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Prime gap
A prime gap is the difference between two successive prime numbers, such as the seven composites between 89 and 97. Gaps grow arbitrarily large and average about ln x near x.
Prime ideal
A prime ideal is a proper ideal in a commutative ring such that whenever a product ab lies in it, one factor lies in it.
Prime k-tuple
A prime k-tuple is a set of k linear forms one asks to be prime simultaneously; the Hardy–Littlewood conjecture (1923) predicts every admissible tuple is all-prime infinitely often.
Prime labeling
Prime labeling is a graph labeling technique assigning the integers 1 through n to a graph's vertices so every pair of adjacent vertices receives coprime labels.
Prime model
A prime model in model theory is a model that can be elementarily embedded into every other model of its complete theory, a notion Robert Vaught introduced in 1961.
Prime notation for derivatives
Prime notation, also called Lagrange's notation, writes derivatives with accent marks, the first derivative of f(x) being f'(x); it was introduced by Joseph-Louis Lagrange in his 1797 work on analytic functions.
Prime number
A prime number is a whole number bigger than 1 that cannot be factored into two smaller whole numbers, such as 2, 3, 5, and 7.
Prime number theorem
The prime number theorem states that the number of primes up to x is asymptotically x/ln x, proved in 1896 by Hadamard and de la Vallée Poussin.
Prime-counting function
The prime-counting function π(x) is a number theory function counting the primes less than or equal to x, so π(100) = 25 since exactly 25 primes lie below 100.
Prime95
Prime95 is a free program written by George Woltman for the Great Internet Mersenne Prime Search, a distributed project founded in 1996, and doubles as a standard CPU stress-testing tool.
Primitive permutation group
A primitive permutation group is a transitive permutation group preserving no nontrivial block system, equivalently one whose point stabilizers are maximal subgroups; these groups are the basic building blocks of all permutation groups.
Primitive recursive arithmetic
Primitive recursive arithmetic (PRA) is a quantifier-free formal theory of the natural numbers that serves in proof theory as the standard formalization of Hilbert's finitist reasoning about numbers.
Primitive recursive function
A primitive recursive function is a function on natural numbers built from basic functions by composition and primitive recursion, isolated by Kurt Gödel in 1931.
Primitive recursive functional
A primitive recursive functional is a functional of finite type definable by extending primitive recursion to higher types, introduced by Stephen Cole Kleene in 1959.
Primitive root modulo n
A primitive root modulo n is an integer whose powers generate all numbers coprime to n; primitive roots exist only for n = 1, 2, 4, p^k, and 2p^k.
Primorial
The primorial is the analog of the factorial for primes: the product of the first n primes, or all primes up to n, written n#.
Principal axis factoring
Principal axis factoring, also called iterated principal factor analysis, is an extraction method in exploratory factor analysis that repeatedly estimates communalities to model shared rather than total variance.
Principal bundle
A principal bundle is a fiber bundle whose fibers carry a free and transitive right action of a group G, locally resembling the product of the base with G.
Principal component regression
Principal component regression (PCR) is a two-step regression method that applies PCA to the predictors and regresses the response on the component scores, reducing dimensionality and mitigating multicollinearity.
Principal curvature
Principal curvatures are the maximum and minimum values of the normal curvature of a surface at a point, occurring along perpendicular principal directions; their product gives the Gaussian curvature.
Principal ideal domain
A principal ideal domain (PID) is an integral domain in which every ideal is generated by a single element, examples including the integers and the Gaussian integers.
Principal ideal theorem
The principal ideal theorem, also called the Artin–Furtwängler theorem, states that every ideal of a number field becomes principal in its Hilbert class field, proved in 1930.
Principal stratification
Principal stratification is a causal inference framework introduced by Constantine Frangakis and Donald Rubin in 2002 for comparing treatments while adjusting for a variable measured after treatment.
Principia Mathematica
Principia Mathematica is a three-volume work of formal logic by Alfred North Whitehead and Bertrand Russell, published by Cambridge University Press in 1910, 1912, and 1913, defending logicism.
Principle of compositionality
The principle of compositionality, also called Frege's principle, is the thesis that an expression's meaning is determined by its structure and the meanings of its constituents.
Principle of explosion
The principle of explosion, also known as ex falso quodlibet or ex contradictione quodlibet, is the rule of inference that anything at all follows from a contradiction.
Prior probability
A prior probability distribution, or prior, is the probability distribution assigned to a statistical model's parameters before the current data are observed, combined with the likelihood in Bayesian analysis to form the posterior distribution.
Priority method
The priority method is a technique in computability theory for constructing computably enumerable sets by satisfying ranked requirements, invented independently by Friedberg and Muchnik in the 1950s.
Prism (geometry)
In geometry, a prism is a three-dimensional solid with two identical parallel polygonal bases joined by parallelogram faces; its volume is the base area times its height.
Prisoner's dilemma
The prisoner's dilemma is a two-person game where each player is better off defecting, though both would gain by cooperating; Flood and Dresher devised it at RAND around 1950.