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Prime numbers so memorable that people hunt for them

scientificamerican.com

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Re: Prime numbers so memorable that people hunt for them

#41

Post by andrewla »

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.

You can create your own using PARI/GP. To render the HN prime (a prime that has "HN" graphically with some garbage at the end, just go to [1] and type in:

    a = nextprime(0b1\
    0000000000000000\
    0100001010000010\
    0100001011000010\
    0100001010100010\
    0111111010010010\
    0100001010001010\
    0100001010000110\
    0100001010000010\
    0000000000000000\
    0000000000000000\
    )
1461507431067219818927492061258791363947404460153 is the HN prime (it looks better in binary and split to length-16 lines)

    >>> print("\n".join([bin(1461507431067219818927492061258791363947404460153)[3:][a*16:a*16+16] for a in range(10)]))
    0000000000000000
    0100001010000010
    0100001011000010
    0100001010100010
    0111111010010010
    0100001010001010
    0100001010000110
    0100001010000010
    0000000000000000
    0000000001111001
[1] https://pari.math.u-bordeaux.fr/gpwasm.html

Re: Prime numbers so memorable that people hunt for them

#42

Post by im3w1l »

zellyn wrote: post #35
susam wrote: post #13

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 q…

One of my pet hobbies is trying to figure out the least prime prime number and most prime composite numbers under 100. My votes are 61 or 89 for least prime-seeming primes and 87 and --yep-- 57 for more prime-seeming composites.

I'm gonna vote 91, since it has large divisors that can't be seen at a glance. 57 and 87 fall apart if you remember that 60 and 90 are divisible by 3.

Re: Prime numbers so memorable that people hunt for them

#43

Post by vdjskshi »

TeMPOraL wrote: post #31
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.

> Belphegor (or Baal Peor, Hebrew: בַּעַל-פְּעוֹר baʿal-pəʿōr – “Lord of the Gap”) is, in the Abrahamic religions, a demon associated with one of the seven deadly sins. According to religious tradition, he helps people make discoveries. He seduces people by proposing incredible inventions that will make them rich. Huh. Would feel right at home in our industry. > According to some demonologists from the 17th century,…

Sounds like the patron saint of LLMs

Re: Prime numbers so memorable that people hunt for them

#44

Post by miki123211 »

TeMPOraL wrote: post #31
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.

> Belphegor (or Baal Peor, Hebrew: בַּעַל-פְּעוֹר baʿal-pəʿōr – “Lord of the Gap”) is, in the Abrahamic religions, a demon associated with one of the seven deadly sins. According to religious tradition, he helps people make discoveries. He seduces people by proposing incredible inventions that will make them rich. Huh. Would feel right at home in our industry. > According to some demonologists from the 17th century,…

How was this never mentioned in Unsong? Not a single time?

Re: Prime numbers so memorable that people hunt for them

#45

Post by TeMPOraL »

miki123211 wrote: post #44
TeMPOraL wrote: post #31

Earlier quoted context omitted.

> Belphegor (or Baal Peor, Hebrew: בַּעַל-פְּעוֹר baʿal-pəʿōr – “Lord of the Gap”) is, in the Abrahamic religions, a demon associated with one of the seven deadly sins. According to religious tradition, he helps people make discoveries. He seduces people by proposing incredible inventions that will make them rich. Huh. Would feel right at home in our industry. > According to some demonologists from the 17th century,…

How was this never mentioned in Unsong? Not a single time?

IDK, I guess Scott Alexander didn't do his research thoroughly enough. Still, UNSONG is already pretty much a fractal of references and callouts to such things.

On that note, how is it I've never seen anyone connecting the famous "God of the gaps"[0] with a demon literally named "Lord of the Gap"?

(In case no one really did, let history and search engines mark this comment as the first.)

--

[0] - https://en.wikipedia.org/wiki/God_of_the_gaps

Re: Prime numbers so memorable that people hunt for them

#46

Post by quuxplusone »

sdwr wrote: post #22
fuzzythinker wrote: post #18

Earlier quoted context omitted.

"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.

"to either side" or "on either side" commonly means "on both sides" "Either" has two meanings: - verb-wise, it separates different options (you can have either X or Y) - noun-wise, it refers to two similar groups (there was no light on either side of the bridge, or, conversely, the bridge was lit on either side)

Indeed. "On either side the river lie / Long fields of barley and of rye" —Tennyson

Re: Prime numbers so memorable that people hunt for them

#47

Post by gpderetta »

TeMPOraL wrote: post #31
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.

> Belphegor (or Baal Peor, Hebrew: בַּעַל-פְּעוֹר baʿal-pəʿōr – “Lord of the Gap”) is, in the Abrahamic religions, a demon associated with one of the seven deadly sins. According to religious tradition, he helps people make discoveries. He seduces people by proposing incredible inventions that will make them rich. Huh. Would feel right at home in our industry. > According to some demonologists from the 17th century,…

Makes sense, with laziness being one of the three virtues of a great programmer.

Re: Prime numbers so memorable that people hunt for them

#48

Post by bhasi »

susam wrote: post #13

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 q…

But it's not prime - what am I missing? Why is this anecdote significant?

Re: Prime numbers so memorable that people hunt for them

#50

Post by gregschlom »

ColinWright wrote: post #39
gregschlom wrote: post #38

On the topic of palindromic numbers, I remember being fascinated as a kid with the fact that if you square the number formed by repeating the digit 1 between 1 and 9 times (e.g. 111,111^2) you get a palindrome of the form 123...n...321 with n being the number of 1s you squared. The article talks about a very similar number: 2^31-1, which is 12345678910987654321, whereas 1111111111^2 is 12345678900987654321

You have misunderstood or mis-read the article ... 2^{31}-1 is not 12345678910987654321. Specifically, 2^{31}-1 = 2147483647. Borel asked Dyson to name a prime number and, unlike Grothendieck, Dyson provided a number that is only divisible by 1 and itself: 2^{31) – 1. But that reply did not satisfy Borel. He wanted Dyson to recite all of the digits of a large prime number. Dyson fell silent, so after a moment, Sloane…

Oh, thank you. Knowing very well that 2^32 is around 4 billion, I should have immediately noticed that 12345678910987654321 is way to big to be 2^31
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