Generator
Every single-digit error in 3141592653, under weights 1…10 mod 11
A generator in the computation library, called 2 times across 1 essays. Below: what it draws with nothing chosen 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.
With nothing chosen
What each check-digit scheme catches
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.
- a scheme that weights every position the same catches no transposition ×1
- and every single-digit error too ×1
- descending weights over a prime modulus catch every transposition ×1
- every single-digit error is caught exactly when the modulus is at least ten and coprime to every weight ×1
- the error kinds are single, transpose or twin ×1
- the number is between four and fourteen digits ×1
- the number is between six and fourteen digits ×1
- the scheme is one of sum-9, sum-10, flat-11, weighted-10, isbn-11 ×1
Where it is called
Every figure on this list is drawn by the same rule, so a change to the rule changes all of them at once. That is why the list is published.