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Undirected graph defined from a group
In the mathematics of graph theory and finite groups, a prime graph is an undirected graph defined from a group. These graphs were introduced in a 1981
Prime_graph
induced subgraph of a graph G for vertex subset S. Prime symbol ' The prime symbol is often used to modify notation for graph invariants so that it applies
Glossary_of_graph_theory
Programmable graphing calculator
The HP Prime Graphing Calculator is a graphing calculator introduced by Hewlett-Packard in 2013 and manufactured by HP Inc. until the licensees Moravia
HP_Prime
Complete bipartite cut in a graph
In graph theory, a split of an undirected graph is a cut whose cut-set forms a complete bipartite graph. A graph is prime if it has no splits. The splits
Split_(graph_theory)
Spectral graph theory concept
spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are
Ramanujan_graph
Infinite graph containing all countable graphs
In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with
Rado_graph
Graph of numbers differing by a square
Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices. Paley graphs allow graph-theoretic
Paley_graph
combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Operation in graph theory
In graph theory, the Cartesian product G □ H of graphs G and H is a graph such that: the vertex set of G □ H is the Cartesian product V(G) × V(H); and
Cartesian_product_of_graphs
Natural number
In graph theory, all graphs with four or fewer vertices are planar, however, there is a graph with five vertices that is not: K5, the complete graph with
5
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
In graph theory, a circulant graph is an undirected graph acted on by a cyclic group of symmetries which takes any vertex to any other vertex. It is sometimes
Circulant_graph
Recursively splitting a graph into subsets of nodes
In graph theory, the modular decomposition is a decomposition of a graph into subsets of vertices called modules. A module is a generalization of a connected
Modular_decomposition
Italian mathematician (1963–2008)
a Ph.D. at Padua in 1996 with the dissertation Il Prime Graph dei gruppi finiti [the prime graphs of finite groups], supervised by Napolitani and co-advised
Maria_Silvia_Lucido
Partition of a graph into spanning subgraphs
mathematics In graph theory, a factor of a graph G is a spanning subgraph, i.e., a subgraph that has the same vertex set as G. A k-factor of a graph is a spanning
Graph_factorization
Graph defined from a mathematical group
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract
Cayley_graph
Graph representing a permutation
rise to the same permutation graph; a given graph has a unique representation (up to permutation symmetry) if it is prime with respect to the modular decomposition
Permutation_graph
Clustering and community detection algorithm
well-connected. Consider, for example, the following graph: Three communities are present in this graph (each color represents a community). Additionally
Leiden_algorithm
In mathematics, a fibration of graphs, or graph fibration, is a homomorphism of directed graphs that satisfies a unique lifting property analogous to that
Fibrations_of_graphs
Graph of chess rook moves
the graph distance-transitive). For rectangular chessboards whose width and height are relatively prime, the rook's graphs are circulant graphs. With
Rook's_graph
In mathematics, the commuting graph of a semigroup, or in particular of a group, is an undirected graph in which the vertices are elements of the semigroup
Commuting_graph
Mathematical function
the prime zeta function". arXiv:0811.4739 [math.NT]. Li, Ji (2008). "Prime graphs and exponential composition of species". Journal of Combinatorial Theory
Prime_zeta_function
0 bsdiff binary patch 7C 61 8A B2 |aŠ² 0 hpapp hpprgm hpsettings HP Prime graphing calculator file 43 5A 50 58 CZPX 0 czx Czip X encrypted archive (v4
List_of_file_signatures
Regular graph with fewest possible nodes for its girth
of graph theory, a cage is a regular graph that has as few vertices as possible for its girth. Formally, an (r, g)-graph is defined to be a graph in which
Cage_(graph_theory)
Instantaneous rate of change (mathematics)
chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation
Derivative
Mathematical group that can be generated as the set of powers of a single element
graph is a cycle graph, and for an infinite cyclic group with its generator the Cayley graph is a doubly infinite path graph. However, Cayley graphs can
Cyclic_group
In mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. Both directed and
Rooted_graph
Special case of a strongly regular graph
graphs are known to exist for all small values of v allowed by the restrictions, e.g., v = 5, 9, 13, 17, 25, 29, and (the Paley graphs) for all prime
Conference_graph
Study of discrete mathematical structures
continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics
Discrete_mathematics
Graph that misrepresents data
In statistics, a misleading graph, also known as a distorted graph, is a graph that misrepresents data, constituting a misuse of statistics and with the
Misleading_graph
Natural number
number and the eighth square-prime. 68 is a composite number; a square-prime, of the form (p2, q) where q is a higher prime. It is the eighth of this form
68_(number)
Operation in graph theory
In graph theory, local complementation (also known as vertex inversion) is an operation on a graph that toggles adjacencies among the neighbours of a
Local_complementation
Prime number congruent to 1 mod 4
{\displaystyle p} is an odd prime but is not Pythagorean. For every Pythagorean prime p {\displaystyle p} , there exists a Paley graph with p {\displaystyle
Pythagorean_prime
Graph structure studied in group theory
cycle graph of a group is an undirected graph that illustrates the various cycles of that group, given a set of generators for the group. Cycle graphs are
Cycle_graph_(algebra)
the set of prime numbers, proved by Jared Duker Lichtman in 2022. The Erdős–Sauer problem about the maximum number of edges an n-vertex graph can have without
List of conjectures by Paul Erdős
List_of_conjectures_by_Paul_Erdős
On coloring infinite graphs
In graph theory, the De Bruijn–Erdős theorem relates graph coloring of an infinite graph to the same problem on its finite subgraphs. It states that,
De Bruijn–Erdős theorem (graph theory)
De_Bruijn–Erdős_theorem_(graph_theory)
number of undirected Hamiltonian paths in 4 by 5 square grid graph; record gap between twin primes; number that is the sum of 7 positive 5th powers. In decimal:
1000_(number)
Natural number
digits) is prime. There are exactly 743 independent sets in a four-dimensional (16 vertex) hypercube graph, and exactly 743 connected cubic graphs with 16
743_(number)
Series of graphing calculators from Casio
Casio PRIZM or PRIZM Color Grapher is a series of programmable graphing calculators (succeeded by Casio ClassWiz CG) introduced by Casio in 2011, notable
Casio_Prizm
Algorithm for the directed version of the minimum spanning tree problem
now define a new weighted directed graph D ′ = ⟨ V ′ , E ′ ⟩ {\displaystyle D^{\prime }=\langle V^{\prime },E^{\prime }\rangle } in which the cycle C {\displaystyle
Edmonds'_algorithm
Graph linking pairs of comparable elements in a partial order
Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability
Comparability_graph
Unit of plane angle where a full circle equals 360°
50g graphing calculator user's guide (UG) (1 ed.). Hewlett-Packard. 1 April 2006. HP F2229AA-90006. Retrieved 10 October 2015. HP Prime Graphing Calculator
Degree_(angle)
Graph of zero divisors of a commutative ring
{\displaystyle n} is a semiprime number (the product of two prime numbers) then the zero-divisor graph of the ring of integers modulo n {\displaystyle n} (with
Zero-divisor_graph
Prime number of the form 2^n – 1
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some
Mersenne_prime
Electronic calculator capable of plotting graphs
A graphing calculator (also graphics calculator or graphic display calculator) is a handheld computer that is capable of plotting graphs, solving simultaneous
Graphing_calculator
Embedding of the circle in three dimensional Euclidean space
mathematics that studies knots is known as knot theory and has many relations to graph theory. A knot is an embedding of the circle (S1) into three-dimensional
Knot_(mathematics)
In the mathematical field of graph theory, the F26A graph is a symmetric bipartite cubic graph with 26 vertices and 39 edges. It has chromatic number 2
F26A_graph
Class of expander graphs arising in computational number theory
curves. A supersingular isogeny graph is determined by choosing a large prime number p {\displaystyle p} and a small prime number ℓ {\displaystyle \ell }
Supersingular_isogeny_graph
Natural number
233 is a prime number 233 is a Sophie Germain prime, a Pillai prime, and a Ramanujan prime It is a Fibonacci number, one of the Fibonacci primes There are
233_(number)
Structure-preserving correspondence between node-link graphs
In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a
Graph_homomorphism
Numerical prefix meaning "ten"
HP 50g graphing calculator user's guide (UG) (1 ed.). Hewlett-Packard. 2006-04-01. HP F2229AA-90006. Retrieved 2015-10-10. HP Prime Graphing Calculator
Deca-
In graph theory, the McKay–Miller–Širáň graphs are an infinite class of vertex-transitive graphs with diameter two, and with a large number of vertices
McKay–Miller–Širáň_graph
Bipartite 4-regular graph with 20 nodes and 40 edges
mathematical field of graph theory, the Folkman graph is a 4-regular graph with 20 vertices and 40 edges. It is a regular bipartite graph with symmetries taking
Folkman_graph
British mathematician (born 1943)
interests lie in graph theory, particularly in colouring problems, e.g. the four colour problem, and algebraic properties of graphs. He also researches
Robin_Wilson_(mathematician)
Algorithmically defined graph
In the study of graph algorithms, an implicit graph representation (or more simply implicit graph) is a graph whose vertices or edges are not represented
Implicit_graph
Path-finding using high-weight graph edges
In graph algorithms, the widest path problem is the problem of finding a path between two designated vertices in a weighted graph, maximizing the weight
Widest_path_problem
Characterization of how many integers are prime
{\displaystyle \log _{e}(x)} . In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of prime numbers among the positive integers. It
Prime_number_theorem
Graph where every edge is in one triangle
In graph theory, a locally linear graph is an undirected graph in which every edge belongs to exactly one triangle. Equivalently, for each vertex of the
Locally_linear_graph
The product in the definition is taken over all prime closed geodesics p {\displaystyle p} of the graph G = ( V , E ) {\displaystyle G=(V,E)} , where geodesics
Ihara_zeta_function
fuel amid global concerns over supply". RNZ. Retrieved 16 March 2026. "NZ Prime Minister Christopher Luxon calls for election on November 7". Australian
Opinion polling for the 2026 New Zealand general election
Opinion_polling_for_the_2026_New_Zealand_general_election
Natural number
required to make a hollow cube of edge length 12, 72864 + 1 is prime, number of connected graphs on 5 labelled vertices 729 = 272 = 93 = 36. the square of
700_(number)
Finiteness of sets of forbidden graph minors
graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph minor
Robertson–Seymour_theorem
Problem in theoretical computer science
{\displaystyle G=(V,E)} , H = ( V ′ , E ′ ) {\displaystyle H=(V^{\prime },E^{\prime })} be graphs. Is there a subgraph G 0 = ( V 0 , E 0 ) ∣ V 0 ⊆ V , E 0 ⊆
Subgraph_isomorphism_problem
Natural number
= 211 – 11 2038 – Number of unlabeled Euler graphs with 9 nodes 2039 – Sophie Germain prime, safe prime 2040 = 15 × 16 × 17 2 {\displaystyle {\frac {15\times
2000_(number)
function: polynomial of degree zero, graph is a horizontal straight line Linear function: First degree polynomial, graph is a straight line. Quadratic function:
List of mathematical functions
List_of_mathematical_functions
In extremal graph theory, the forbidden subgraph problem is the following problem: given a graph G {\displaystyle G} , find the maximal number of edges
Forbidden_subgraph_problem
Natural number
the greatest prime factor of 392 + 1 = 1522 is 761, which is more than 39 twice, 39 is a Størmer number. The F26A graph is a symmetric graph with 39 edges
39_(number)
Class of hand-held calculator
A graphing calculator is a class of hand-held calculator that is capable of plotting graphs and solving complex functions. While there are several companies
Comparison of HP graphing calculators
Comparison_of_HP_graphing_calculators
annually between 2016 and 2021 consistently listed Modi as the most popular prime minister among Indian public. A YouGov-Mint-CPR survey in 2022 also ranked
Opinion polling on the Narendra Modi premiership
Opinion_polling_on_the_Narendra_Modi_premiership
Function representing the number of primes less than or equal to a given number
is exactly a prime number, and equal to π(x) otherwise. That is, the number of prime numbers less than x, plus half if x equals a prime. Of great interest
Prime-counting_function
Geometry problem on grid points
{\displaystyle p} is a prime congruent to 3 mod 4. Just as the original no-three-in-line problem can be used for two-dimensional graph drawing, one can use
No-three-in-line_problem
Natural number
number following 6 and preceding 8. It is the only prime number preceding a cube. As an early prime number in the series of positive integers, the number
7
Cristina Tomàs. "Coronavirus in Catalonia: daily figures explained in graphs". Catalan News. Retrieved 2020-04-16. "Sanidad se ve obligada a corregir
COVID-19_pandemic_in_Spain
Number of times an object must be counted for making true a general formula
has a multiple root. The graph of a polynomial function f intersects the x-axis at the real roots of the polynomial. The graph is tangent to this axis
Multiplicity_(mathematics)
Branch of discrete mathematics
right. One of the oldest and most accessible parts of combinatorics is graph theory, which by itself has numerous natural connections to other areas
Combinatorics
Maria Silvia Lucido (1963–2008), Italian mathematician, expert on the prime graphs of finite groups Malwina Łuczak, Polish-Australian probability theorist
List_of_women_in_mathematics
Number of integers coprime to and less than n
graph below: In the graph at right the top line y = n − 1 is an upper bound valid for all n other than one, and attained if and only if n is a prime number
Euler's_totient_function
constitution after a military conflict with the parliament in 1993. Acting Prime Minister until 17 May 2000. Aluf, I. A. (1979). February Bourgeois Democratic
List_of_presidents_of_Russia
Topics referred to by the same term
graphing calculator model Prime Computer, a producer of minicomputers Prime F.C., a Nigerian football club Prime parry, a parry form in fencing Prime
Prime_(disambiguation)
Swiss mathematician (1707–1783)
logician, geographer, music theorist and engineer. He founded the studies of graph theory and topology and made influential discoveries in many other branches
Leonhard_Euler
German mathematician (1934–2025)
Bertram Wehrfritz, was influential in the subfield. Prime graphs are also known as Gruenberg-Kegel graphs due to early unpublished work of Kegel with Karl
Otto_H._Kegel
Natural number
N=n\times n} where N − 1 {\displaystyle N-1} is a prime number. The four-color theorem states that a planar graph (or, equivalently, a flat map of two-dimensional
4
Primary time standard globally used to regulate clocks and time
then added). In the graph of DUT1 above, the excess of LOD above the nominal 86,400 s corresponds to the downward slope of the graph between vertical segments
Coordinated_Universal_Time
Ideals in a Boolean algebra can be extended to prime ideals
number k in any graph coloring, then it has a finite subgraph that also requires k. A not too well known application of the Boolean prime ideal theorem
Boolean_prime_ideal_theorem
new initiative in April 2026 geared towards those with disabilities. This graph shows the polling trends from the 2022 elections until the next election
2026 Israeli legislative election
2026_Israeli_legislative_election
Norwegian mathematician (1899–1968)
most of all, graph theory. His early work was on algebraic number fields, how to decompose the ideal generated by a prime number into prime ideals. He then
Øystein_Ore
In mathematics, with negligible exceptions
no other prime between p − g and p + g. In graph theory, if A is a set of (finite labelled) graphs, it can be said to contain almost all graphs, if the
Almost_all
2007 mortgage crisis in the United States
least not rise) for another year (see "Fed Funds Rate & Mortgage Rates" graph). Construction of new homes did not peak until January 2006. Bernanke speculates
Subprime_mortgage_crisis
Elections featuring UK Prime Minister
history of Rishi Sunak, the Leader of the Conservative Party who served as Prime Minister of the United Kingdom from October 2022 to July 2024. Sunak previously
Electoral history of Rishi Sunak
Electoral_history_of_Rishi_Sunak
India's national-level mathematics contest conducted by the (AMTI)
Diophantine equations, congruence relations, prime numbers and elementary results on prime numbers. Combinatorics & Graph Theory: Counting techniques, pigeon hole
National Mathematics Talent Contest
National_Mathematics_Talent_Contest
Statement in mathematical combinatorics
its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. As
Ramsey's_theorem
On linear-time algorithms for graph logic
study of graph algorithms, Courcelle's theorem is the statement that every graph property definable in the monadic second-order logic of graphs can be decided
Courcelle's_theorem
grounds". The graph displays the results of the polls. Those who responded "don't know" are removed, where relevant. The following graph displays a local
Opinion polling for the 2026 Hungarian parliamentary election
Opinion_polling_for_the_2026_Hungarian_parliamentary_election
Natural number
spanning trees in a 2 × 5 grid graph, 209 partial permutations on four elements, and 209 distinct undirected simple graphs on 7 or fewer unlabeled vertices
209_(number)
Project for an open source artificial intelligence framework
project, Hanson Robotics, SingularityNET and others. OpenCog consists of: A graph database, dubbed the AtomSpace, that holds "atoms" (that is, terms, atomic
OpenCog
Interest rate at which banks lend to customers with good credit
International Prime Rates published by The Wall Street Journal Online HSH Associates, Financial Publishers Current Rate, Definition & Historical Graph
Prime_rate
Aspect of British political history
dominance in Scotland. He succeeded Rishi Sunak as prime minister on 5 July 2024, becoming the first Labour prime minister since Gordon Brown in 2010 and the
History of the Labour Party (UK)
History_of_the_Labour_Party_(UK)
Computational complexity class
exponential time hypothesis. Finding a graph with the fewest vertices that does not appear as an induced subgraph of a given graph can be solved in time n O ( log
Quasi-polynomial_time
Prime such that p^2 divides 2^(p-1)-1
In number theory, a Wieferich prime is a prime number p such that p2 divides 2p − 1 − 1, therefore connecting these primes with Fermat's little theorem
Wieferich_prime
Graph obeys some properties of random graphs
In graph theory, a graph is said to be a pseudorandom graph if it obeys certain properties that random graphs obey with high probability. There is no concrete
Pseudorandom_graph
Type of incidence structure
Cage. Incidence graphs of configurations are today generally called Levi graphs, but the original Levi graph was the incidence graph of the GQ(2,2). If
Generalized_quadrangle
PRIME GRAPH
PRIME GRAPH
Girl/Female
Hindu
Love, Affection
Boy/Male
Indian, Italian, Latin
First Born
Surname or Lastname
German
German : of uncertain origin; possibly from the Latin personal name Primus (‘the first’), borne by several saints; or one composed with a Germanic word meaning ‘to prick or stab’; or from a personal name of Slavic origin Primm, from prēmu ‘right’.French : from a personal name (from Latin Primus).French : nickname from Old French prim ‘first’, possibly given to the eldest child in a family, or alternatively a nickname from Old French and Occitan prim ‘shrewd’, ‘clever’, ‘artful’, ‘sly’.Dutch : variant of Priem.English : variant of Prime.Some of the Prim families in VT descend from a Simon Laval dit Printemps, who was known in English-speaking areas as Seymour Prim.
Boy/Male
Muslim
Prime minister
Boy/Male
Arabic, Muslim
Prime Minister
Boy/Male
Australian, British, Christian, English, Welsh
Son of Rhys; Ardent; Son of the Ardent; Prize
Male
Italian
Italian and Spanish form of Latin Primus, PRIMO means "first."
Male
English
English surname transferred to forename use, derived from the Middle English element pris, PRICE means "price" or "prize."Â
Surname or Lastname
English
English : from the Old Norse personal name GrÃmr, which remained popular as a personal name in the form Grim in Anglo-Scandinavian areas well into the 12th century. It was a byname of Woden with the meaning ‘masked person’ or ‘shape-changer’, and may have been bestowed on male children in an attempt to secure the protection of the god. The Continental Germanic cognate grÄ«m was also used as a first element in compound names. Compare Grimaud and Gribble, with the original sense ‘mask’, ‘helmet’. Some examples of the surname may derive from short forms of such names.
Boy/Male
Indian, Tamil
Important; Prime
Boy/Male
Hindu, Indian
Chief; Prime
Surname or Lastname
English
English : unexplained.Serbian : unexplained.
Surname or Lastname
English
English : from a Middle English personal name or nickname. The personal name existed in Old English, and is probably derived from Old English prim ‘early morning’ (from Latin primus ‘first’, used as the name of one of the canonical hours). The surname may be derived from this word as a Middle English nickname in the sense ‘fine’, ‘excellent’.French : feminine form of Prim 3.Dutch : variant of Priem.Probably an Americanized spelling of German Preim, a topographic name (of Slavic origin), perhaps from a river near Hannover; or of Preime, a variant of Primus.
Girl/Female
Latin
Firstborn.
Surname or Lastname
Welsh
Welsh : Anglicized form of Welsh ap Rhys ‘son of Rhys’ (see Reece). This is one of the commonest of Welsh surnames. It has also been established in Ireland since the 14th century, where it is sometimes a variant of Bryson.English : the name is also found very early in parts of England far removed from Welsh influence (e.g. Richard Prys, Essex 1320), and in such cases presumably derives from Middle English, Old French pris ‘price’, ‘prize’, perhaps as a metonymic occupational name for a fixer of prices.Americanized spelling of Jewish Preuss or Preis.
Girl/Female
Australian, French, German, Italian, Latin, Swedish
First-born
Boy/Male
Indian
Prime
Boy/Male
Welsh American
Son of Rhys.
Female
English
English name derived from Latin prima, PRIMULA means "first, prime."
Boy/Male
Arabic, Muslim, Pashtun
Prime Chief
PRIME GRAPH
PRIME GRAPH
Boy/Male
English Anglo Saxon
Noble or bright.
Boy/Male
Australian
Sunrays; Sunlight
Boy/Male
Hindu, Indian
Gods Avattar; Follower of God
Boy/Male
Hindu
Glory, Fame
Girl/Female
Indian
Boy/Male
Muslim
Eloquent by grace of Rahman
Boy/Male
Arabic, Muslim
Yearning; Desire
Girl/Female
Latin American Spanish
Treasure.
Boy/Male
Irish
Handsome.
Boy/Male
British, English, Jamaican
From the Rock Meadow; Rocky Field
PRIME GRAPH
PRIME GRAPH
PRIME GRAPH
PRIME GRAPH
PRIME GRAPH
a.
First in excellence; of highest quality; as, prime wheat; a prime quality of cloth.
a.
To prepare; to make ready; to instruct beforehand; to post; to coach; as, to prime a witness; the boys are primed for mischief.
n.
See Price, and 1st Prize.
n.
One who, or that which, primes
#
Donne (#) (pl. ) of Prima donna
v. t.
To pay the price of.
a.
A prime number. See under Prime, a.
v. t.
To set a price on; to value. See Prize.
n. & v.
Reward; recompense; as, the price of industry.
n.
Highest pitch; elevation reached; loftiness; prime; glory; as, to be in the pride of one's life.
n. & v.
See Prize, n., 5. Also Prize, v. t.
a.
To mark with a prime mark.
a.
Being in its prime.
v. t.
To ask the price of; as, to price eggs.
a.
First in rank, degree, dignity, authority, or importance; as, prime minister.
a.
Marked or distinguished by a mark (') called a prime mark.
imp. & p. p.
of Prime
a.
To lay the first color, coating, or preparation upon (a surface), as in painting; as, to prime a canvas, a wall.
n.
That which occasion crime.
a.
Formal; precise; affectedly neat or nice; as, prim regularity; a prim person.