Etymology
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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.

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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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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.

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time (v.)
Old English getimian "to happen, befall," from time (n.). Meaning "to appoint a time" (of an action, etc.) is attested from c. 1300; sense of "to measure or record the time of" (a race, event, etc.) is first attested 1660s. Related: Timed; timing.
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time (n.)

Old English tima "limited space of time," from Proto-Germanic *timon- "time" (source also of Old Norse timi "time, proper time," Swedish timme "an hour"), from PIE *di-mon-, suffixed form of root *da- "to divide."

Abstract sense of "time as an indefinite continuous duration" is recorded from late 14c. Personified at least since 1509 as an aged bald man (but with a forelock) carrying a scythe and an hour-glass. In English, a single word encompasses time as "extent" and "point" (French temps/fois, German zeit/mal) as well as "hour" (as in "what time is it?" compare French heure, German Uhr). Extended senses such as "occasion," "the right time," "leisure," or times (v.) "multiplied by" developed in Old and Middle English, probably as a natural outgrowth of such phrases as "He commends her a hundred times to God" (Old French La comande a Deu cent foiz).

to have a good time ( = a time of enjoyment) was common in Eng. from c 1520 to c 1688; it was app. retained in America, whence readopted in Britain in 19th c. [OED]

Time of day (now mainly preserved in negation, i.e. what someone won't give you if he doesn't like you) was a popular 17c. salutation (as in "Good time of day vnto your Royall Grace," "Richard III," I.iii.18), hence to give (one) the time of day "greet socially" (1590s); earlier was give good day (mid-14c.). The times "the current age" is from 1590s. Behind the times "old-fashioned" is recorded from 1831. Times as the name of a newspaper dates from 1788.

Time warp first attested 1954; time-traveling in the science fiction sense first recorded 1895 in H.G. Wells' "The Time Machine." Time capsule first recorded 1938, in reference to the one "deemed capable of resisting the effects of time for five thousand years preserving an account of universal achievements embedded in the grounds of the New York World's fair."

Jones [archaeologist of A.D. 5139] potters about for a while in the region which we have come to regard as New York, finds countless ruins, but little of interest to the historian except a calcified direction sheet to something called a "Time Capsule." Jones finds the capsule but cannot open it, and decides, after considerable prying at the lid, that it is merely evidence of an archaic tribal ceremony called a "publicity gag" of which he has already found many examples. [Princeton Alumni Weekly, April 14, 1939]

To do time "serve a prison sentence" is from 1865. Time frame is attested by 1964; time-limit is from 1880. About time, ironically for "long past due time," is recorded from 1920. To be on time is by 1854 in railroading.

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prime minister 

"leading minister of a government, the chief of the cabinet or ministry," 1640s, see prime (adj.) and minister (n.). Applied to the First Minister of State of Great Britain since 1694.

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time-sharing (n.)
1953, as a computing term, from time (n.) + verbal noun from share (v.). In real estate, as an arrangement in property use, it is recorded from 1976.
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good-time (adj.)
1928, from the noun phrase, from good (adj.) + time (n.). Expression to have a good time "enjoy oneself" attested from 1822; earlier have a good time of it (1771). To make good time "go fast" is from 1838. In Middle English, good time was "prosperous time," also "high time" (that something be done).
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time-span (n.)
also timespan, 1897, from time (n.) + span (n.1).
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small-time (adj.)
1910, originally theater slang for lower-salaried circuits, or ones requiring more daily performances; from noun phrase (also 1910). Compare big time.
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