Generator

check-digit

A generator in the computation library, called 2 times across 1 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.

check-digit is one function. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page — so a figure here is the same figure a reader meets in an essay, and if the generator changes, this page changes with it.

At its defaults

Every single-digit error in 3141592653, under weights 1…10 mod 11A grid with one column per position and one row per replacement digit, marking which substitutions the check digit catches.3141592653 · check 5each column is a position, each row a digit put there instead31415926530123456789··········caughtmissedweights 1…10 mod 11: 90 of the 90 single-digit changes alter the check digit — 100.0%no single wrong digit gets through, because 11 shares no factor with any weight and is largerthan the ten symbols

show: "compare"

What each check-digit scheme catchesBars showing, for several check-digit schemes, the fraction of single-digit errors and of adjacent transpositions the scheme detects.one digit wrongtwo neighbours swappeddigit sum mod 9mod 998%0%digit sum mod 10mod 10100%0%digit sum mod 11mod 11 — prime100%0%weights 3,1 mod 10mod 10100%44%weights 1…10 mod 11mod 11 — prime100%100%every error of each kind was applied to 1605384927 and the check digit recomputed — 90 substitutions and 9 swapsthe two properties that decide it are whether neighbouring positions carry different weights, and whether the modulus isprime

What it checks while it draws

Collected by running the family and recording what it asserted, not written here. The count is how many separate times the claim was put to the test while these drawings were made.

Where it is called

Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.

The whole library · What the figures prove