Etymology
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prime (adj.)

late 14c., "first, original, first in order of time," from Old French prime and directly from Latin primus "first, the first, first part," figuratively "chief, principal; excellent, distinguished, noble" (source also of Italian and Spanish primo), from Proto-Italic *prismos, superlative of PIE *preis- "before," from root *per- (1) "forward," hence "in front of, before, first, chief."

The meaning "of fine quality, of the first excellence" is from c. 1400. The meaning "first in rank, degree, or importance" is from 1610s in English. Arithmetical sense (as in prime number, one indivisible without a remainder except by 1) is from 1560s; prime meridian "the meridian of the earth from which longitude is measured, that of Greenwich, England," is from 1878. Prime time originally (c. 1500) meant "spring time;" the broadcasting sense of "peak tuning-in period" is attested by 1961.

prime (n.)

"earliest canonical hour of the day" (6 a.m.), from Old English prim and Old French prime and directly from Medieval Latin prima "the first service," from Latin prima hora "the first hour" (of the Roman day), from Latin primus "first, the first, first part" (see prime (adj.)).  (In classical Latin, the noun uses of the adjective meant "first part, beginning; leading place.")

By extension, "the first division of the day" 6 a.m. to 9 a.m. (early 13c.). The sense of "beginning of a period or course of events" is from late 14c. From the notion of "the period or condition of greatest vigor in life" (by 1530s) comes the specific sense "springtime of human life" (often meaning ages roughly 21 to 28) is from 1590s. Also from 1590s as "that which is best in quality, highest or most perfect state of anything." As "a prime number," by 1530s.

prime (v.)

"to fill, charge, load" (a weapon, before firing), 1510s, probably from prime (adj.). General sense of "perform the first operation on, prepare (something, especially wood, etc., for painting)" is from c. 1600. To prime a pump (1769) meant to pour water down the tube, which saturated the sucking mechanism and made it draw up water more readily. Related: Primed; priming.

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Definitions of prime
1
prime (adj.)
of or relating to or being an integer that cannot be factored into other integers;
prime number
prime (adj.)
used of the first or originating agent;
prime mover
prime (adj.)
first in rank or degree;
the prime minister
Synonyms: premier
prime (adj.)
of superior grade;
prime beef
Synonyms: choice / prize / quality / select
prime (adj.)
being at the best stage of development; "our manhood's prime vigor"- Robert Browning;
Synonyms: meridian
2
prime (n.)
a natural number that has exactly two distinct natural number divisors: 1 and itself;
Synonyms: prime quantity
prime (n.)
the period of greatest prosperity or productivity;
prime (n.)
the second canonical hour; about 6 a.m.;
prime (n.)
the time of maturity when power and vigor are greatest;
Synonyms: prime of life
3
prime (v.)
insert a primer into (a gun, mine, or charge) preparatory to detonation or firing;
prime a mine
prime a cannon
prime (v.)
cover with a primer; apply a primer to;
Synonyms: ground / undercoat
prime (v.)
fill with priming liquid;
prime a car engine
From wordnet.princeton.edu