det A = 30030, and its residue at 25 primes — 5 of which divide it

At its defaults it draws det a = 30030, and its residue at 25 primes — 5 of which divide it. Each dot is det A mod p, drawn as a fraction of p so the primes are comparable. A dot on the floor is a prime at which the elimination reports a singular matrix — and the matrix is not singular: its determinant is 30030. 5 of 25 primes here are unlucky, a rate of 20 per cent, which is what it looks like when the primes are small. At the 26-bit primes a modular determinant actually uses, a prime divides a 15-bit determinant with probability of order 2.24·10⁻⁷ — but the consequence is unchanged, and there is no way to see it from one residue. What sees it is the budget: computing more residues than Hadamard's bound requires, and refusing to reconstruct when the extra ones disagree.

unlucky-prime is one function in lib/figures/integer.js — exact arithmetic — no residual to print, and a cost measured in the length of the numbers. Everything below came out of it during this build, at arguments taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

Each dot is det A mod p, drawn as a fraction of p so the primes are comparable. A dot on the floor is a prime at which the elimination reports a singular matrix — and the matrix is not singular: its determinant is 30030. 5 of 25 primes here are unlucky, a rate of 20 per cent, which is what it looks like when the primes are small. At the 26-bit primes a modular determinant actually uses, a prime divides a 15-bit determinant with probability of order 2.24·10⁻⁷ — but the consequence is unchanged, and there is no way to see it from one residue. What sees it is the budget: computing more residues than Hadamard's bound requires, and refusing to reconstruct when the extra ones disagree.

Each dot is det A mod p, drawn as a fraction of p so the primes are comparable. A dot on the floor is a prime at which the elimination reports a singular matrix — and the matrix is not singular: its determinant is 30030. 5 of 25 primes here are unlucky, a rate of 20 per cent, which is what it looks like when the primes are small. At the 26-bit primes a modular determinant actually uses, a prime divides a 15-bit determinant with probability of order 2.24·10⁻⁷ — but the consequence is unchanged, and there is no way to see it from one residue. What sees it is the budget: computing more residues than Hadamard's bound requires, and refusing to reconstruct when the extra ones disagree.

Each dot is det A mod p, drawn as a fraction of p so the primes are comparable. A dot on the floor is a prime at which the elimination reports a singular matrix — and the matrix is not singular: its determinant is 30030. 5 of 30 primes here are unlucky, a rate of 16.7 per cent, which is what it looks like when the primes are small. At the 26-bit primes a modular determinant actually uses, a prime divides a 15-bit determinant with probability of order 2.24·10⁻⁷ — but the consequence is unchanged, and there is no way to see it from one residue. What sees it is the budget: computing more residues than Hadamard's bound requires, and refusing to reconstruct when the extra ones disagree.

Each dot is det A mod p, drawn as a fraction of p so the primes are comparable. A dot on the floor is a prime at which the elimination reports a singular matrix — and the matrix is not singular: its determinant is 30030. 5 of 34 primes here are unlucky, a rate of 14.7 per cent, which is what it looks like when the primes are small. At the 26-bit primes a modular determinant actually uses, a prime divides a 15-bit determinant with probability of order 2.24·10⁻⁷ — but the consequence is unchanged, and there is no way to see it from one residue. What sees it is the budget: computing more residues than Hadamard's bound requires, and refusing to reconstruct when the extra ones disagree.

Each dot is det A mod p, drawn as a fraction of p so the primes are comparable. A dot on the floor is a prime at which the elimination reports a singular matrix — and the matrix is not singular: its determinant is 30030. 5 of 40 primes here are unlucky, a rate of 12.5 per cent, which is what it looks like when the primes are small. At the 26-bit primes a modular determinant actually uses, a prime divides a 15-bit determinant with probability of order 2.24·10⁻⁷ — but the consequence is unchanged, and there is no way to see it from one residue. What sees it is the budget: computing more residues than Hadamard's bound requires, and refusing to reconstruct when the extra ones disagree.

Each dot is det A mod p, drawn as a fraction of p so the primes are comparable. A dot on the floor is a prime at which the elimination reports a singular matrix — and the matrix is not singular: its determinant is 30030. 5 of 49 primes here are unlucky, a rate of 10.2 per cent, which is what it looks like when the primes are small. At the 26-bit primes a modular determinant actually uses, a prime divides a 15-bit determinant with probability of order 2.24·10⁻⁷ — but the consequence is unchanged, and there is no way to see it from one residue. What sees it is the budget: computing more residues than Hadamard's bound requires, and refusing to reconstruct when the extra ones disagree.

Every figure above checked its own claims on the way to being drawn, and a claim that failed would have stopped the picture rather than shipped a wrong one. Those checks used to leave no trace at all: a passing one returned true and the only evidence the figure had checked anything was that nothing crashed. The list below is what they actually said, collected by running this generator with an observer installed — not a description of what it is believed to check.

6 distinct claims across 6 sets of arguments, grouped below by shape — because most of them are one sentence with a different number in it, and how many separate times that sentence was put to the test is the informative part.

The rule does not apply to it. It factorises nothing, so there is no residual it could be withholding. That is worth stating rather than leaving blank: a site that reported the rule as satisfied by every generator would be counting mostly generators the rule never reached.

Across the library: the rule bites on 217 of 397 generators — 199 print a residual and 18 are exempt with a published reason; 180 factorise nothing. Read from lib/residual-rule.js, which is the same body the gate enforces from, and the gate's last check fails the build if this page and it disagree about any generator.