stevelosh 10 hours ago

If you were around in the 80's and 90's you might have already memorized the prime 8675309 (https://en.wikipedia.org/wiki/867-5309/Jenny). It's also a twin prime, so you can add 2 to get another prime (8675311).

  • nlh 2 hours ago

    My other favorite fun fact about this number (other than this new prime info which I am excited to have learned) is that in almost every store I’ve tried it, someone has used that (along with a local area code) as the phone number for a store loyalty card.

    I’m a Bay Area guy, so if you’re ever at Safeway and need to get the discount without giving up your personal info, 415-867-5309 has got ya covered ;)

  • jedberg 5 hours ago

    I was around in the 80s, but this is awesome new information!

    • out-of-ideas 3 hours ago

      lol i didnt realize this was a prime number but i re-use this number any time i need a fake phone number in some sample/example data (im pretty certain nobody gets the reference, or takes the time to read it)

tkgally 6 hours ago

My family’s phone number when I was a child was both a palindrome and a prime: 7984897.

My parents had had the number for two decades without noticing it was a palindrome. I still remember my father’s delight when he got off a phone call with a friend: “Doug just said, ‘Hey, I dialed your number backwards and it was still you who answered.’ I never noticed that before!”

A few years later, around 1973, one of the other math nerds at my high school liked to factor seven-digit phone numbers by hand just for fun. I was then taking a programming class—Fortran IV, punch cards—and one of my self-initiated projects was to write a prime factoring program. I got the program to work, and, inspired by my friend, I started factoring various phone numbers. Imagine my own delight when I learned that my home phone number was not only a palindrome but also prime.

Postscript: The reason we hadn’t noticed that 7984897 was a palindrome was because, until around 1970, phone numbers in our area were written and spoken with the telephone exchange name [1]. When I was small, I learned our phone number as “SYcamore 8 4 8 9 7” or “S Y 8 4 8 9 7.” We thought of the first two digits as letters, not as numbers.

Second postscript: I lost contact with that prime-factoring friend after high school. I see now that she went on to earn a Ph.D. in mathematics, specialized in number theory, and had an Erdős number of 1. In 1985, she published a paper titled “How Often Is the Number of Divisors of n a Divisor of n?” [2]. She died two years ago, at the age of sixty-six [3].

[1] https://en.wikipedia.org/wiki/Telephone_exchange_names

[2] https://www.sciencedirect.com/science/article/pii/0022314X85...

[3] https://www.legacy.com/us/obituaries/legacyremembers/claudia...

  • tkgally 3 hours ago

    > In 1985, she published a paper titled “How Often Is the Number of Divisors of n a Divisor of n?”

    Claudia Spiro seems to have remained actively interested in prime numbers into her sixties. In 2017, she published a paper titled “On three consecutive prime-gaps”:

    https://projecteuclid.org/journals/rocky-mountain-journal-of...

  • dhosek 2 hours ago

    I thought everybody factors phone numbers. I also factor the odometer reading in my car while driving.

lehi 14 hours ago

https://en.wikipedia.org/wiki/Belphegor%27s_prime

"666" with 13 0's on either side and 1's on the ends.

  • fuzzythinker 12 hours ago

    "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.

    • sdwr 12 hours ago

      "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)

      • quuxplusone 9 hours ago

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

      • jjtheblunt 12 hours ago

        (Native speaker) i read either in the sense of logical or, so one side alone (tegardless of which side) or both sides at once.

        Interesting how varied the ohrasing can be read, though!

  • TeMPOraL 11 hours ago

    > 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, his powers are strongest in April.

    Any demo days or other significant VC stuff happening in April?

    > The German bishop and witch hunter, Peter Binsfeld (ca. 1540–ca.1600) wrote that Belphegor tempts through laziness. According to Binsfeld's Classification of Demons, Belphegor is the main demon of the deadly sin known as sloth in the Christian tradition. The anonymous author of the Lollard tract The Lanterne of Light, however, believed Belphegor to embody the sin of gluttony rather than sloth.

    Yeah, hits too close to home.

    Via https://en.wikipedia.org/wiki/Belphegor

    • irrational 6 hours ago

      Can’t spell “demon” without “demo”. Cue the church lady.

    • WorldMaker 10 hours ago

      > Any demo days or other significant VC stuff happening in April?

      Lots of tech companies plan elaborate demos for April 1st, for some foolish reason. It certainly gets very busy on HN keeping up.

    • miki123211 9 hours ago

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

      • TeMPOraL 9 hours ago

        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

    • gpderetta 9 hours ago

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

    • vdjskshi 9 hours ago

      Sounds like the patron saint of LLMs

  • idiotsecant 13 hours ago

    It also works with no zeros, or all sorts of other number of zeros. Dude basically just added zeros until the number got cooler.

  • yapyap 13 hours ago

    wow, evil pi.

    very interesting, thanks for sharing.

susam 13 hours ago

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.”

  • zellyn 10 hours ago

    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.

    • im3w1l 9 hours ago

      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.

    • xigoi 9 hours ago

      I once wrote in a Math Olympiad solution that 87 is prime. Not my brightest moment.

  • bhasi 8 hours ago

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

    • eigenket 7 hours ago

      The point is that Grothendieck, easily one of the greatest mathematicians of all time, who regularly proved deep and fundamental facts about prime numbers, cared so little about particular numbers that he accidentally gave an easy to see non-prime as an example of a prime.

      He was used to working on completely different levels of abstraction, so when faced with concrete numbers he could easily make a mistake that a school-child (or hacker news commenter) could spot.

hatthew 7 hours ago

> Since prime numbers are very useful in secure communication, such easy-to-remember large prime numbers can be of great advantage in cryptography

What's the use of notable prime numbers in cryptography? My understanding is that a lot of cryptography relies on secret prime numbers, so choosing a notable/memorable prime number is like choosing 1234 as your PIN. Are there places that need a prime that's arbitrary, large, and public?

  • arh68 3 hours ago

    I believe they're talking about something like ECC

    > To use ECC, all parties must agree on all the elements defining the elliptic curve, that is, the domain parameters of the scheme. The size of the field used is typically either prime (and denoted as p) or is a power of two

    like "25519"

    > An EdDSA signature scheme is a choice: ... of finite field F q over odd prime power q ... Ed25519 is the EdDSA signature scheme where q = 2^255 - 19

    [1] https://en.wikipedia.org/wiki/Elliptic-curve_cryptography#Do...

    [2] https://en.wikipedia.org/wiki/EdDSA#Ed25519

xigency 13 hours ago

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]

  • DerekL 7 hours ago

    > 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.

slwvx 3 days ago

The title of the Scientific American article is "These Prime Numbers Are So Memorable That People Hunt for Them", which matches the content much better than the title above.

quuxplusone 13 hours ago

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
nurumaik 14 hours ago

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?

  • elcomet 12 hours ago

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

  • euroderf 11 hours ago

    Why do we care about base 10 ? Because we have five digits per appendage ? BFD. Accident of evolution.

    What about palindromes in binary ? That's about as close to a mathematical ideal as we could get. Yes?

    Let's see. decimal 11 = binary 1011, its palindrome = 1101 = decimal 13, GOLD!

  • Retr0id 13 hours ago

    If we allow non-decimal bases, (2^n)-1 works for a lot of memorable values of n (e.g. 2, 3, 5, 7... and 31, per the article), or some less memorable but very long values of n, like 136279841

    They're all technically palindromes in base-2.

dchichkov 11 hours ago

ChatGPT o1: https://chatgpt.com/share/678feedb-0b2c-8001-bd77-4e574502e4...

> Thought about large prime check for 3m 52s: "Despite its interesting pattern of digits, 12,345,678,910,987,654,321 is definitely not prime. It is a large composite number with no small prime factors."

Feels like this Online Encyclopedia of Integer Sequences (OEIS) would be a good candidate for a hallucination benchmark...

  • scotty79 11 hours ago

    I think firmly marrying llms with symbolic math calculator/database, so they can check things they don't really know "by heart" would go a long way towards making them seem smart.

    I really hope Wolfram is working on LLM that is trying to learn what it means to be WolframAlpha user.

  • bongodongobob 7 hours ago

    Can we stop with the "haha llms can't do math" nonsense? You'll one shot it every time if you tell it to use Python. You're holding it wrong.

    • dchichkov 6 hours ago

      Sorry, but this was ChatGPT/o1 with access to code execution (Python) and it used almost 4 minutes to do reasoning. It had done a few checks with smaller numbers, all of which had failed. And it proceeded to make a wrong conclusion (with high confidence).

gregschlom 10 hours ago

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

  • ColinWright 10 hours ago

    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 jumped in and said, “1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1.”

    So Sloane was supplying a different prime, but one where he could recite all the digits.

    • gregschlom 8 hours ago

      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

lpolovets 13 hours ago

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)

pavlov 13 hours ago

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.

  • andrewla 9 hours ago

    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
  • pavel_lishin 13 hours ago

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

    Why not?

    • pavlov 13 hours ago

      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.”

gmuslera 13 hours ago

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.

  • pavel_lishin 13 hours ago

    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.

    • shagie 12 hours ago

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

      The name is derived from a conversation ca. 1919 involving mathematicians G. H. Hardy and Srinivasa Ramanujan. As told by Hardy:

      I remember once going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

jonhohle 8 hours ago

I there any more l33t prime than 31337?

fxtentacle 11 hours ago

34567876543

333 2 111 2 333

1111 4 7 4 1111

35753 3 35753

At one time, in university, I wrote a tool to aesthetically score primes.

Retric 12 hours ago

> Sloane calls them “memorable” primes

Excluding 11 seems arbitrary here.

  • DerekL 7 hours ago

    No, that doesn't fit the pattern. The number in the middle can't be repeated.

    • Retric 7 hours ago

      That’s how it’s excluded, not why we should care about the pattern being exactly that formula.

      • DerekL 4 hours ago

        Sure, you could also look for primes of the form 123…(n-1)n⋅n(n-1)…321.