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Coprime vs. Prime — What's the Difference?

Difference Between Coprime and Prime

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Definitions

Coprime

Having no positive integer factors in common, aside from 1.
24 and 35 are coprime.

Prime

First or highest in rank or importance; main
Our prime consideration is for the children's safety. See Usage Note at perfect.

Coprime

Having no positive integer factors, aside from 1, in common with one or more specified other positive integers.
24 is coprime to 35.

Prime

Highest in quality; excellent
Prime real estate.

Coprime

Whose greatest common divisor is a nonzero constant (i.e., polynomial of degree 0).
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Prime

Being the most desired or suitable example of something
A prime candidate for the study.

Prime

Of or relating to the USDA highest grade of beef, having abundant marbling and usually only sold at restaurants.

Prime

First or early in time, order, or sequence
The prime action of the drug.

Prime

(Mathematics) Of, relating to, or being a prime number.

Prime

The period of greatest physical and mental robustness
Athletes in the prime of their lives.
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Prime

The period of best performance or peak activity
This car is definitely past its prime.

Prime

To make ready; prepare
Guard dogs primed for attack.

Prime

To prepare (a gun or mine) for firing by inserting a charge of gunpowder or a primer.

Prime

To prepare for operation, as by pouring water into a pump or gasoline into a carburetor.

Prime

To prepare (a surface) for painting by covering with size, primer, or an undercoat.

Prime

To inform or instruct beforehand; coach.

Prime

To become prepared for future action or operation.

Prime

First in importance, degree, or rank.
Our prime concern here is to keep the community safe.

Prime

First in time, order, or sequence.
Both the English and French governments established prime meridians in their capitals.

Prime

First in excellence, quality, or value.
This is a prime location for a bookstore.

Prime

Having exactly two integral factors: itself and unity (1 in the case of integers).
Thirteen is a prime number.

Prime

Such that if it divides a product, it divides one of the multiplicands.

Prime

(mathematics) Having its complement closed under multiplication: said only of ideals.

Prime

Marked or distinguished by the prime symbol.

Prime

Early; blooming; being in the first stage.

Prime

(obsolete) Lecherous, lewd, lustful.

Prime

(historical) The first hour of daylight; the first canonical hour.

Prime

(Christianity) The religious service appointed to this hour.

Prime

(obsolete) The early morning generally.

Prime

The earliest stage of something.

Prime

The most active, thriving, or successful stage or period.

Prime

The chief or best individual or part.

Prime

(music) The first note or tone of a musical scale.

Prime

(fencing) The first defensive position, with the sword hand held at head height, and the tip of the sword at head height.

Prime

A prime element of a mathematical structure, particularly a prime number.
3 is a prime.

Prime

(card games) A four-card hand containing one card of each suit in the game of primero; the opposite of a flush in poker.

Prime

(backgammon) Six consecutive blocks, which prevent the opponent's pieces from passing.
I'm threatening to build a prime here.

Prime

The symbol ′ used to indicate feet, minutes, derivation and other measures and mathematical operations.

Prime

Any number expressing the combining weight or equivalent of any particular element; so called because these numbers were respectively reduced to their lowest relative terms on the fixed standard of hydrogen as 1.

Prime

An inch, as composed of twelve seconds in the duodecimal system.

Prime

(obsolete) The priming in a flintlock.

Prime

A feather, from the wing of the cock ostrich, that is of the palest possible shade.

Prime

(cycling) An intermediate sprint within a race, usually offering a prize and/or points.

Prime

(transitive) To prepare a mechanism for its main work.
You'll have to press this button twice to prime the fuel pump.

Prime

(transitive) To apply a coat of primer paint to.
I need to prime these handrails before we can apply the finish coat.

Prime

To be renewed.

Prime

(intransitive) To serve as priming for the charge of a gun.

Prime

To work so that foaming occurs from too violent ebullition, which causes water to become mixed with, and be carried along with, the steam that is formed.

Prime

To apply priming to (a musket or cannon); to apply a primer to (a metallic cartridge).

Prime

To prepare; to make ready; to instruct beforehand; to coach.
To prime a witness
The boys are primed for mischief.

Prime

To trim or prune.
To prime trees

Prime

(math) To mark with a prime mark.

Prime

First in order of time; original; primeval; primitive; primary.
She was not the prime cause, but I myself.

Prime

First in rank, degree, dignity, authority, or importance; as, prime minister.

Prime

First in excellence; of highest quality; as, prime wheat; a prime quality of cloth.

Prime

Early; blooming; being in the first stage.
His starry helm, unbuckled, showed him primeIn manhood where youth ended.

Prime

Lecherous; lustful; lewd.

Prime

Marked or distinguished by a mark (´) called a prime mark.

Prime

Divisible by no number except itself or unity; as, 7 is a prime number.

Prime

The first part; the earliest stage; the beginning or opening, as of the day, the year, etc.; hence, the dawn; the spring.
In the very prime of the world.
Hope waits upon the flowery prime.

Prime

The spring of life; youth; hence, full health, strength, or beauty; perfection.

Prime

That which is first in quantity; the most excellent portion; the best part.
Give him always of the prime.

Prime

The morning; specifically (R. C. Ch.), the first canonical hour, succeeding to lauds.
Early and late it rung, at evening and at prime.
They sleep till that it was pryme large.

Prime

The first of the chief guards.

Prime

Any number expressing the combining weight or equivalent of any particular element; - so called because these numbers were respectively reduced to their lowest relative terms on the fixed standard of hydrogen as 1.

Prime

To apply priming to, as a musket or a cannon; to apply a primer to, as a metallic cartridge.

Prime

To lay the first color, coating, or preparation upon (a surface), as in painting; as, to prime a canvas, a wall.

Prime

To prepare; to make ready; to instruct beforehand; to post; to coach; as, to prime a witness; the boys are primed for mischief.

Prime

To trim or prune, as trees.

Prime

To mark with a prime mark.

Prime

To be renewed, or as at first.
Night's bashful empress, though she often wane,As oft repeats her darkness, primes again.

Prime

To serve as priming for the charge of a gun.

Prime

To work so that foaming occurs from too violent ebullition, which causes water to become mixed with, and be carried along with, the steam that is formed; - said of a steam boiler.

Prime

A number that has no factor but itself and 1

Prime

The period of greatest prosperity or productivity

Prime

The second canonical hour; about 6 a.m.

Prime

The time of maturity when power and vigor are greatest

Prime

Insert a primer into (a gun, mine, charge, etc.) preparatory to detonation or firing;
Prime a cannon
Prime a mine

Prime

Cover with a primer; apply a primer to

Prime

Fill with priming liquid;
Prime a car engine

Prime

First in rank or degree;
An architect of premier rank
The prime minister

Prime

Used of the first or originating agent;
Prime mover

Prime

Of superior grade;
Choice wines
Prime beef
Prize carnations
Quality paper
Select peaches

Prime

Of or relating to or being an integer that cannot be factored into other integers;
Prime number

Prime

At the best stage;
Our manhood's prime vigor

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