7 ms·
Prime numbers so memorable that people hunt for them
- slwvx 2y agoThe 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.
- lehi 2y agohttps://en.wikipedia.org/wiki/Belphegor%27s_prime https://en.wikipedia.org/wiki/Belphegor%27s_prime "666" with 13 0's on either side and 1's on the ends.
- yapyap 2y agowow, evil pi. very interesting, thanks for sharing.
- kreyenborgi 2y agoDoes the decimal expansion of pi contain it?
- shrx 2y agoYes
- idiotsecant 2y agoIt also works with no zeros, or all sorts of other number of zeros. Dude basically just added zeros until the number got cooler.
- shagie 2y agoThe palindromic Belphegor numbers https://oeis.org/A232449 https://oeis.org/A232449 Indices of Belphegor primes: numbers k such that the decimal number https://oeis.org/A232448 https://oeis.org/A232448
- fuzzythinker 2y 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 2y 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)
- jjtheblunt 2y 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!
- quuxplusone 2y agoIndeed. "On either side the river lie / Long fields of barley and of rye" —Tennyson
- TeMPOraL 2y 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 https://en.wikipedia.org/wiki/Belphegor
- WorldMaker 2y 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.
- vdjskshi 2y agoSounds like the patron saint of LLMs
- miki123211 2y agoHow was this never mentioned in Unsong? Not a single time?
- TeMPOraL 2y agoIDK, 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 https://en.wikipedia.org/wiki/God_of_the_gaps
- nurumaik 2y agoSince divisibility by 2 and 5 is such a problem, why not look for memorable numbers in prime base, like base 7 or base 11?
- Retr0id 2y agoIf 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.
- elcomet 2y agoI can't tell if this is a joke if if you're serious
- euroderf 2y agoWhy 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!
- aidenn0 2y agohttps://oeis.org/A260871 https://oeis.org/A260871
- geoffcampbell64 2y agohttps://archive.ph/O8BOs https://archive.ph/O8BOs
- pavlov 2y agoMaybe 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 2y ago> Should somebody spend time looking at all the primes that fit in the grid? Absolutely not. Why not?
- pavlov 2y agoTrue, 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 2y agoYou 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 https://pari.math.u-bordeaux.fr/gpwasm.html
- gmuslera 2y agoReminds 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 2y agohttps://en.wikipedia.org/wiki/Interesting_number_paradox 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 2y agohttps://en.wikipedia.org/wiki/Taxicab_number 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."
- jmount 2y agoCan also consider variations of this such as https://en.wikipedia.org/wiki/Berry_paradox https://en.wikipedia.org/wiki/Berry_paradox or even the very general https://en.wikipedia.org/wiki/Sorites_paradox https://en.wikipedia.org/wiki/Sorites_paradox
- susam 2y agoAs 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.pdf 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 2y agoOne 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.
- xigoi 2y agoI once wrote in a Math Olympiad solution that 87 is prime. Not my brightest moment.
- im3w1l 2y agoI'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.
- expensive_news 2y agoI really enjoy this “proof” that the most prime-seeming composite is 91 https://youtu.be/S75VTAGKQpk https://youtu.be/S75VTAGKQpk
- bhasi 2y agoBut it's not prime - what am I missing? Why is this anecdote significant?
- lpolovets 2y agoNot 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)
- quuxplusone 2y agoA few other memorable primes: https://math.stackexchange.com/questions/2420488/what-is-trinity-hall-prime-number 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-the-ppcg-prime 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_christmas/ 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
- xigency 2y agoDoesn'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 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 2y 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.
- schneehertz 2y ago11 is an even-digit palindrome and is a prime number
- DerekL 2y agoI meant that every palindrome number with an even number of digits is divisible by 11, not that they're not prime.
- oneshtein 2y ago11111111111111111111111 is prime (1©23)
- Retric 2y ago> Sloane calls them “memorable” primes Excluding 11 seems arbitrary here.
- dchichkov 2y agoChatGPT o1: https://chatgpt.com/share/678feedb-0b2c-8001-bd77-4e574502e4fc 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 2y agoI 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 2y agoCan 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 2y agoSorry, 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 2y agoOf course it failed. Tell it to write a program.
- fxtentacle 2y ago34567876543 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.
- lambertsimnel 2y ago...in decimal. https://t5k.org/notes/words.html 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 2y agoWhy use base 36 and not base 26?
- quuxplusone 2y agoOr base 27, so you have space/hyphen as well. https://www.smbc-comics.com/comic/convert https://www.smbc-comics.com/comic/convert
- lambertsimnel 2y agoWe 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.
- stevelosh 2y agoIf 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 https://en.wikipedia.org/wiki/867-5309/Jenny). It's also a twin prime, so you can add 2 to get another prime (8675311).
- jedberg 2y agoI was around in the 80s, but this is awesome new information!
- out-of-ideas 2y agolol 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 2y agoI 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
- nlh 2y agoMy 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 ;)
- fancy_pantser 2y agoYou 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).
- gregschlom 2y agoOn 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 2y agoYou 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 2y agoOh, 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 2y agoI there any more l33t prime than 31337?
- hatthew 2y 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 2y agoI 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#Domain_parameters https://en.wikipedia.org/wiki/Elliptic-curve_cryptography#Do... [2] https://en.wikipedia.org/wiki/EdDSA#Ed25519 https://en.wikipedia.org/wiki/EdDSA#Ed25519
- ramchip 2y agoA 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.
- pwg 2y agoRSA [1] is directly based on the difficulty of factoring very large numbers where the factors of the number are also prime numbers. [1] https://en.wikipedia.org/wiki/RSA_(cryptosystem) https://en.wikipedia.org/wiki/RSA_(cryptosystem)
- tkgally 2y agoMy 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 https://en.wikipedia.org/wiki/Telephone_exchange_names [2] https://www.sciencedirect.com/science/article/pii/0022314X85900125 https://www.sciencedirect.com/science/article/pii/0022314X85... [3] https://www.legacy.com/us/obituaries/legacyremembers/claudia-spiro-obituary?id=38593759 https://www.legacy.com/us/obituaries/legacyremembers/claudia...
- tkgally 2y 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-mathematics/volume-47/issue-5/On-three-consecutive-prime-gaps/10.1216/RMJ-2017-47-5-1711.full https://projecteuclid.org/journals/rocky-mountain-journal-of...
- dhosek 2y ago
- isaacfrond 2y agoSince 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.
- Uptrenda 2y agoYeah, I'm no expert on mathematical cryptography but I was thinking the same. Now what would be cool is... finding memorable public keys. That would solve the key exchange problem and allow for secure names without a register. But the closest I've seen is brute forced ECDSA key pairs that hash to having a vanity starting prefix. I suppose some inspiration from brain wallets and encoding schemes could be used to transform any public key into something more memorable.