Prime numbers so memorable that people hunt for them

Original Article ↗ Hacker News Discussion ↗

Memorable and “Artistic” Primes

  • Discussion centers on primes with visually or culturally striking patterns: Belphegor’s prime (1 + zeros + 666 + zeros + 1), Trinity Hall prime, “PPcg prime,” Christmas-tree primes, and the “HN prime” rendered as a bitmap in binary.
  • People note that families of such primes exist (e.g., Belphegor primes with varying zero counts) and that many are cataloged in OEIS.
  • Several participants link this to the idea of hunting for primes that encode images or text in their digit patterns.

Palindromes and “Interesting” Numbers

  • Multiple comments explore palindromic primes, including facts like: any palindrome with an even number of decimal digits (beyond 11) is divisible by 11.
  • Examples of palindromic or pattern-based primes (e.g., 3,212,123; powers of repeated 1s; 111…1² giving 123…n…321) are shared.
  • The “interesting number paradox” and the taxicab number anecdote are used to argue that every integer can be considered interesting in some way.

Base Choice and Non-Decimal Representations

  • Some argue base 10 is an evolutionary accident and suggest searching in other bases (binary, base‑7, base‑11, base‑36).
  • Binary palindromes and primes that spell words in base‑36 (e.g., “did”, “nun”, “primetest”) are mentioned.
  • There’s experimentation with mapping letters to digits and checking which palindromic words yield prime numbers.

Anecdotes About Specific Numbers

  • The “Grothendieck prime” story (choosing 57 as a “prime”) is discussed as illustrating extreme abstraction from concrete numbers.
  • Debate over which composite feels “most prime” (e.g., 57, 87, 91), with references to arguments that 91 “wins.”
  • Personal stories include prime and palindromic phone numbers and factoring odometer readings for fun.

Cryptography and Memorable Primes

  • Some skepticism is expressed about the article’s claim that memorable primes help cryptography; RSA needs secret primes, so memorability is seen as a liability.
  • Others note public, structured primes are important as domain parameters in systems like elliptic-curve cryptography; examples include primes of the form 2^n − k (e.g., “25519”).

LLMs, Math, and OEIS

  • A shared example shows an LLM confidently misclassifying a large patterned number as composite despite code access.
  • This leads to calls for tighter integration of LLMs with symbolic math tools and databases like OEIS, and debate over whether “LLMs can’t do math” is a fair criticism.