other primes will have a 1, 3, 7, or 9 as its least significant digit. So, for starters, you'd never guess a number with any other least significant digit.
tobyjsullivan 5y ago
I used this site to explore options. http://compoasso.free.fr/primelistweb/page/prime/liste_online_en.php http://compoasso.free.fr/primelistweb/page/prime/liste_onlin... It's a bit tedious but still fun-ish and seemed better than guessing. Unlike Wordle, I assume it's unreasonable to expect a player to know primes so I don't think I'd call this cheating.
jerf 5y ago
If you are on Unix: primes 10000 99999 | less Then recall that "less" includes a regex-based search on the / key. This doesn't give you direction as to the best to try, of course, but it's hard to beat it in terms of bang for the buck if you're just going to try a few.
Mogzol 5y ago
Yeah I would really rather this just let me guess non-primes even though that would make it more challenging. Trying to find a prime by guessing randomly over and over is pretty frustrating.

eganist 5y ago

I intuited a probably-inaccurate trick with exponentially raising a small prime (e.g 7*7*7etc), doubling the multiple (*2), and subtracting 1 (to get an odd number). That got me two substantially-different primes and narrowed my numbers a lot, which then became guesswork. My guesses in the end: -?--- ?---! ?-??! ?!??! !!!!!

metalliqaz 5y ago
lol this would not help me at all by the way am I supposed to take some meaning from the italicized '7' or was that just a typo?
- ColinWright 5y ago
  He probably had 7x7x7, but with asterisks instead of the "x"s.
  - eganist 5y ago
    correct, thanks for the heads up. Fixed
madcaptenor 5y ago
The number you come up with in that way is at least guaranteed to not be divisible by 2 or 7. Obviously that doesn't mean it's prime but it definitely helps your odds.
- naniwaduni 5y ago
  Also usefully, (2(a+1)^n-1) % a = (2a(a+1)^(n-1) + 2(a+1)^(n-1) - 1) % a = 1. So if you choose one of the 3k+1 primes, it's also guaranteed not divisible by 3.

NeoTar 5y ago

apparently 9.3% of all '5 digit' numbers are prime, so random guessing isn't a bad strategy - you'll find one in 10.75 totally randomly chosen numbers to be prime. Being a little smarter, prime number can only end in a 1, 3, 7 or 9 - (ending in 0, 2, 4, 6, 8 would be even, ending in 5 would be odd), so in fact it's more like 25% of 'likely' guesses.

kadoban 5y ago
IIRC, randomly guessing is _always_ a good strategy for "give me a prime in the range [a, b]" , in other words that's what's used for algorithms that need primes anyway. Either guess and check or guess and increase-by-2-until-prime. Does work _much_ better in this range than at crypto sizes though.

NikolaeVarius 5y ago

Its a weird thing where in smaller scales, primes numbers that LOOK prime are decent candidates of actually being prime.

madcaptenor 5y ago
All one- and two-digit numbers that look prime are prime, except 91. This assumes that you can easily identify - multiples of 2 and 5 (by their last digit) - multiples of 3 (the sum of their digits is divisible by 3) - multiples of 11 (for two-digit ones, they have both digits the same: 11, 22, 33, ..., 99) - squares So the first number that looks prime but isn't is the product of the two smallest primes that aren't "easy", which is 7*13 = 91.

emaro 5y ago

I thought the same, but it rejects guesses that are not valid prime numbers. So you'll find some with trial and error. With that it took me only three guesses.

Maursault 5y ago

You can guess a prime relatively easily given a few attempts, as besides 2 and 5, all other primes will have a 1, 3, 7, or 9 as its least significant digit. So, for starters, you'd never guess a number with any other least significant digit.

tobyjsullivan 5y ago

I used this site to explore options. http://compoasso.free.fr/primelistweb/page/prime/liste_online_en.php http://compoasso.free.fr/primelistweb/page/prime/liste_onlin... It's a bit tedious but still fun-ish and seemed better than guessing. Unlike Wordle, I assume it's unreasonable to expect a player to know primes so I don't think I'd call this cheating.

jerf 5y ago

If you are on Unix: primes 10000 99999 | less Then recall that "less" includes a regex-based search on the / key. This doesn't give you direction as to the best to try, of course, but it's hard to beat it in terms of bang for the buck if you're just going to try a few.

Mogzol 5y ago

Yeah I would really rather this just let me guess non-primes even though that would make it more challenging. Trying to find a prime by guessing randomly over and over is pretty frustrating.