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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number (v.)

c. 1300, "to count," from Old French nombrer "to count, reckon," from nombre (n.) "number" (see number (n.)). Meaning "to assign a distinctive number to" is late 14c.; that of "to ascertain the number of" is from early 15c. Related: Numbered; numbering.

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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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number (n.)

c. 1300, "sum, aggregate of a collection," from Anglo-French noumbre, Old French nombre and directly from Latin numerus "a number, quantity," from PIE root *nem- "assign, allot; take."

Meaning "written symbol or figure of arithmetic value" is from late 14c. Meaning "single (numbered) issue of a magazine" is from 1795. Colloquial sense of "a person or thing" is by 1894. Meaning "dialing combination to reach a particular telephone receiver" is from 1879; hence wrong number (1886). The modern meaning "musical selection" (1885) is from vaudeville theater programs, where acts were marked by a number. Earlier numbers meant "metrical sound or utterance, measured or harmonic expression" (late 15c.) and, from 1580s, "poetical measure, poetry, verse."

Number one "oneself" is from 1704 (mock-Italian form numero uno attested from 1973); the biblical Book of Numbers (c. 1400, Latin Numeri, Greek Arithmoi) is so called because it begins with a census of the Israelites. Childish slang number one and number two for "urination" and "defecation" attested from 1902. Number cruncher is 1966, of machines; 1971 of persons. To get or have (someone's) number "have someone figured out" is attested from 1853; to say one's number is up (1806) meaning "one's time has come" is a reference to the numbers on a lottery, draft, etc. The numbers "illegal lottery" is from 1897, American English.

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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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cardinal number (n.)
1590s, "one, two, three," etc. as opposed to ordinal numbers "first, second, third," etc.; so called because they are the principal numbers and the ordinals depend on them (see cardinal (adj.)).
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Downing Street 
short street in London, named for British diplomat Sir George Downing (c. 1624-1684). It contains the residence of the prime minister (at Number 10), hence its metonymic use for "the British government," attested from 1781.
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subprime (adj.)
also sub-prime, of loans, etc., by 1978, in frequent use from 1996, from sub- + prime (adj.).
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primer (n.2)
"explosive cap," 1819, agent noun from prime (v.).
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