[HN Gopher] Prime numbers so memorable that people hunt for them
___________________________________________________________________
Prime numbers so memorable that people hunt for them
Author : georgecmu
Score : 170 points
Date : 2025-01-18 14:41 UTC (4 days ago)
(HTM) web link (www.scientificamerican.com)
(TXT) w3m dump (www.scientificamerican.com)
| slwvx wrote:
| 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.
| lehi wrote:
| https://en.wikipedia.org/wiki/Belphegor%27s_prime
|
| "666" with 13 0's on either side and 1's on the ends.
| yapyap wrote:
| wow, evil pi.
|
| very interesting, thanks for sharing.
| kreyenborgi wrote:
| Does the decimal expansion of pi contain it?
| shrx wrote:
| Yes
| idiotsecant wrote:
| 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 wrote:
| The palindromic Belphegor numbers https://oeis.org/A232449
|
| Indices of Belphegor primes: numbers k such that the decimal
| number https://oeis.org/A232448
| fuzzythinker wrote:
| "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 wrote:
| "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 wrote:
| (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 wrote:
| Indeed. "On either side the river lie / Long fields of
| barley and of rye" --Tennyson
| TeMPOraL wrote:
| > _Belphegor (or Baal Peor, Hebrew: ba'`al-p@'`vor ba'al-p@'or
| - "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
| WorldMaker wrote:
| > 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 wrote:
| Sounds like the patron saint of LLMs
| miki123211 wrote:
| How was this never mentioned in Unsong? Not a single time?
| TeMPOraL wrote:
| 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 wrote:
| Makes sense, with laziness being one of the three virtues of
| a great programmer.
| irrational wrote:
| Can't spell "demon" without "demo". Cue the church lady.
| alphan0n wrote:
| Startup > trapt (archaic) us
| nurumaik wrote:
| 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?
| Retr0id wrote:
| 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.
| elcomet wrote:
| I can't tell if this is a joke if if you're serious
| euroderf wrote:
| 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!
| aidenn0 wrote:
| https://oeis.org/A260871
| geoffcampbell64 wrote:
| https://archive.ph/O8BOs
| pavlov wrote:
| 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 wrote:
| > _Should somebody spend time looking at all the primes that
| fit in the grid? Absolutely not._
|
| Why not?
| pavlov wrote:
| 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 wrote:
| 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(14615074310672198189274920612587913639
| 47404460153)[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
| gmuslera wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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
| susam wrote:
| 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 wrote:
| 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.
| xigoi wrote:
| I once wrote in a Math Olympiad solution that 87 is prime.
| Not my brightest moment.
| im3w1l wrote:
| 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.
| expensive_news wrote:
| I really enjoy this "proof" that the most prime-seeming
| composite is 91
|
| https://youtu.be/S75VTAGKQpk
| bhasi wrote:
| But it's not prime - what am I missing? Why is this anecdote
| significant?
| bongodongobob wrote:
| Yeah I don't get it either.
| eigenket wrote:
| 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.
| lpolovets wrote:
| 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)
| quuxplusone wrote:
| 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
| jmward01 wrote:
| 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!)
| quuxplusone wrote:
| 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.bradyharanblog.com/blog/artistic-prime-numbers
|
| https://www.futilitycloset.com/2017/09/10/trinity-hall-
| prime...
|
| https://www.futilitycloset.com/2020/01/12/more-prime-images/
| noman-land wrote:
| These are so cool.
| xigency wrote:
| 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 wrote:
| > 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.
| oneshtein wrote:
| 11111111111111111111111 is prime (1(c)23)
| Retric wrote:
| > Sloane calls them "memorable" primes
|
| Excluding 11 seems arbitrary here.
| DerekL wrote:
| No, that doesn't fit the pattern. The number in the middle
| can't be repeated.
| Retric wrote:
| That's how it's excluded, not why we should care about the
| pattern being exactly that formula.
| DerekL wrote:
| Sure, you could also look for primes of the form
| 123...(n-1)n[?]n(n-1)...321.
| oneshtein wrote:
| 11
|
| 131
|
| 13331
|
| 100000000000000000000333000000000000000000001 (20 zeroes on
| both sides)
|
| 11111111111111111111111 (1(c)23)
| dchichkov wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| Of course it failed. Tell it to write a program.
| fxtentacle wrote:
| 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.
| lambertsimnel wrote:
| ...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 wrote:
| Why use base 36 and not base 26?
| quuxplusone wrote:
| Or base 27, so you have space/hyphen as well.
| https://www.smbc-comics.com/comic/convert
| lambertsimnel wrote:
| 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.
| stevelosh wrote:
| 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).
| jedberg wrote:
| I was around in the 80s, but this is awesome new information!
| out-of-ideas wrote:
| 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 wrote:
| 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
| nlh wrote:
| 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 ;)
| fancy_pantser wrote:
| 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).
| pwg wrote:
| > 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.
|
| [1] https://en.wikipedia.org/wiki/867-5309/Jenny
| noahjk wrote:
| 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.
| pwg wrote:
| 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 wrote:
| 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.
| gregschlom wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| I there any more l33t prime than 31337?
| hatthew wrote:
| > 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 wrote:
| 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
| ramchip wrote:
| 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.
| pwg wrote:
| RSA [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)
| tkgally wrote:
| 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
| Erdos 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 wrote:
| > 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 wrote:
| I thought everybody factors phone numbers. I also factor the
| odometer reading in my car while driving.
| noman-land wrote:
| How do you do mental factoring?
| dhosek wrote:
| 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=149x31
| 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 3x37=111, 27x37=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.
| tkgally wrote:
| 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, ...
| isaacfrond wrote:
| _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.
| Uptrenda wrote:
| Yeah, 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.
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