Prime numbers so memorable that people hunt for them • Hacker News Board

Re: Prime numbers so memorable that people hunt for them

#101

Post by hakfoo » Thu, Jan 23, 2025, 5:11 AM UTC

noahjk wrote: post #86

pwg wrote: post #84

Earlier quoted context omitted.

> someone has used that (along with a local area code) as the phone number for a store loyalty card. Usually because for far too long, noisy retailers wanted a "phone number" upon checkout (even if one was paying cash -- Radio Shack was an especially bad one back in the day). For those who didn't want to get yet more telemarketing calls, repeating "Jenny's number" [1] from the song was a way to "just buy" whatever it…

Does contactless payment help at all? I know it uses a different card number, but I’m not sure if it’s a rotating number.

There's a conceptually linked concept called the PAR (Payment Account Reference) which some payment systems return.

You can't transact with it directly, but theoretically it refers to the same payment instrument whether you accessed it by the 16-digit PAN on the card, a mobile wallet that generates a new dPAN each time, or a token that corresponds to a secure vault platform.

It's useful for things like transit payments where someone might tap their card when entering the train and their phone when exiting, and they need to treat them as equivalent for "fares for a single traveller/card can be no more than $x per day"

Re: Prime numbers so memorable that people hunt for them

#102

Post by jodrellblank » Thu, Jan 23, 2025, 7:16 AM UTC

tkgally wrote: post #99

jodrellblank wrote: post #97

Earlier quoted context omitted.

I wondered if we map English letters to digits (a=0, b=1, c=2, ... , z=25) is there anything which is both a palindrome in its English form and in its number form, and prime? I took a list of palindromes from Wikipedia[1] and tested them, and yes: deified 3485843 bib 181 did 383 I note that none of them use letters which map to double-digits (k=10, l=11, m=12, etc.); none of the palindrome sentences make palindromic…

How about representing the words as numbers in base 26? That would preserve the palidromicity for both the word and the number, and primality would not be affected by the base representation. Might not be as much fun, though.

Retesting the words like that does find some: REPAPER/5305958597, DUD/2551, DID/2239, LEMEL/5105267, PEEWEEP/4683479543.

With this hackish code to interpret the text as base 26, rebase that to base10, test primality, I can't test the sentences (I think it might be overflowing on the higher value words, even). I think it's not so fun if the base 10 numbers are not palindromic.

Re: Prime numbers so memorable that people hunt for them

#103

Post by tkgally » Thu, Jan 23, 2025, 10:57 AM UTC

jodrellblank wrote: post #102

tkgally wrote: post #99

Earlier quoted context omitted.

How about representing the words as numbers in base 26? That would preserve the palidromicity for both the word and the number, and primality would not be affected by the base representation. Might not be as much fun, though.

Retesting the words like that does find some: REPAPER/5305958597, DUD/2551, DID/2239, LEMEL/5105267, PEEWEEP/4683479543. With this hackish code to interpret the text as base 26, rebase that to base10, test primality, I can't test the sentences (I think it might be overflowing on the higher value words, even). I think it's not so fun if the base 10 numbers are not palindromic.

Thanks for trying! I was thinking of creating a set of digits for base 26 using emoji or other Unicode characters. Then the numbers would at least look like palindromes. But I don't know how interesting palindromes in an ad hoc character set would be.

Re: Prime numbers so memorable that people hunt for them

#104

Post by DerekL » Fri, Jan 24, 2025, 3:02 AM UTC

schneehertz wrote: post #95

DerekL wrote: post #55

Earlier quoted context omitted.

> Interestingly, there are no four digit palindrome primes because they would be divisible by 11. In fact, this holds for any even number of digits.

11 is an even-digit palindrome and is a prime number

I meant that every palindrome number with an even number of digits is divisible by 11, not that they're not prime.

Re: Prime numbers so memorable that people hunt for them

#105

Post by CurtMonash » Fri, Jan 24, 2025, 12:14 PM UTC

dhosek wrote: post #93

noman-land wrote: post #90

Earlier quoted context omitted.

How do you do mental factoring?

I don’t usually keep the factors, but I have a variety of techniques. Putting aside the trivial cases of divisibility by 2, 3, 5, 11¹ and 37², a lot of it comes down to find ways to make the numbers smaller, so, for example. my current odometer reading is 13,857. To test for divisibility by 7, I can turn that into 14,000-13852=143 which I can tell at a glance isn’t divisible by 7. It is divisible by 3, so I can reduc…

My first step would be to note that 13,857 is divisible by 7 if and only if 1385 is. But yes, my second step would be a lot like yours, in my case subtracting from 1400.

Re: Prime numbers so memorable that people hunt for them

#106

Post by jodrellblank » Fri, Jan 24, 2025, 1:40 PM UTC

tkgally wrote: post #103

jodrellblank wrote: post #102

Earlier quoted context omitted.

Retesting the words like that does find some: REPAPER/5305958597, DUD/2551, DID/2239, LEMEL/5105267, PEEWEEP/4683479543. With this hackish code to interpret the text as base 26, rebase that to base10, test primality, I can't test the sentences (I think it might be overflowing on the higher value words, even). I think it's not so fun if the base 10 numbers are not palindromic.

Thanks for trying! I was thinking of creating a set of digits for base 26 using emoji or other Unicode characters. Then the numbers would at least look like palindromes. But I don't know how interesting palindromes in an ad hoc character set would be.

My view on that is that DEIFIED is seven symbols, and I was treating those as the 'Unicode' set of digits for base 26. Swapping them out for different symbols would only change the presentation, e.g. adding a +600 offset in Unicode codepoints to each character gives ʜʝʡʞʡʝʜ but ... the same thing just in a different presentation, so not a very useful transform.

Treating the word as a base 26 number means that if the word is palindromic, the number is too since they're the same thing, so that's a single test, and primality is a second test. In the original idea with a=1, b=2, if the word is a palindrome in letters, the number form might not be (zz -> 2525), so that's two different palindrome tests and a primality test which "deified" passes. (Incidentally: if the digits don't need to being a palindrome, then: "Live not on evil, Madam, live not on evil" is prime).

This has been a mishmash of PowerShell which has convenient string/char code handling, SWI Prolog which has implicit bignums and a builtin fast probabalistic prime test with bignum support in "crypto_is_prime/2"; Dyalog APL which has excellent base conversion: 26⊥⎕A⍳'WORD'. Each language doesn't have the other things: C#/PowerShell/APL/Python have no builtin fast bignum-supporting prime test, Prolog has awkward or tedious file/string handling, APL has no bignums or prime test.