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

Re: Prime numbers so memorable that people hunt for them

#11

Post by pavel_lishin » Tue, Jan 21, 2025, 5:28 PM UTC

pavlov wrote: post #9

Maybe there's a prime number that makes a mildly interesting picture when rendered in base-2 in a 8*8 grid. Should somebody spend time looking at all the primes that fit in the grid? Absolutely not.

> Should somebody spend time looking at all the primes that fit in the grid? Absolutely not.

Why not?

Re: Prime numbers so memorable that people hunt for them

#12

Post by pavel_lishin » Tue, Jan 21, 2025, 5:29 PM UTC

gmuslera wrote: post #10

Reminds me the demonstration that all whole numbers are interesting in a way or another. Being memorable in this case is not so much about memory but about having an easy to notice pattern of digits, or a clear trivial algorithm to build them.

https://en.wikipedia.org/wiki/Interesting_number_paradox

> The interesting number paradox is a humorous paradox which arises from the attempt to classify every natural number as either "interesting" or "uninteresting". The paradox states that every natural number is interesting.[1] The "proof" is by contradiction: if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting number – but the smallest uninteresting number is itself interesting because it is the smallest uninteresting number, thus producing a contradiction.

Re: Prime numbers so memorable that people hunt for them

#13

Post by susam » Tue, Jan 21, 2025, 5:29 PM UTC

As soon as I read the title of this post, the anecdote about the Grothendieck prime came to mind. Sure enough, the article kicks off with that very story! The article also links to https://www.ams.org/notices/200410/fea-grothendieck-part2.pd... which has an account of this anecdote. But the article does not reproduce the anecdote as stated in the linked document. So allow me to share it here as I've always found it quite amusing:

> One striking characteristic of Grothendieck’s mode of thinking is that it seemed to rely so little on examples. This can be seen in the legend of the so-called “Grothendieck prime”. In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.”

Re: Prime numbers so memorable that people hunt for them

#14

Post by pavlov » Tue, Jan 21, 2025, 5:33 PM UTC

pavel_lishin wrote: post #11

pavlov wrote: post #9

Maybe there's a prime number that makes a mildly interesting picture when rendered in base-2 in a 8*8 grid. Should somebody spend time looking at all the primes that fit in the grid? Absolutely not.

> Should somebody spend time looking at all the primes that fit in the grid? Absolutely not. Why not?

True, it’s not any of my business.

Maybe superhuman AI will have humans do this kind of work to make us feel useful. “Oh, you’re right, does look a bit like a duck! Fun! You’re doing so well helping me discover the secrets of the universe! I enjoy working with people.”

Re: Prime numbers so memorable that people hunt for them

#15

Post by lpolovets » Tue, Jan 21, 2025, 5:35 PM UTC

Not quite the same, but this reminds me of bitcoin, where miners are on the hunt for SHA hashes that start with a bunch of zeroes in a row (which one could say is memorable/unusual)

Re: Prime numbers so memorable that people hunt for them

#16

Post by quuxplusone » Tue, Jan 21, 2025, 5:45 PM UTC

A few other memorable primes:

https://math.stackexchange.com/questions/2420488/what-is-tri...

    888888888888888888888888888888
    888888888888888888888888888888
    888888888888888888888888888888
    888111111111111111111111111888
    888111111111111111111111111888
    888111111811111111118111111888
    888111118811111111118811111888
    888111188811111111118881111888
    888111188811111111118881111888
    888111888811111111118888111888
    888111888881111111188888111888
    888111888888111111888888111888
    888111888888888888888888111888
    888111888888888888888888111888
    888111888888888888888888111888
    888811188888888888888881118888
    188811188888888888888881118881
    188881118888888888888811188881
    118888111888888888888111888811
    111888811118888888811118888111
    111188881111111111111188881111
    111118888111111111111888811111
    111111888811111111118888111111
    111111188881111111188881111111
    111111118888811118888811111111
    111111111888881188888111111111
    111111111118888888811111111111
    111111111111888888111111111111
    111111111111118811111111111111
    111111111111111111111111111111
    062100000000000000000000000000
    000000000000000000000000000000
    000000000000000000000000000000
    000000000000000000000000000000
    000000000000000000000000000000
    000000000000000000000000000000
    000000000000000000000000000000
    000000000000000000000000000000
    000000000000000000000000000000
    000000000000000000000000000000
    000000000000000000000000000000
    000000000000000000000000000000
    000000000000000000000000000000
    000000000000000000000000000000
    000000000000000000000000000001

https://codegolf.stackexchange.com/questions/146017/output-t...

    777777777777777777777777777777777777777
    777777777777777777777777777777777777777
    777777777777777777777777777777777777777
    777777777777777777777777777777777777777
    111111111111111111111111111111111111111
    111111111111111111111111111111111111111
    188888888118888888811188888811188888811
    188111118818811111881881111881881111881
    188111118818811111881881111111881111111
    188888888118888888811881111111881118888
    188111111118811111111881111111881111881
    188111111118811111111881111881881111881
    188111111118811111111188888811188888811
    111111111111111111111111111111111111111
    111111111111111111111111111111111111111
    333333333333333333333333333333333333333

https://www.reddit.com/r/math/comments/a9544e/merry_christma...

    20181111111111111111111111111111111111
    11111111111111111166111111111111111111
    11111111111111111868011111111111111111
    11111111111111118886301111111111111111
    11111111111111168863586111111111111111
    11111111111111803608088361111111111111
    11111111111193386838898668111111111111
    11111111111111163508800111111111111111
    11111111111111806560885611111111111111
    11111111111118630808083861111111111111
    11111111111585688085086853511111111111
    11111111116355560388530533881111111111
    11111111506383308388080803858311111111
    11111183585588536538563360080880111111
    11111111111118383588055585111111111111
    11111111111568838588536853611111111111
    11111111118830583888838553631111111111
    11111111808885338530655586888811111111
    11111183886860888066566368806366111111
    11115385585036885386888980683008381111
    11055880566883886086806355803583885511
    11111111111111111685311111111111111111
    11111111111111111863311111111111111111
    11111111111111111035611111111111111111

Re: Prime numbers so memorable that people hunt for them

#17

Post by xigency » Tue, Jan 21, 2025, 5:50 PM UTC

Doesn't take very much searching to find this pretty nifty palindrome prime:

3,212,123 (the 333rd palindrome prime)

Interestingly, there are no four digit palindrome primes because they would be divisible by 11. This is obvious in retrospect but I found this fact by giving NotebookLM a big list of palindrome primes (just to see what it could possibly say about it over a podcast).

For the curious, here's a small set of the palindrome primes: http://brainplex.net/pprimes.txt

The format is x. y. z. n signifying the x-th prime#, y-th palindrome#, z-th palindrome-prime#, and the number (n). [Starting from 2]

Re: Prime numbers so memorable that people hunt for them

#18

Post by fuzzythinker » Tue, Jan 21, 2025, 5:51 PM UTC

lehi wrote: post #3

https://en.wikipedia.org/wiki/Belphegor%27s_prime "666" with 13 0's on either side and 1's on the ends.

"on both sides" because "on either side" to me meant it may be duo of 1-13zeros-6661 and 1666-13zeros-1.

More for those who don't click the link, other Belphegor primes numbers are with the following number of zeros in both ends (and 1 to cap off the ends): 0, 13, 42, 506, 608, 2472, 2623, maybe more.

Re: Prime numbers so memorable that people hunt for them

#19

Post by jmward01 » Tue, Jan 21, 2025, 5:56 PM UTC

quuxplusone wrote: post #16

A few other memorable primes: https://math.stackexchange.com/questions/2420488/what-is-tri... 888888888888888888888888888888 888888888888888888888888888888 888888888888888888888888888888 888111111111111111111111111888 888111111111111111111111111888 888111111811111111118111111888 888111118811111111118811111888 888111188811111111118881111888 888111188811111111118881111888 888111888811111111118888111888 8881118888811111…

These are great! I wonder if Carl Sagan knew about them when writing Contact. The movie doesn't go into the part of the book that is relevant here (trying to avoid spoilers but if you read the book you know!)

Re: Prime numbers so memorable that people hunt for them

#20

Post by elcomet » Tue, Jan 21, 2025, 6:05 PM UTC

nurumaik wrote: post #4

Since divisibility by 2 and 5 is such a problem, why not look for memorable numbers in prime base, like base 7 or base 11?

I can't tell if this is a joke if if you're serious