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Physical world and mathematics

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Pressurized liquid extraction

Pressurized liquid extraction (PLE), also called accelerated solvent extraction (ASE), is an analytical chemistry technique that extracts compounds from solid samples using organic solvents at elevated temperature and pressure.

Preston Cloud

Preston Cloud (1912–1991) was an American paleontologist and geologist who helped found the study of Precambrian life and explained how rising atmospheric oxygen shaped Earth's earliest rocks.

Preston Webster

Preston T. Webster is a physicist at the Air Force Research Laboratory who works on infrared semiconductor detectors and leads a team developing space sensor technologies for missile warning and weather monitoring.

Pretest–posttest design

A pretest–posttest design is a study design measuring the same experimental unit before and after an intervention, ranging from a single untreated group to randomized controlled trials.

Prethermalization

Prethermalization is the relaxation of a many-body system toward a long-lived, thermal-like intermediate state that precedes slower full thermalization; the term was coined in 2004 for heavy-ion collisions.

Prevailing winds

A prevailing wind is the direction from which wind blows most often at a place over a period, produced by global circulation, the Coriolis effect, and local factors like sea breezes.

PREX

PREX (Lead Radius Experiment) is a Jefferson Lab experiment that measured the neutron skin of lead-208 with parity-violating electron scattering, finding it 0.283 femtometers thick.

Priabonian

The Priabonian is the last and youngest stage of the Eocene Epoch, from about 37.71 to 33.9 million years ago, named for the Italian village of Priabona.

Primality test

A primality test (prime testing) is an algorithm deciding whether an integer is prime or composite; Miller–Rabin is the practical workhorse, and AKS proved in 2002 a deterministic polynomial-time test exists.

Primary decomposition

Primary decomposition represents an ideal of a commutative ring as an intersection of primary ideals, generalizing prime factorization of integers; it was proved for Noetherian rings by Emmy Noether.

Primary endpoint

A primary endpoint is the main outcome of a clinical trial, chosen in advance, on which its hypothesis is tested and regulatory approval is judged.

Primary fatty amines

Primary fatty amines are organic compounds with a long fatty alkyl chain attached to ammonia, derived from natural fats and oils and produced at over 1 million tons per year.

Primary ideal

A primary ideal is a proper ideal of a commutative ring such that a product in it forces one factor, or a power of the other, into it.

Primary migration

Primary migration, also called hydrocarbon expulsion, is the movement of petroleum out of its low-permeability source rock into a reservoir, the first step of the petroleum system.

Primary standard

A primary standard is the top of the calibration hierarchy, established by a primary reference measurement procedure or chosen by convention, from which all other standards derive.

Prime (symbol)

The prime (′), also called the prime mark, is a typographic symbol marking minutes of arc, feet, and the derivative in calculus, attributed to Lagrange.

Prime and irreducible elements

Prime and irreducible elements are related notions in ring theory: every prime element of an integral domain is irreducible, while the converse fails, as in Z[√−5].

Prime element

A prime element is a nonzero, noninvertible element of a commutative ring such that when it divides a product ab, it divides a or b, the ring-theoretic generalization of ordinary prime numbers.

Prime Focus Spectrograph

The Prime Focus Spectrograph (PFS, Hawaiian Onohi'ula) is a fiber-fed spectrograph at the Subaru Telescope on Maunakea, capturing about 2,400 objects per exposure since 2025.

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 meridian

The prime meridian, known as the Greenwich Meridian, is the internationally agreed line of 0° longitude at the Royal Observatory Greenwich, chosen by 25 nations in 1884.

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.