My family’s phone number when I was a child was both a palindrome and a prime: 7984897.<p>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!”<p>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.<p>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.<p>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 <i>n</i> a Divisor of <i>n</i>?” [2]. She died two years ago, at the age of sixty-six [3].<p>[1] <a href="https://en.wikipedia.org/wiki/Telephone_exchange_names" rel="nofollow">https://en.wikipedia.org/wiki/Telephone_exchange_names</a><p>[2] <a href="https://www.sciencedirect.com/science/article/pii/0022314X85900125" rel="nofollow">https://www.sciencedirect.com/science/article/pii/0022314X85...</a><p>[3] <a href="https://www.legacy.com/us/obituaries/legacyremembers/claudia-spiro-obituary?id=38593759" rel="nofollow">https://www.legacy.com/us/obituaries/legacyremembers/claudia...</a>
If you were around in the 80's and 90's you might have already memorized the prime 8675309 (<a href="https://en.wikipedia.org/wiki/867-5309/Jenny" rel="nofollow">https://en.wikipedia.org/wiki/867-5309/Jenny</a>). It's also a twin prime, so you can add 2 to get another prime (8675311).
<a href="https://en.wikipedia.org/wiki/Belphegor%27s_prime" rel="nofollow">https://en.wikipedia.org/wiki/Belphegor%27s_prime</a><p>"666" with 13 0's on either side and 1's on the ends.
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 <a href="https://www.ams.org/notices/200410/fea-grothendieck-part2.pdf" rel="nofollow">https://www.ams.org/notices/200410/fea-grothendieck-part2.pd...</a> 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:<p>> 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.”
> Since prime numbers are very useful in secure communication, such easy-to-remember large prime numbers can be of great advantage in cryptography<p>What's the use of notable prime numbers in cryptography? My understanding is that a lot of cryptography relies on <i>secret</i> 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?
Doesn't take very much searching to find this pretty nifty palindrome prime:<p>3,212,123 (the 333rd palindrome prime)<p>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).<p>For the curious, here's a small set of the palindrome primes:
<a href="http://brainplex.net/pprimes.txt" rel="nofollow">http://brainplex.net/pprimes.txt</a><p>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]
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.
ChatGPT o1: <a href="https://chatgpt.com/share/678feedb-0b2c-8001-bd77-4e574502e4fc" rel="nofollow">https://chatgpt.com/share/678feedb-0b2c-8001-bd77-4e574502e4...</a><p>> Thought about large prime check for 3m 52s: <i>"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."</i><p>Feels like this Online Encyclopedia of Integer Sequences (OEIS) would be a good candidate for a hallucination benchmark...
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)
Maybe there's a prime number that makes a mildly interesting picture when rendered in base-2 in a 8*8 grid.<p>Should somebody spend time looking at all the primes that fit in the grid? Absolutely not.
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.<p>The article talks about a very similar number: 2^31-1, which is 12345678910987654321, whereas 1111111111^2 is 12345678900987654321
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.
...in decimal.<p><a href="https://t5k.org/notes/words.html" rel="nofollow">https://t5k.org/notes/words.html</a> 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.
<i>Since prime numbers are very useful in secure communication, such easy-to-remember large prime numbers can be of great advantage in cryptography,</i><p>That's nonsense. I'm sure there thinking of RSA, but that needs <i>secret</i> 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.