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Complement

Prime #
719
Origin domain
Mathematics
Subdomain
set theory → Mathematics

Core Idea

A complement is the residual: everything in a declared reference universe that is not in a designated subset. Formally, given a universe \(U\) and a subset \(A \subseteq U\), the complement \(A^c\) (equivalently \(U \setminus A\)) is the set \(\{x \in U : x \notin A\}\). The structural commitment is small but consequential — you declare a containing whole, you specify a part of it, and you reason about what is left over — and the complement is precisely that leftover, fixed once those two specifications are fixed. Change either the universe or the subset and the complement changes with it, which means the complement, despite its unary-looking notation, is always a three-way relation among universe, part, and residual.

Three structural features travel with the complement role and are what make it a genuine prime rather than a piece of set-theoretic notation. Universe-relativity: a complement is undefined until a universe is declared, so the complement of "vertebrates" inside the universe "animals" is one set and inside "all living things" another, and many apparent disputes about a complement turn out to be undeclared-universe disputes in which the two parties are reasoning in different containing wholes. Closure under double application: \((A^c)^c = A\) — the complement of the complement returns the original — a symmetry that, when it fails in some substrate, is the diagnostic that the substrate is not doing classical complementation (intuitionistic logic, fuzzy categories, and partial-information settings all break it). Negative-definition power: a complement specifies a set by what it excludes, which is often far easier than enumerating what it includes; defining "lawful conduct" as "everything not prohibited" or "non-fiction" as "everything not fictional" compresses an unbounded extension into a finite intension. The same role — a residual relative to a declared universe, closed under double application, useful for definition-by-exclusion — recurs across substrates that have nothing to do with formal set theory.

How would you explain it like I'm…

The Leftovers

Put all your toys in one big box. Pick out the red ones and hold them. The Complement is everything STILL in the box — all the toys that aren't red. If you'd picked a different box, or picked the blue ones instead, the leftover pile would be different too.

Everything Else

First you have to say what the whole group is — like 'all the animals at the zoo.' Then you pick a part of it — like 'the lions.' The complement is everything in the whole group that isn't your part: all the not-lions. If you change the whole group, or change your part, the leftovers change too. So a complement is really three things working together: the whole, the part, and what's left.

The Residual Set

A complement is the 'everything else' once you've fixed two things: a containing whole (the universe) and a chosen part of it. The complement is precisely the part of the universe NOT in your chosen subset. It looks like it's about one set, but it's secretly a three-way relationship — change the universe or change the subset and the complement shifts. A neat trick: complementing twice gets you back where you started, because the 'not-not' of a part is the part itself. And often it's easier to define something by what it leaves out — 'non-fiction' just means 'everything not fictional.'

 

Given a universe U and a subset A inside it, the complement of A is the set of all elements of U that are not in A — written A-complement or U minus A. The structural commitment is deliberately small: declare a containing whole, designate a part, and reason about the residual. Three features make this a genuine pattern rather than mere notation. Universe-relativity: a complement is undefined until you declare U, so 'the complement of vertebrates' means one thing inside 'animals' and another inside 'all living things' — and many disputes are really undeclared-universe disputes. Closure under double application: complementing twice returns the original, and when that symmetry fails in some setting (intuitionistic logic, fuzzy categories, partial information) it's the diagnostic that the setting isn't doing classical complementation. Negative-definition power: specifying a set by what it excludes can be far easier than listing what it includes, compressing an unbounded extension into a compact rule like 'everything not prohibited.'

Structural Signature

the declared containing whole (universe) — the designated part (subset) — the residual (everything-else) operator — the universe-relativity dependence — the double-application closure — the definition-by-exclusion capacity

A configuration exhibits complementation when each of the following holds:

  • A declared universe. There is an explicit containing whole relative to which membership is decided; the residual is undefined until this whole is fixed, so the construction is irreducibly relative to a declared reference set.
  • A designated subset. Some part of the universe is singled out, by enumeration, by a predicate, or by an explicit boundary.
  • A residual relation. The complement is precisely what remains — the universe minus the subset — which makes the apparently-unary "complement" a three-way relation among whole, part, and leftover, changing whenever either of the first two changes.
  • Double-application closure. Complementing twice returns the original. Where this invariant holds, classical complementation is in force; where it fails (intuitionistic, fuzzy, or partial-information settings), the substrate is non-classical and complement reasoning must be re-justified.
  • A complexity asymmetry. Specifying one side is often dramatically easier than specifying the other, which licenses definition-by-exclusion and the "solve the complement instead" reformulation.
  • A polarity choice. Which side is the explicit set and which is the residual is a free structural decision (permitted-unless-prohibited vs. prohibited-unless-permitted; allow-list vs. deny-list).

These compose into a residual operator: declare a whole, specify a part, and take what is left — a leftover fixed by those two choices, closed under double application, and exploitable by reasoning about whichever side is simpler to describe.

What It Is Not

  • Not measurement_uncertainty_and_complementarity. Despite the shared word, quantum complementarity is about a trade-off between jointly-unmeasurable conjugate quantities; set complement is a partition of a declared universe into a part and its residual, with no uncertainty relation and no incompatibility of observation.
  • Not inversion. Inversion reverses an ordering, a direction, or a mapping (turning a relation around); complementation takes the residual of a subset within a fixed universe. The complement of \(A\) is everything-not-\(A\), not the reverse of \(A\).
  • Not negative_space alone. Negative space is one artistic instance of the complement — the unoccupied region of a canvas treated as a designed object. Complement is the substrate-independent operator; negative space is its application in visual composition.
  • Not disjointness. Two disjoint sets merely fail to overlap; a set and its complement are disjoint and exhaustive — they partition the universe with nothing left over. Disjointness is one of the two complement conditions, not the whole relation (see disjointness).
  • Not duality. Duality pairs structures by a symmetry-preserving correspondence (points and lines, AND and OR); complement is the specific residual operation, even though De Morgan duality is built from complementation. Duality is the broader pairing principle.
  • Common misclassification. Speaking of "not-X" as if it named an absolute set. A complement is undefined until the universe is declared; treating "non-fiction" or "lawful conduct" as universe-independent residuals is the recurring error, caught by asking "complement relative to what whole?".

Broad Use

  • Mathematics and logic. Set complement, the basis of negation in classical propositional logic, characteristic-function inversion, and complement-closed families such as Boolean algebras and σ-algebras.
  • Probability. \(P(A^c) = 1 - P(A)\); many problems are tractable only via the complement, as when "at least one" in a long list is computed as one minus the probability of "none."
  • Law and policy. "Everything not prohibited is permitted" (the legality principle) is a complement-of-explicit-prohibitions construction; "everything not in the public record is private by default" is the same move at a different layer.
  • Strategy and competition. Market white space is the complement of competitors' coverage — the residual demand or geography not currently served — and the strategic move is often to find a large, valuable, defensible complement to incumbents' positions.
  • Ecology. A species' realized niche is the complement, within its fundamental niche, of the zones excluded by competition and predation: a complement-restricted residual.
  • Linguistics and semantics. Many concepts are defined by exclusion — "secular" as not-religious, "non-metal" as not-metal — and the complementary structure is what licenses the productive prefix "non-."
  • Design and cognition. Figure–ground reasoning treats negative space (the complement of the depicted object) as itself a designed object; foregone-alternative reasoning evaluates a chosen action against the complement of the option set.

Clarity

Naming the complement explicitly forces the question what is the universe? into the open, and that single diagnostic resolves a recurring class of confusion. Disputes about whether a category is "small" or "large," or whether something "counts," are frequently not about the category at all but about the implicit universe each party is silently using; the complement-aware analyst surfaces the universe and the dispute often dissolves. In legal reasoning the universe is jurisdictional and authoritative; in statistical reasoning it is the sample space; in design it is the visible canvas — and in each case the residual is only as well-defined as the universe against which it is computed. The complement also clarifies exactly what a negative definition commits one to: defining X as "not-Y" claims that a definite universe contains both, that the boundary between them is determinate, and that the residual is a coherent category in its own right. When any of those three fails — the universe is ill-specified, the boundary is fuzzy, or the residual is too heterogeneous to be a usable category — the negative definition leaks, and recognizing the complement structure is what makes the leak visible before it causes trouble.

Manages Complexity

The complement is a compression device. Rather than enumerate an infinite or vaguely-bounded set, one names it as the residual relative to a smaller, simpler subset of a clearly-defined universe: "all numbers that are not prime" is far easier to specify by reference to the primes than by listing the composites, and "all conduct that is not regulated" is far easier to specify by reference to the regulations than by enumeration. The complement trades enumeration-of-the-thing for definition-of-the-universe-minus-a-tractable-part, which is a net simplification exactly when the part is simpler to describe than the residual. The probability case makes the saving dramatic: computing the probability of at least one success in \(n\) trials directly is a long inclusion–exclusion sum, while computing one minus the probability of zero successes is a single step. The discipline the complement teaches is to look for the asymmetry of complexity between an event and its complement, and to reformulate toward whichever side is simpler. That asymmetry is itself substrate-independent — a hard inclusive specification often has an easy exclusive one, and vice versa — so the move of "solve the complement instead" is available wherever a universe and a subset can be declared, not only in probability.

Abstract Reasoning

Recognizing the complement pattern supports several portable reasoning moves. Negative reformulation: when the affirmative version of a problem is intractable, ask whether the complement is tractable — "what is the probability of at least one X?" becomes "what is the probability of zero Xs?", "what is permitted?" becomes "what is prohibited?", "where is the white space?" becomes "what is covered?" — and one solves whichever side is simpler. Universe surfacing: when two analyses of the same quantity disagree, ask what universe each is computing in, since implicit universe-disagreement is among the most common sources of cross-talking analysis. Double-negation calibration: check in any substrate whether \((A^c)^c = A\); if it holds, classical complementation is in force and the standard moves apply, and if it fails — as in intuitionistic logic, fuzzy categories, or regulatory regimes where un-regulation does not return to a clean baseline — the substrate is non-classical and complement-based reasoning must be re-justified rather than assumed. Closure-under-complement diagnosis: families closed under complement, such as σ-algebras and Boolean algebras and the regular languages, carry structural guarantees (a measurable event has a measurable complement; a regular language has a regular complement) that simplify proofs, so detecting closure-under-complement is itself a useful structural lens. Each move is stated purely in terms of universe, subset, and residual, which is why each transfers unchanged to any domain in which a containing whole and a designated part can be named.

Knowledge Transfer

The transferable content of the complement is a family of interventions that attach to the declare-universe / specify-subset / reason-about-residual skeleton and therefore carry across substrates intact. The probability complement-trick transfers into reliability engineering: computing a system's failure probability as the complement of "all components work," or its success probability as the complement of "any component fails," is one structural move that reliability analysts trade between formulations all day, and the same move serves anywhere a hard inclusive event has an easy exclusive one. The legal complement transfers into regulatory and security design: a regime in which the default is "permitted unless prohibited" and one in which it is "prohibited unless permitted" are the same structural construction — declare a universe, specify the explicit set, reason about the complement — differing only in which side receives the complement, and the same polarity choice reappears as allow-list versus deny-list in software security and as default-permitted versus default-blocked in content moderation. The white-space move transfers into strategy and beyond: mapping what competitors cover and targeting the complement is one operation whether the universe is a product market, an academic research landscape, or an artistic genre space. The niche-complement move transfers into organizational design: just as a realized ecological niche is the fundamental niche minus competitive exclusion, the role a person actually fills is the role they were hired into minus what colleagues have taken over, and naming the universe and the exclusions makes the residual role explicit. The foregone-alternative move transfers into decision review: judging a choice against the complement of the option set — what was not chosen — is a complement operation, and importing the discipline of explicit universe specification ("relative to what option set?") sharpens the evaluation. The legality principle is the paradigm case worth holding in view: partitioning conduct by the explicit prohibitions and treating the lawful as the complement puts the burden of specification on the prohibiting authority, makes the lawful robust to legislative gaps, and sets up the double-negation diagnostic by which a switch to "un-permitted unless permitted" is recognized as a structural change with major consequences — and the identical pattern, with the identical diagnostic apparatus, recurs in software allow/deny lists, content-moderation defaults, and editorial policy.

Examples

Formal/abstract

Compute the probability that at least one of fifty independent components in a system fails during a mission, where each fails with probability $0.02$. The declared universe is the sample space of all \(2^{50}\) joint failure outcomes; the designated subset "at least one component fails" is sprawling and would require a fifty-term inclusion–exclusion sum to enumerate directly. The residual operator supplies the escape: the complement of "at least one fails" is the single, compact event "none fails," and the complexity asymmetry is stark — the exclusive side is one product, \(P(\text{none fail}) = (1 - 0.02)^{50} = 0.98^{50} \approx 0.364\), while the inclusive side is a combinatorial mess. Definition-by-exclusion then gives the answer in one step: \(P(\text{at least one fails}) = 1 - 0.364 \approx 0.636\). The double-application closure is what licenses the move and guarantees its exactness — taking the complement of "none fails" returns precisely "at least one fails," with nothing lost, because the probability space is classical and \((A^c)^c = A\) holds. The universe-relativity dependence is visible too: the same numerical answer is undefined until we fix that the universe is exactly these fifty components on exactly this mission; widen the universe to a hundred components and the residual changes.

Mapped back: The "at least one" reliability computation instantiates the full signature — a declared probability universe, an awkward designated subset, a tractable residual exploited via the complexity asymmetry, and exactness guaranteed by double-application closure.

Applied/industry

Network firewall and content-moderation policy is complement reasoning made operational, and the polarity choice is the entire design decision. A deny-list (blocklist) firewall declares the universe of all possible traffic, designates an explicit subset of known-bad sources/ports/signatures, and permits the residual by default: everything not on the list passes. An allow-list (whitelist) firewall makes the opposite polarity choice — it designates the explicitly-trusted subset and blocks the residual by default. Both are the identical declare-universe / specify-subset / reason-about-residual construction; they differ only in which side receives the complement, and that single structural decision determines the security posture. The complexity asymmetry drives the choice: in a hostile environment the set of bad things is unbounded and growing while the set of legitimately-needed services is small and stable, so specifying the allow-list (and treating everything else as the residual to block) is both easier and safer than chasing an ever-expanding deny-list — the same reasoning that makes a probability problem easier from whichever side is smaller. Surfacing the universe is the practitioner's recurring diagnostic: a rule that "blocks all external traffic" is only as well-defined as the boundary between internal and external, and disputes about whether some flow "should be allowed" are frequently undeclared-universe disputes about what counts as the trusted perimeter. The same polarity structure recurs in market strategy, where a firm maps competitors' coverage and targets the white space — the residual demand or geography not currently served — choosing to compete in the complement of incumbents' positions.

Mapped back: Allow-list versus deny-list security and white-space market strategy both pivot on the complement's polarity choice over a declared universe, exploiting the complexity asymmetry between specifying a side and specifying its residual — the same structural operation in security-engineering and competitive-strategy substrates.

Structural Tensions

T1 — Universe-Relativity versus Absolute Residual (frame-dependence). The complement is undefined until a universe is declared, yet "not-X" is habitually spoken as if it named an absolute set. The competing discipline is explicit-universe specification. The failure mode is the undeclared-universe dispute: two parties argue about whether something "counts" while silently computing residuals against different containing wholes, and the argument is irresolvable because it is really about the universe, not the part. Diagnostic: ask "complement relative to what whole?"; if the answer is unstated or differs across the disputants, the complement has no determinate referent and the disagreement is structural, not factual.

T2 — Classical Closure versus Non-Classical Substrates (logical). Double-application closure, \((A^c)^c = A\), is what licenses the standard complement moves, but it fails in intuitionistic logic, fuzzy categories, and partial-information settings. The failure mode is importing classical complement reasoning — negation, definition-by-exclusion, "solve the complement instead" — into a substrate where the leftover does not cleanly return the original, so de-regulating does not restore a clean baseline and not-not-X is weaker than X. Diagnostic: test whether complementing twice returns the original; if it does not, the substrate is non-classical and every complement-based inference must be re-justified rather than assumed.

T3 — Complexity Asymmetry as Genuine versus Illusory (measurement). The payoff move is "specify whichever side is simpler," presupposing one side is actually easier to describe than the other. The failure mode is reformulating to a complement that is no more tractable — or worse, equally heterogeneous — so the asymmetry was illusory and the negative definition buys nothing while obscuring structure. The residual of a coherent category can be a junk drawer with no usable intension. Diagnostic: before adopting a negative definition, ask whether the residual is itself a coherent, finitely-specifiable category; if "everything not Y" spans wildly unlike things, the asymmetry has not been exploited, only hidden.

T4 — Sharp Boundary versus Fuzzy Membership (boundary). Complementation assumes a determinate boundary: every element is in A or in \(A^c\), never both, never neither. Where membership is graded or contested — secular/religious, regulated/unregulated at the margin — the residual leaks at the edge. The failure mode is treating a negative definition as exhaustive and exclusive when a band of cases belongs to neither side cleanly, so "non-fiction" or "lawful conduct" inherits a fuzzy frontier the binary frame denies. Diagnostic: probe the boundary for cases that resist classification; if they exist, the complement is an idealization and reasoning that depends on exhaustive partition will mishandle the margin.

T5 — Polarity Choice versus Burden Placement (sign/direction). Which side is the explicit set and which is the residual is a free structural decision (permitted-unless-prohibited vs. prohibited-unless-permitted; allow-list vs. deny-list), and the two are formally identical residual constructions. But the choice silently assigns the burden of specification and the default treatment of the unspecified. The failure mode is choosing the wrong polarity for the threat environment — a deny-list against an unbounded, growing adversary set, which can never be complete. Diagnostic: ask which side is small, stable, and enumerable; place the explicit specification there and let the residual absorb the large, shifting side, or the default will be systematically wrong.

T6 — Static Snapshot versus Drifting Universe (temporal). A complement is fixed once the universe and subset are fixed, but both can move: the containing whole expands, the explicit set grows, and the residual silently changes underneath conclusions drawn from an earlier snapshot. The failure mode is reasoning from a stale complement — a deny-list computed against last year's universe of known-bad signatures, or a "white space" that competitors have since entered — treating a residual as durable when it is recomputed by every change to the whole or the part. Diagnostic: ask whether the universe or the designated subset has shifted since the residual was last taken; if either moved, the complement must be recomputed, not reused.

Structural–Framed Character

Complement sits at the structural pole of the structural–framed spectrum: a pure set-theoretic operation that means the same thing in every substrate where a containing whole and a designated part can be named, with a flat zero aggregate and every diagnostic pointing the same way.

The pattern carries no home vocabulary that must travel with it: the residual-relative-to-a-universe move is told in a probabilist's "one minus P(none)," a lawyer's "everything not prohibited," a strategist's "white space," and an ecologist's "realized niche," each in its own field's words, with the set-theoretic notation \(A^c\) being convenient shorthand rather than imported baggage. It carries no inherent approval or disapproval: a complement is neither good nor bad — a deny-list and an allow-list are the same residual construction with opposite polarity, and which is "safer" depends entirely on the threat environment, not on anything in the operation itself. Its origin is formal, definable purely as \(\{x \in U : x \notin A\}\) with no appeal to any human institution or practice. It is not bound to any human role to exist: a species' realized niche is the complement of competitively-excluded zones within its fundamental niche, a fact about populations and habitats that holds with no observer present, and the same residual structure sits latent in any probability space or Boolean algebra. And invoking it recognizes a pattern already wired into the structure — declare the universe and the part, and the residual is already determined — rather than importing an interpretive frame. Every diagnostic reads structural, which is precisely why the grade is a clean zero.

Substrate Independence

Complement is about as substrate-independent as a prime can be — composite 5 / 5 on the substrate-independence scale. Its signature is bare set theory — declare a containing universe, designate a part, and take the residual, closed under double application and exploitable from whichever side is simpler — and that structure carries no commitment to any medium, so it is recognized rather than translated when it surfaces in a new field. And it surfaces almost everywhere the same residual-relative-to-a-universe move appears under different names: a probabilist's "one minus P(none)," a lawyer's "everything not prohibited," a strategist's market white space, an ecologist's realized niche (the fundamental niche minus competitively-excluded zones), a linguist's productive "non-" prefix, and a designer's negative space are all the identical operation with the universe and subset swapped out. The abstraction is maximal — the notation \(A^c\) is convenient shorthand, not imported baggage, and the operation is definable purely as \(\{x \in U : x \notin A\}\) with no appeal to any human practice. The transfer is concrete and well-documented: the probability complement-trick ports into reliability engineering, the legal polarity choice into allow-list/deny-list security design and content-moderation defaults, the white-space move across product markets, research landscapes, and genre spaces, each carrying the same diagnostic apparatus (surface the universe, check double-application closure). Maximal abstraction, maximal breadth, and heavily documented transfer all line up at the ceiling.

  • Composite substrate independence — 5 / 5
  • Domain breadth — 5 / 5
  • Structural abstraction — 5 / 5
  • Transfer evidence — 5 / 5

Relationships to Other Primes

One-hop neighborhood: parents above, mutual partners to the right, children below.Complementsubsumption: Set and MembershipSet andMembershipsubsumption: Negative SpaceNegative Space

Parents (1) — more general patterns this builds on

  • Complement is a kind of, typical Set and Membership

    The complement is a set operation — the residual (universe minus subset) — defined on membership in a declared universe. A derived set-theoretic construction.

Children (1) — more specific cases that build on this

  • Negative Space is a kind of Complement

    The file: 'Negative space is one ARTISTIC INSTANCE of the complement... Complement is the substrate-independent operator; negative space is its application in visual composition.' complement is the general parent, negative_space the art-aesthetics child. Add complement as parent (negative_space keeps figure_ground).

Path to root: Complement → Set and Membership

Neighborhood in Abstraction Space

Complement sits in a moderately populated region (44th percentile for distinctiveness): it has near-neighbors but no dense thicket of synonyms.

Family — Algebraic & Set-Theoretic Structure (28 primes)

Nearest neighbors

Computed from structural-signature embeddings · 2026-06-14

Not to Be Confused With

The complement's nearest-sounding neighbor is measurement_uncertainty_and_complementarity, and the shared root "complement" invites a genuine confusion that dissolves on inspection. Quantum complementarity is a claim about jointly unmeasurable conjugate quantities: sharpening knowledge of position blurs knowledge of momentum, and the two descriptions are mutually exclusive yet jointly necessary for a full account. Its structure is a trade-off governed by an uncertainty relation, not a partition. Set complement, by contrast, makes no claim about measurement or incompatibility at all; it declares a universe, designates a subset, and names the residual, with the part and its complement coexisting and jointly exhausting the universe. Where complementarity says "you cannot have both sharply at once," complementation says "everything is in exactly one of these two, and together they are everything." The practitioner who imports complementarity's trade-off intuition into a set-theoretic complement will look for a tension that is not there; the one who imports complementation's clean partition into a complementarity setting will miss the irreducible trade-off that is the whole point.

A more structurally tempting confusion is with disjointness, because a set and its complement never overlap, so complementation looks like a special case of disjointness. The difference is exactly one extra condition. Disjointness is the single requirement that two sets share no elements — \(A \cap B = \varnothing\) — and many disjoint pairs leave a great deal of the universe uncovered (two non-adjacent intervals on the line are disjoint but together cover almost nothing). Complementation requires disjointness and exhaustiveness: \(A \cap A^c = \varnothing\) and \(A \cup A^c = U\), so the two pieces partition the universe with no remainder. This is why complement, but not disjointness, supports definition-by-exclusion and the double-application closure \((A^c)^c = A\): those moves rely on the residual being everything else, not merely something else. A reader who treats disjointness as sufficient for complement reasoning will wrongly assume that the absence of overlap licenses "the rest is automatically the other category," when in fact a third, uncovered region may exist.

Complement is also worth separating from duality, with which it is intertwined through De Morgan's laws. Duality is the broad principle that two structures correspond under a symmetry that swaps roles while preserving form — points and lines in projective geometry, AND and OR in Boolean algebra, min and max in optimization. Complementation is the specific residual operator, and while De Morgan duality is constructed from complement (the complement of a union is the intersection of complements), the two are not the same: duality is a meta-level pairing of whole theories or operations, complement is an object-level operation on a single set within a single universe. One can have complementation without any interesting duality (a plain set and its residual), and dualities exist that are not built from complementation at all. Conflating them leads to expecting a symmetric partner-structure wherever a complement appears, when often there is just a part and its leftover.

For a practitioner the cluster matters because each neighbor carries a different invariant: complementarity carries a trade-off, disjointness carries non-overlap-without-exhaustion, and duality carries a role-swapping symmetry. The complement carries exactly the conjunction of disjointness and exhaustiveness relative to a declared universe — and the single discipline that keeps it distinct from all three is to name the universe first, then check that the two pieces are both non-overlapping and jointly everything. That check is what licenses negative definition, the "solve the complement instead" reformulation, and the double-negation diagnostic, none of which the neighboring concepts underwrite.

Solution Archetypes

No catalogued solution archetypes reference this prime yet.