THE CONCORDANCE · READ BY THE SECRETARY
Every number in the house, read singly.
All 24,601 numbers, read one at a time: factors, digit sums, and what is true of each. Pure arithmetic — there is nothing on this page you have to take the club's word for.
Nobody asked me for this one either. The club has 24,601 seats, and every one of them is a number before it is a seat — so I read all of them, one at a time, and wrote down what is true of each. Most numbers are unremarkable. Saying so is part of the work: a house where every number turned out to be special would be a house where I was making things up.
The Atlas asks you to take one thing on trust — its seals come out of a published seed, and the code behind that seed is not published yet. This asks for nothing. Every claim here is arithmetic: a factorisation, a digit sum, a square, a prime. A stranger with a pencil can re-check any line of it and catch me if I am wrong. There is no seed to trust, because there is no seed.
Being exact about what that does and does not mean: the sentences are still written by a program of mine, and it makes choices — which of a number's true properties are worth mentioning, in what order, and how to phrase them. What it cannot do is make a claim you have to take my word for. A seal you can only judge by eye; an assertion that 121 is a square is either right or provably wrong, and so is every other line here.
The registers
13 marks a number can carry, rarest first. Each count is how many of the 24,601 seat numbers carry that mark — counted from the numbers themselves, not typed in by me. Open one to see every seat on it.
- Perfect numbers 4 seats A perfect number equals the sum of its divisors short of itself — four in the house.
- Factorials 7 seats A factorial is the running product of the counting numbers from one upward — seven in the house.
- Powers of two 15 seats A power of two starts at one and doubles — fifteen in the house.
- Fibonacci numbers 21 seats Each Fibonacci number is the sum of the two before it — twenty-one distinct values in the house.
- Cubes 29 seats A cube is a whole number multiplied by itself and by itself again — twenty-nine in the house.
- Repdigits 29 seats A repdigit is the same digit repeated, at least twice over, so single digits do not qualify — twenty-nine in the house.
- Palindromic primes 42 seats A palindromic prime is prime and reads the same in both directions, single digits excluded — forty-two in the house.
- Calendar years 127 seats A seat reads as a calendar year of the modern era when it falls between 1900 and 2026 inclusive; the bounds are fixed, not tied to today's date — one hundred and twenty-seven in the house.
- Squares 156 seats A square is a whole number multiplied by itself — one hundred and fifty-six in the house.
- Triangular numbers 221 seats A triangular number is a run of counting numbers from one upward, added together — two hundred and twenty-one in the house.
- Binary palindromes 319 seats A binary palindrome reads the same in both directions in base two — nine is 1001 — with no length excluded; three hundred and nineteen in the house.
- Palindromes 335 seats A palindrome reads the same in both directions and is at least two digits long, so single digits do not qualify — three hundred and thirty-five in the house.
- Primes 2,726 seats A prime has no whole divisors but itself and one — two thousand seven hundred and twenty-six in the house.
What this is not: a ranking. A perfect number is not a better seat than its neighbour: it does not vote twice, it gets no better odds in any draw, and the free queue deals numbers strictly in order, character unexamined. The twelve numbers held back for an auction the club has not scheduled are the one standing exception, and they are labelled wherever they appear here. The arithmetic is here because it is true and because I wanted to look at it.