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Function representing the number of primes less than or equal to a given number
{\displaystyle \log _{e}(x)} . In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number
Prime-counting_function
Prime fulfilling an inequality related to the prime-counting function
mathematics, a Ramanujan prime is a prime number that satisfies a result proven by Srinivasa Ramanujan relating to the prime-counting function. In 1919, Ramanujan
Ramanujan_prime
Characterization of how many integers are prime
Riemann zeta function). The first such distribution found is π(N) ~ N/log(N), where π(N) is the prime-counting function (the number of primes less than
Prime_number_theorem
Special function defined by an integral
according to the prime number theorem, it is a very good approximation to the prime-counting function, which is defined as the number of prime numbers less
Logarithmic_integral_function
Formula whose values are the prime numbers
p_{n}} as the smallest integer m {\displaystyle m} for which the prime-counting function π ( m ) {\displaystyle \pi (m)} is at least n {\displaystyle n}
Formula_for_primes
Mathematical function
the prime-counting function, π(x) (see the exact formula below.) Both Chebyshev functions are asymptotic to x, a statement equivalent to the prime number
Chebyshev_function
Function whose domain is the positive integers
the prime-counting functions. This article provides links to functions of both classes. An example of an arithmetic function is the divisor function whose
Arithmetic_function
Large number used in number theory
{\displaystyle x} for which the prime-counting function π ( x ) {\displaystyle \pi (x)} exceeds the logarithmic integral function li ( x ) . {\displaystyle
Skewes's_number
Mathematical concept
Mangoldt, see below) for the normalized prime-counting function π0(x) which is related to the prime-counting function π(x) by[citation needed] π 0 ( x ) =
Explicit formulae for L-functions
Explicit_formulae_for_L-functions
Prime-counting algorithm
algorithm that computes exact values of the prime-counting function. The problem of counting the exact number of primes less than or equal to x, without actually
Meissel–Lehmer_algorithm
Natural number
Adrien-Marie Legendre to express the asymptotic behavior of the prime-counting function. The Weil's conjecture on Tamagawa numbers states that the Tamagawa
1
formulae to evaluate the prime-counting function (the number of primes smaller than a given value) faster than computing the primes. This has been used to
List_of_prime_numbers
Analytic function in mathematics
find expressions which relate to prime numbers and the prime number theorem. If π(x) is the prime-counting function, then ln ζ ( s ) = s ∫ 0 ∞ π ( x
Riemann_zeta_function
Description of limiting behavior of a function
prime numbers less than or equal to x {\textstyle x} . The function, x / ln ( x ) {\textstyle x/\ln(x)} , approximates the prime counting function for
Asymptotic_analysis
a given one. Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write
List of mathematical functions
List_of_mathematical_functions
Topics referred to by the same term
four different functions are known as the pi or Pi function: π ( x ) {\displaystyle \pi (x)\,\!} (pi function) – the prime-counting function Π ( x ) {\displaystyle
Pi_function
Greek letter
"Prime Counting Function". mathworld.wolfram.com. Retrieved 2025-01-18. The prime counting function is the function π(x) giving the number of primes less
Pi_(letter)
Difference between two successive prime numbers
refers to the big O notation, ζ denotes the Riemann zeta function and π the prime-counting function. Knowing that any c > 1/6 is admissible, one obtains that
Prime_gap
Function on an integer n which is log(p) if n equals p^k and zero otherwise
Pafnuty Chebyshev who used it to show that the true order of the prime counting function π ( x ) {\displaystyle \pi (x)} is x / log x {\displaystyle x/\log
Von_Mangoldt_function
the Prime Counting Function" (PDF). Integers. 21: 3. doi:10.5281/zenodo.10807579. Retrieved 26 February 2026. Because H_n ~ log n (n → ∞), the prime number
List of logarithmic identities
List_of_logarithmic_identities
German mathematician (1826–1866)
geometric treatment of complex analysis. His 1859 paper on the prime-counting function, containing the original statement of the Riemann hypothesis, is
Bernhard_Riemann
Conjecture on zeros of the zeta function
of many other arithmetic functions, in addition to the primes counting function above. One example involves the Möbius function μ. The statement that the
Riemann_hypothesis
Number divisible only by 1 and itself
Euler's method to solve the twin prime conjecture, that there exist infinitely many twin primes. The prime-counting function π ( n ) {\displaystyle \pi (n)}
Prime_number
Mathematical function
{\displaystyle \pi } denotes the prime counting function, Li {\displaystyle \operatorname {Li} } the logarithmic integral function with inverse Li − 1 {\displaystyle
Landau's_function
Infinitely many prime numbers exist
Let π(x) be the prime-counting function that gives the number of primes less than or equal to x, for any real number x. The prime number theorem then
Euclid's_theorem
1859 mathematics paper by Bernhard Riemann
Akademie der Wissenschaften zu Berlin. This paper studies the prime-counting function using analytic methods. Although it is the only paper Riemann ever
On the Number of Primes Less Than a Given Magnitude
On_the_Number_of_Primes_Less_Than_a_Given_Magnitude
about 10120 Skewes's number – Large upper bound related to the prime-counting function, about 10101033.94705 or exactly eee79 Moser's number Graham's
Names_of_large_numbers
Number of prime factors of a natural number
_{2}+\cdots +\alpha _{k}} . These prime-factor-counting functions have many important number theoretic relations. The function ω ( n ) {\displaystyle \omega
Prime_omega_function
Topics referred to by the same term
infinity, then the limit is 1 (where π is the prime-counting function). This result has been superseded by the prime number theorem. This disambiguation page
Chebyshev's_theorem
Branch of pure mathematics
primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects
Number_theory
Danish actuary and mathematician (1850–1916)
zeta function (the leading function in Riemann's exact prime-counting function). Instead of using a series of logarithmic integrals, Gram's function uses
Jørgen_Pedersen_Gram
British mathematician (1885–1977)
term of the prime-counting function. If π ( x ) {\displaystyle \pi (x)} denotes the number of primes up x {\displaystyle x} , then the prime number theorem
John_Edensor_Littlewood
Result on density of prime numbers
relationship with π ( x ) {\displaystyle \pi (x)} , the prime-counting function (number of primes less than or equal to x {\displaystyle x} ): π ( x ) −
Bertrand's_postulate
Product of two prime numbers
( x ) {\displaystyle \pi (x)} is the prime-counting function and p k {\displaystyle p_{k}} denotes the kth prime. Semiprime numbers have no composite
Semiprime
Theorem on finite linear groups
finite, one can take ƒ(n) = n! 12n(π(n+1)+1) where π(n) is the prime-counting function. This was subsequently improved by Hans Frederick Blichfeldt who
Jordan–Schur_theorem
Theorem about prime numbers
wrong answer. The theorem states (Maier 1985) that if π is the prime-counting function and λ > 1, then π ( x + ( log x ) λ ) − π ( x ) ( log x ) λ
Maier's_theorem
Constant of proportionality of prime number density
constructed by Adrien-Marie Legendre to approximate the behavior of the prime-counting function π ( x ) {\displaystyle \pi (x)} . The value that corresponds precisely
Legendre's_constant
Staudt–Clausen theorem Dirichlet series Euler product Prime number theorem Prime-counting function Meissel–Lehmer algorithm Offset logarithmic integral
List_of_number_theory_topics
Algorithm for generating prime numbers
resolves the above three issues, as well converting the code to a prime-counting function that also displays the total number of composite-culling operations:
Sieve_of_Sundaram
Probabilistic primality test
\left(2^{b-1}\right)}{2^{b-2}}}} where π is the prime-counting function. Using an asymptotic expansion of π (an extension of the prime number theorem), we can approximate
Miller–Rabin_primality_test
Exploring properties of the integers with complex analysis
theory was inspired by the prime number theorem. Let π(x) be the prime-counting function that gives the number of primes less than or equal to x, for
Analytic_number_theory
Bound on the gaps between prime numbers
the prime-counting function) and the left-hand inequality is Farhadian's (since p n / log p n < n {\displaystyle p_{n}/\log p_{n}<n} ; see prime-counting
Firoozbakht's_conjecture
Integer factorization algorithm
the prime-counting function, the number of primes less than x. This does not take into account the overhead of primality testing to obtain the prime numbers
Trial_division
Counts the number of necklaces of n colored beads picked from α available colors
the necklace polynomial, or Moreau's necklace-counting function, introduced by C. Moreau (1872), counts the number of distinct necklaces of n colored
Necklace_polynomial
logarithmic integral gives a somewhat too high estimate of the prime-counting function. The evidence also seemed to indicate this. However, in 1914 J. E
List_of_conjectures
On the distribution of prime numbers in arithmetic progressions
notation. Let π ( x ) {\displaystyle \pi (x)} , the prime-counting function, denote the number of primes less than or equal to x {\displaystyle x} . If q
Elliott–Halberstam_conjecture
Matrix of binary truth values
The prime factors of a list of m square-free, n-smooth numbers can be described as an m × π(n) (0, 1)-matrix, where π is the prime-counting function, and
Logical_matrix
Topics referred to by the same term
projection onto the n-th component π-calculus, a process calculus Prime-counting function or π(x) π {\displaystyle \pi } , the population proportion in statistics
Pi_(disambiguation)
Topics referred to by the same term
approximation of the prime-counting function π(x), see Prime-counting function#Exact form. Almost nowhere differentiable Riemann function, on which the Weierstrass
Riemann_function
Symbols for constants, special functions
support a solid angle the omega baryon the arithmetic function counting a number's prime factors counted with multiplicity the density parameter in cosmology
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
the nth prime, p n # {\displaystyle p_{n}\#} is the primorial of the nth prime, and π ( n ) {\displaystyle \pi (n)} is the prime-counting function. Also:
List_of_representations_of_e
Unanswered conjecture in number theory
(y)} for integers x, y ≥ 2, where π(z) denotes the prime-counting function, giving the number of prime numbers up to and including z. The statement of the
Second Hardy–Littlewood conjecture
Second_Hardy–Littlewood_conjecture
Product of numbers from 1 to n
separate choice at this value. The earliest uses of the factorial function involve counting permutations: there are n ! {\displaystyle n!} different ways
Factorial
Mathematical operation
transform is used in analysis of the prime-counting function and occurs in discussions of the Riemann zeta function. Inverse Mellin transforms commonly
Mellin_transform
Type of prime number
{p_{n}}{log(p_{n})}}} , where π ( p ) {\displaystyle \pi (p)} is the prime counting function, we would expect n {\displaystyle n} to be in the region of 1.42
Balanced_prime
Mathematical operation on arithmetical functions
the characteristic function of the primes. This last identity shows that the prime-counting function is given by the summatory function π ( x ) = ∑ n ≤ x
Dirichlet_convolution
German mathematician (1854–1925)
succeeded by Otto Blumenthal. Prime-counting function Cartan–Hadamard theorem Riemann–von Mangoldt formula Von Mangoldt function Schneider, Erich (1960). "Hans
Hans Carl Friedrich von Mangoldt
Hans_Carl_Friedrich_von_Mangoldt
Polish mathematician
also fits the distribution. The prime-counting function π ( n ) {\displaystyle \pi (n)} is defined as the number of primes not greater than n {\displaystyle
Stanisław_Knapowski
include the integer square root function and the prime-counting function. On an arbitrary set X, integer-valued functions form a ring with pointwise operations
Integer-valued_function
Family of probability distributions
{\displaystyle \Lambda (n)} is the von Mangoldt function. The function ψ(x) is related to the prime-counting function π(x), and as such provides information with
Tweedie_distribution
due to the prime number theorem, π ( x ) ∼ x ln x {\displaystyle \pi (x)\sim {\frac {x}{\ln x}}} , where π(x) is the prime counting function. lim n →
List_of_limits
Inverse of the average of the inverses of a set of numbers
Asymptotic Behavior of Hölder Means, and an Elementary Estimate for the Prime Counting Function". p. 2. arXiv:2211.10751 [math.NT]. "Average: How to calculate
Harmonic_mean
Product of the first "n" prime numbers
\atop p\,{\text{prime}}}p=\prod _{i=1}^{\pi (n)}p_{i}=p_{\pi (n)}\#,} where π ( n ) {\displaystyle \pi (n)} is the prime-counting function (sequence A000720
Primorial
net) The dimensions required for p-limit tuning are equal to the prime-counting function minus one: = π ( p ) − 1 . {\displaystyle \ =\ \pi (p)-1~
Lattice_(music)
Topics referred to by the same term
giving the total number of prime factors of n {\displaystyle n\,\!} , counting them with their multiplicity. The Lambert W function Ω ( x ) {\displaystyle
Omega_function
Existence of a prime number between each square and pronic number
n(n+1)} . It can also be phrased equivalently as stating that the prime-counting function must take unequal values at the endpoints of each range. That is:
Oppermann's_conjecture
Estimatation in number theory
maximal gaps G ( x ) {\displaystyle G(x)} expressed in terms of the prime-counting function π ( x ) {\displaystyle \pi (x)} : G ( x ) ∼ x π ( x ) ( 2 log
Cramér's_conjecture
Axiomatic definition of a class of L-functions
and π {\textstyle \pi } is the prime-counting function. This result can be thought of as a generalization of the prime number theorem. Nagoshi & Steuding
Selberg_class
On integer partitions from monotonic functions
prime numbers as an example, following earlier work by Viggo Brun and D. H. Lehmer. If π ( n ) {\displaystyle \pi (n)} is the prime-counting function
Lambek–Moser_theorem
German astronomer, mathematician, and physicist
prime numbers was cited by Riemann in "On the Number of Primes Less Than a Given Magnitude", Riemann's seminal paper on the prime-counting function.
Carl Wolfgang Benjamin Goldschmidt
Carl_Wolfgang_Benjamin_Goldschmidt
Number used for counting
"counting to 10"), or by applying the count to objects (as in "counting the students in the class"). When applied to a collection of objects, counting
Natural_number
Problem a computer might be able to solve
a positive integer n, count the number of nontrivial prime factors of n." A counting problem can be represented by a function f from {0, 1}* to the nonnegative
Computational_problem
exponential function, hyperbolic functions, Inverse hyperbolic functions, Bell numbers, Lucas numbers, Stirling numbers, prime-counting function, exponential
MXparser
Instantaneous rate of change (mathematics)
dynamical systems: A simple way to get the box-counting dimension of the graph of the Weierstrass function", Proceedings of the International Geometry Center
Derivative
Count of the possible partitions of a set
{\displaystyle B_{n}} also counts the different rhyme schemes for n {\displaystyle n} -line poems. As well as appearing in counting problems, these numbers
Bell_number
Integer having a non-trivial divisor
composite numbers is by counting the number of prime factors. A composite number with two prime factors is a semiprime or 2-almost prime (the factors need not
Composite_number
(x)\sim {\frac {x}{\log x}}} denotes the prime-counting function. Here we typically make the assumption that the function f is continuous and differentiable
Divisor_sum_identities
Mathematical operation
Mertens function, or summatory function of the Moebius function, the prime zeta function and the prime-counting function, and the Riemann prime-counting function:
Dirichlet_series_inversion
Function that can be written as a sum over prime factors
function Ω(n), defined as the total number of prime factors of n, counting multiple factors multiple times, sometimes called the "Big Omega function"
Additive_function
{x} represents the fractional part of x, and π represents the prime-counting function. For example, if we divide 29 by 2, we get 14.5, which falls short
Poussin_proof
Natural number
Sequences. OEIS Foundation. "Counting polyhedra". Numericana. Retrieved 2022-04-20. Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York:
34_(number)
Number of integers coprime to and less than n
theory, Euler's totient function counts the positive integers up to a given integer n {\displaystyle n} that are relatively prime to n {\displaystyle n}
Euler's_totient_function
Mathematical function, inverse of an exponential function
describe frequency ratios of musical intervals, appear in formulas counting prime numbers or approximating factorials, inform some models in psychophysics
Logarithm
American mathematician
x}{8\pi }}} for all x ≥ 2657, based on the prime-counting function π(x) and the logarithmic integral function li(x), and | ψ ( x ) − x | ≤ x ln 2 x 8
Lowell_Schoenfeld
Unsolved problem in number theory
M>\prod _{p\leq x}p} . In Moser's original paper, bounds on the prime-counting function are used to observe that ∑ p ≤ 10 7 1 p < 3.16. {\displaystyle
Erdős–Moser_equation
English mathematician
any θ > (1+4c)/(2+4c). Here ζ denotes the Riemann zeta function and π the prime-counting function. Using the best published value for c at the time, an
Albert_Ingham
Provides an asymptotic formula for counting the number of prime ideals of a number field
theory, the prime ideal theorem is the number field generalization of the prime number theorem. It provides an asymptotic formula for counting the number
Landau_prime_ideal_theorem
German mathematician (1894–1968)
is known for a result on gaps between prime numbers: He proved that if π(x) denotes the prime-counting function, then there exists a constant θ < 1 such
Guido_Hoheisel
Multiplicative function in number theory
product of }}k{\text{ distinct primes}}\\0&{\text{if }}n{\text{ is divisible by a square}}>1.\end{cases}}} The Möbius function can alternatively be represented
Möbius_function
Arithmetic function related to the divisors of an integer
a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number of
Divisor_function
Type of computational problem
R(x,y)\}\vert \,} be the counting function. That is, it counts the total number of admissible solutions. This is a function problem, not a decision problem
Counting_problem_(complexity)
Mathematical function
\rho (u)} . This function is used to estimate a function Ψ ( x , y , z ) {\displaystyle \Psi (x,y,z)} similar to de Bruijn's, but counting the number of
Dickman_function
Mathematical conjecture
large n {\displaystyle n} , similarly to Cramér's conjecture. Prime-counting function Legendre's conjecture Oppermann's conjecture Cramér's conjecture
Brocard's_conjecture
Number
numbers, containing zero values in a decimal power, on counting devices, that include counting rods, and abacus. Chinese authors had been familiar with
0
Integer filtered out using a sieve similar to that of Eratosthenes
the counting-out game in the Josephus problem. Lucky numbers share some properties with primes, such as asymptotic behaviour according to the prime number
Lucky_number
Function in mathematical number theory
The Carmichael lambda function of a prime power can be expressed in terms of the Euler totient. Any number that is not 1 or a prime power can be written
Carmichael_function
Head of government of Slovakia
people have occupied the function. On 25 October 2023, Robert Fico became the prime minister of Slovakia. The office of the prime minister of Slovakia was
Prime_Minister_of_Slovakia
Summatory function of the divisor-counting function
In number theory, the divisor summatory function is a function that is a sum over the divisor function. It frequently occurs in the study of the asymptotic
Divisor_summatory_function
Mapping arbitrary data to fixed-size values
A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support
Hash_function
Numbers obtained by adding the two previous ones
{\textstyle F_{1}=F^{\prime }(0)=1} , the exponential generating function of the Fibonacci numbers is given by the entire function F ( x ) = e φ x − e ψ
Fibonacci_sequence
PRIME COUNTING-FUNCTION
PRIME COUNTING-FUNCTION
Girl/Female
Hindu
Love, Affection
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.
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.
Surname or Lastname
English (eastern counties)
English (eastern counties) : unexplained.
Boy/Male
Hindu, Indian
Counting
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.
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.
Surname or Lastname
English (southern counties)
English (southern counties) : apparently a variant of Hapgood.
Surname or Lastname
English
English : variant spelling of Countess.
Surname or Lastname
English (southern counties)
English (southern counties) : unexplained.German : patronymic form of Old 2.
Surname or Lastname
English
English : occupational name from Old English hunting, a derivative of huntian ‘to hunt’.
Surname or Lastname
English (northeastern counties)
English (northeastern counties) : unexplained. Compare Hedgepeth.
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
Boy/Male
Welsh American
Son of Rhys.
Surname or Lastname
English
English : nickname from some fancied resemblance to the songbird (Emberiza spp.).German : patronymic from an unexplained Frisian-Lower Saxon personal name, or a derivative of Bunt- (see Bunten).Sarah Bunting (1686–1762), born in Matlock, Derbyshire, became a noted Quaker minister in Cross Wicks, NJ. It is believed but not certain that other members of her family, including her father, John Bunting, came with her to NJ sometime before 1704, when her marriage to William Murfin is recorded.
Surname or Lastname
English (eastern counties)
English (eastern counties) : apparently a variant of German.
Boy/Male
Australian, British, Christian, English, Welsh
Son of Rhys; Ardent; Son of the Ardent; Prize
Surname or Lastname
English
English : unexplained.Serbian : unexplained.
Girl/Female
Latin
Firstborn.
PRIME COUNTING-FUNCTION
PRIME COUNTING-FUNCTION
Boy/Male
Hindu
To practice
Male
African
witness.
Male
Swiss
, Christ-bearer.
Boy/Male
Arabic, Australian, Muslim
Servant of the Benefactor; Slave of the Generous
Boy/Male
Hindu
King among men
Girl/Female
Muslim/Islamic
Beautiful Recitation
Girl/Female
Arabic, Muslim
Wife of the Prophet Muhammad
Girl/Female
Tamil
Tanvitasri | தாநà¯à®µà¯€à®¤à®¾à®¸à®°à¯€Â
Girl/Female
Spanish
Merciful.
Boy/Male
American, British, English
From East Town
PRIME COUNTING-FUNCTION
PRIME COUNTING-FUNCTION
PRIME COUNTING-FUNCTION
PRIME COUNTING-FUNCTION
PRIME COUNTING-FUNCTION
v. t.
To pay the price of.
v. t.
To ask the price of; as, to price eggs.
n.
One who, or that which, primes
#
Donne (#) (pl. ) of Prima donna
a.
To lay the first color, coating, or preparation upon (a surface), as in painting; as, to prime a canvas, a wall.
n.
Highest pitch; elevation reached; loftiness; prime; glory; as, to be in the pride of one's life.
v. t.
To set a price on; to value. See Prize.
n.
That which occasion crime.
imp. & p. p.
of Prime
a.
To prepare; to make ready; to instruct beforehand; to post; to coach; as, to prime a witness; the boys are primed for mischief.
a.
A prime number. See under Prime, a.
a.
First in excellence; of highest quality; as, prime wheat; a prime quality of cloth.
a.
Being in its prime.
a.
To mark with a prime mark.
a.
Marked or distinguished by a mark (') called a prime mark.
n.
See Price, and 1st Prize.
a.
First in rank, degree, dignity, authority, or importance; as, prime minister.
n. & v.
See Prize, n., 5. Also Prize, v. t.
n. & v.
Reward; recompense; as, the price of industry.
a.
Formal; precise; affectedly neat or nice; as, prim regularity; a prim person.