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Thus 2, 3, 5, 7 and I I are primes, for each of these occurs twice only in the table.

31In 1717 Abraham Sharp published in his Geometry Improv'd the Briggian logarithms of numbers from 1 to 100, and of primes from 100 to 1100, to 61 places; these were copied into the later editions of Sherwin and other works.

21The number r is usually included amongst the primes; but, if this is done, the last paragraph requires modification, since 144 could be expressed as 1.2 4.32, or as 1 2.2 4.3 2, or as IP. 2 4.32, where p might be anything.

10In the old times the grand-prince was simply primes inter pares among the minor princes, and these lived with their boyars almost on a footing of equality.

11The seventh article provided that bountied sugars (sucres primes) must be excluded from import into the territories of the signatory powers, by absolute prohibition of entry or by levying thereon a special duty in excess of the amount of the bounties, from which duty sugars coming from the contracting countries, and not bountyfed, must be free.

11For square measure 12 square inches = I superficial prime, 12 superficial primes = I square foot; while for cubic measure 12 cubic inches = I solid second, 12 solid seconds = I solid prime, 12 solid primes = I cubic foot.

11When an area has been calculated in terms of square feet, primes and square inches, the primes and square inches have to be reduced to square inches; and similarly with the calculation of volumes.

11His best-known papers, however, deal with prime numbers; in one of these (" Sur les nombres premiers," 1850) he established the existence of limits within which must be comprised the sum of the logarithms of the primes inferior to a given number.

11His table gives the logarithms of all numbers up to 2200, and of primes (and also of a great many composite numbers) from 2200 to 10,009, to 48 decimal places.

11His method of finding the logarithms of the small primes, which consists in taking a great number of continued geometric means between unity and the given primes, may be described as follows.

11All the great rivals of Abdalmalik having now disappeared, he was no longer like his predecessors primes inter pares, but dominus.

11Factors, Primes and Prime Factors.

11arithmetic progression of consecutive primes for any given (finite) length?

00degreases: The old metal degreasing process, which primes the metal prior to painting, was a ' dirty ' process.

00If 6 k +1, 12 k +1, 12 k +1 and 18 k +1 are primes their product is such a number.

00Bcc LPS acts as a potent cytokine stimulator but also primes human neutrophils to over respond to other inflammatory stimulants.

00Davenport was most attracted by Littlewood ' s lectures on the theory of primes and those of Besicovitch on almost periodic functions.

00The weirdest formulas for generating primes that I've come across are these.

00We've seen that twin primes seem to occur forever, yet we can find arbitrarily large gaps between primes.

00Heard from a distance, in changes, bells with flat primes sound merely characterful rather than nasty.

00For many years numbers of this form provided the largest known primes.

00Are there infinitely many sets of 3 consecutive primes in arithmetic progression.

00They tend to suffer from very sharp hums, sharp primes, very sharp quints and rather chaotic nominals.

00This is perfectly reasonable; in principle then we can find primes quickly.

00To Napier seems to be due the first use of the decimal point in arithmetic. Decimal fractions were first introduced by Stevinus in his tract La Disme, published in 1585, but he used cumbrous exponents (numbers enclosed in circles) to distinguish the different denominations, primes, seconds, thirds, &c. Thus, for example, he would have written 123.456 as 123@4050603.

00(1) he saw that a point or separatrix was quite enough to separate integers from decimals, and that no signs to indicate primes, seconds, &c., were required; (2) he used ciphers after the decimal point and preceding the first significant figure; and (3) he had no objection to a decimal standing by itself without any integer.

00This set covers the basics and primes you for a more challenging follow up course.

00This redistributes the hair's natural oils and primes the scalp for shampoo.

00At first, he thinks he is going crazy, but he soon learns that these symbols are a riddle to find the spot where the Matrix of Leadership, where a tomb of Primes holds the key for Earth's survival.

00As has been stated, Abraham Sharp's table contains 61-decimal 10 b= log 24 = - log (1-160) d =10g 49 = - log (1-160) 17253 8 35 62 21868 Briggian logarithms of primes up to I ioo, so that the logarithms of all composite numbers whose greatest prime factor does not exceed this number may be found by simple addition; and Wolfram's table gives 48-decimal hyperbolic logarithms of primes up to 10,009.

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