FilterHN

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

14 days ago

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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].

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

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

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

14 days ago

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> 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”:

14 days ago

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

noman-land

13 days ago

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How do you do mental factoring?

13 days ago

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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 reduce it to 4619 which isn’t divisible by 3 and I can also tell it’s not divisible by 11. I can also rule out 19 at a glance. To check 13, I might do my right-side divisibility test where I start by subtracting 39 from the right, which gives 458. I could continue with that, but taking 39 from the left gets me to a small enough number faster of 68 which isn’t divisible by 13. Right-side divisibility for 17 takes 119 from the right leaving 45 which isn’t divisible by 17. For 23, I can do a left-side removal of 46 to rule that out. 29, go right to bring it to 459 and then 43, not divisible by 29. For 31, I’ll do right side to get 434 and then 31 so 4619=149×31 and 149 is prime and I’m done.

⸻

1. To check for divisibility by 11, subtract the sum of even numbered digits from the sub of odd numbered digits. If 11∣n, then you’ll have a multiple of 11. E.g., for 13,857, we compare (3+5)-(1+8+7)=-8 which is not a multiple of 11.³

2. To check for divisibility by 111, we take advantage of the fact that 3×37=111, 27×37=999 and thus 1000≡1(mod 37) and we can then add up the digits in groups of 3, and pull out the most convenient multiple of 111 to see if we have 0, 37 or 74. E.g., with our example about, 13+852=865-888=-23 which is not a multiple of 37.

3. As an added bonus that number is the remainder when dividing by 11. Similarly the number I get with the check in footnote 2 is the remainder when dividing by 37.

flancian

13 days ago

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Hello fellow hobby factorizer :)

I wanted to share this small gem of a paper in case it helps you like it's helped me:

"Simple divisibility rules for the 1st 1000 prime numbers": https://arxiv.org/pdf/math/0001012

13 days ago

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Meh, most of those aren’t all that helpful. Multiplying the last digit by -17 and adding that to the rest of the number to do a divisibility test for 19? I’d be more inclined to do the right-side reduction which isn’t appreciably different and, if you’re good at keeping some side numbers in working memory can give you the actual quotient if it is divisible which these rules won’t give you.

13 days ago

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Interesting! What do you do when you try to factor a large number that doesn't yield to any of your mental factoring techniques? It might be prime, after all, or composite with only large prime factors. Do you give up after a while? Run it through a factoring program? Keep plugging away until you get to the number's square root?

13 days ago

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With the odometer I have a time limit to factor the number (around one minute on the highway, up to four on surface streets). I usually have no problem factoring a four digit number (time in 24-hour format) within the minute given, especially since the worst case scenario would be 22:09=47×47. When factoring, it’s less about recognizing the primes as the key composites once you get down to four digits or less, which usually happens surprisingly quickly.

CurtMonash

12 days ago

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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.

14 days ago

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Follow-up: My formal study of programming stopped with that Fortran IV class a half century ago, but LLMs now delude me into thinking I can program. I just had Claude write me a Python program to list all of the seven-digit numbers that are both primes and palindromes. It found 668: 1003001, 1008001, 1022201, 1028201, 1035301, ...

[1] https://en.wiktionary.org/wiki/Appendix:English_palindromes

jodrellblank

13 days ago

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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 numbers (ignoring case, stripping all punctuation); could there be one which does?

13 days ago

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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.

jodrellblank

13 days ago

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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.

13 days ago

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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.

jodrellblank

12 days ago

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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.

stevelosh

14 days ago

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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

14 days ago

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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 ;)

[1] https://en.wikipedia.org/wiki/867-5309/Jenny

pwg

14 days ago

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> 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 was you wanted. The minimum wage cashier didn't care, but the cash register demanded "a number". So giving the cashier Jenny's number worked.

This has largely faded now that they can track everyone via one's credit card numbers.

noahjk

14 days ago

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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.

hakfoo

13 days ago

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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"

pwg

14 days ago

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If a given retailer gets the same number off your card each time you do contactless, then that retailer /could/ track you via that number.

If all retailers get the same number, then they can each track you, and correlate your purchases between themselves.

Note, there just needs to be /some/ constant number from whatever comes through via contactless, the number does not have to be the magic numbers that post the sale to the card.

Dylan16807

13 days ago

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It doesn't rotate. Also it looks like if you use the contactless method built into the actual card it doesn't use a different number.

fancy_pantser

14 days ago

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You can use the number with your local area code just about anywhere at the pump to get a gas discount as well (a common loyalty reward program benefit).

jedberg

14 days ago

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

out-of-ideas

14 days ago

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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)

freedomben

14 days ago

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I do the same thing! Downside is every time I read my tests I get that song stuck in my head. Upside is it's a joy for some people when they discover it in the test

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

lehi

15 days ago

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

fuzzythinker

15 days ago

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"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

14 days ago

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"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)

14 days ago

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

jjtheblunt

14 days ago

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(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!

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

TeMPOraL

14 days ago

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> 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.

irrational

14 days ago

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

alphan0n

13 days ago

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Startup > trapt (archaic) us

WorldMaker

14 days ago

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> 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

14 days ago

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

TeMPOraL

14 days ago

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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

14 days ago

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

vdjskshi

14 days ago

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Sounds like the patron saint of LLMs

idiotsecant

15 days ago

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

shagie

14 days ago

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The palindromic Belphegor numbers https://oeis.org/A232449

Indices of Belphegor primes: numbers k such that the decimal number https://oeis.org/A232448

yapyap

15 days ago

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wow, evil pi.

very interesting, thanks for sharing.

kreyenborgi

14 days ago

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Does the decimal expansion of pi contain it?

shrx

14 days ago

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Yes

susam

15 days ago

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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

14 days ago

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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

14 days ago

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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.

https://youtu.be/S75VTAGKQpk

expensive_news

14 days ago

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I really enjoy this “proof” that the most prime-seeming composite is 91

xigoi

14 days ago

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

bhasi

14 days ago

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

eigenket

14 days ago

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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.

bongodongobob

14 days ago

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Yeah I don't get it either.

hatthew

14 days ago

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> 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?

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

arh68

14 days ago

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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

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

ramchip

14 days ago

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A lot of public-key cryptography is based on finite fields, and the integers modulo N combined with addition and multiplication form a finite field iff N is prime. This brings some extremely useful properties e.g. every non-zero element has a multiplicative inverse. N must also be public so people can compute things (e.g. to verify a signature), and big to resist brute force attacks.

[1] https://en.wikipedia.org/wiki/RSA_(cryptosystem)

pwg

14 days ago

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RSA [1] is directly based on the difficulty of factoring very large numbers where the factors of the number are also prime numbers.

xigency

15 days ago

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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]

14 days ago

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> 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.

schneehertz

13 days ago

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

12 days ago

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

oneshtein

14 days ago

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11111111111111111111111 is prime (1©23)

geoffcampbell64

15 days ago

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https://archive.ph/O8BOs

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

15 days ago

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A few other memorable primes:

    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

jmward01

15 days ago

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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!)

https://www.bradyharanblog.com/blog/artistic-prime-numbers

14 days ago

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Here's a previous HN submission about finding Waldo in pi (spoiler: only by cheating significantly re what counts as "Waldo"): https://news.ycombinator.com/item?id=30872676

I googled around trying to figure out what year James McKee created the Trinity Hall prime. The internet is (IMO) presenting it mainly as some kind of Wonder of the Ancient World — with the date of creation conveniently filed off. The first post below claims that the year McKee left Cambridge and created the prime was 1996. It seems to have hit peak internet presence only in the 2010s, though, so I wish there were an authoritative source to confirm (or deny) the 1996 date.

https://www.futilitycloset.com/2017/09/10/trinity-hall-prime...

https://www.futilitycloset.com/2020/01/12/more-prime-images/

noman-land

13 days ago

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These are so cool.

slwvx

17 days ago

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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.

nurumaik

15 days ago

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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

15 days ago

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

euroderf

14 days ago

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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

15 days ago

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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.

aidenn0

14 days ago

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https://oeis.org/A260871

dchichkov

14 days ago

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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

14 days ago

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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

14 days ago

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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

14 days ago

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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).

bongodongobob

13 days ago

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Of course it failed. Tell it to write a program.

lpolovets

15 days ago

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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

15 days ago

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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.

pavel_lishin

15 days ago

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

Why not?

pavlov

15 days ago

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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.”

andrewla

14 days ago

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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

gregschlom

14 days ago

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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

14 days ago

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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

14 days ago

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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

jonhohle

14 days ago

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I there any more l33t prime than 31337?

gmuslera

15 days ago

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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

pavel_lishin

15 days ago

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> 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.

jmount

14 days ago

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Can also consider variations of this such as https://en.wikipedia.org/wiki/Berry_paradox or even the very general https://en.wikipedia.org/wiki/Sorites_paradox

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

shagie

14 days ago

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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."

fxtentacle

14 days ago

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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

14 days ago

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> Sloane calls them “memorable” primes

Excluding 11 seems arbitrary here.

14 days ago

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

Retric

14 days ago

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

14 days ago

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

oneshtein

14 days ago

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131

13331

100000000000000000000333000000000000000000001 (20 zeroes on both sides)

lambertsimnel

14 days ago

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...in decimal.

https://t5k.org/notes/words.html points out that "When we work in base 36 all the letters are used - hence all words are numbers." Primes can be especially memorable in base 36. "Did," "nun," and "pop" are base-36 primes, as is "primetest" and many others.

norswap

14 days ago

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Why use base 36 and not base 26?

lambertsimnel

14 days ago

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We certainly could, but we already use 0-9 and then letters for hexadecimal. Using all 26 letters for base 36, but not base 26, is just an extension of that.

14 days ago

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Or base 27, so you have space/hyphen as well. https://www.smbc-comics.com/comic/convert

isaacfrond

14 days ago

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

That's nonsense. I'm sure there thinking of RSA, but that needs secret prime numbers. So easy-to-remember is pretty much the opposite of one want. Also they are way to big. 2048 bit RSA needs two 300 digit prime numbers.