Prime factor exponent notation - AbsoluteAstronomy.com

The Whetstone of Witte

The Whetstone of Witte is the shortened title of Robert Recorde's mathematics book published in 1557. The full title being, The Whetstone of Witte, whiche is the seconde parte of Arithmeteke: containing the extraction of rootes; the cossike practise, with the rule of equation; and the workes of...

, British

British people

The British are citizens of the United Kingdom, of the Isle of Man, any of the Channel Islands, or of any of the British overseas territories, and their descendants...

mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

Robert Recorde

Robert Recorde was a Welsh physician and mathematician. He introduced the "equals" sign in 1557.-Biography:A member of a respectable family of Tenby, Wales, he entered the University of Oxford about 1525, and was elected a fellow of All Souls College in 1531...

proposed an exponent notation by prime factorisation, which remained in use up until the eighteenth century and acquired the name Arabic exponent notation. The principle of Arabic exponents was quite similar to Egyptian fractions; large exponents were broken down into smaller prime numbers. Squares and cubes were so called; prime numbers from five onwards were called sursolids.

Although the terms used for defining exponents differed between authors and times, the general system was the primary exponent notation until René Descartes

René Descartes

René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...

devised the Cartesian exponent notation, which is still used today.

This is a list of Recorde's terms.

Cartesian indice	Arabic index	Recordian symbol !! Explanation
1	Simple
2	Square (compound form is zenzic)	z
3	Cubic	&
4	Zenzizenzic (biquadratic)	zz	square of squares
5	First sursolid	sz	first prime exponent greater than three
6	Zenzicubic	z&	square of cubes
7	Second sursolid	Bsz	second prime exponent greater than three
8	Zenzizenzizenzic (quadratoquadratoquadratum)	zzz	square of squared squares
9	Cubicubic	&&	cube of cubes
10	Square of first sursolid	zsz	square of five
11	Third sursolid	csz	third prime number greater than 3
12	Zenzizenzicubic	zz&	square of square of cubes
13	Fourth sursolid	dsz
14	Square of second sursolid	zbsz	square of seven
15	Cube of first sursolid	&sz	cube of five
16	Zenzizenzizenzizenzic	zzzz	"square of squares, squaredly squared"
17	Fifth sursolid	esz
18	Zenzicubicubic	z&&
19	Sixth sursolid	fsz
20	Zenzizenzic of first sursolid	zzsz
21	Cube of second sursolid	&bsz
22	Square of third sursolid	zcsz

By comparison, here is a table of prime factors:

1 − 20
1	unit
2	2
3	3
4	2²
5	5
6	2·3
7	7
8	2³
9	3²
10 10 (number) 10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and...	2·5
11 11 (number) 11 is the natural number following 10 and preceding 12.Eleven is the first number which cannot be counted with a human's eight fingers and two thumbs additively. In English, it is the smallest positive integer requiring three syllables and the largest prime number with a single-morpheme name...	11
12 12 (number) 12 is the natural number following 11 and preceding 13.The word "twelve" is the largest number with a single-morpheme name in English. Etymology suggests that "twelve" arises from the Germanic compound twalif "two-leftover", so a literal translation would yield "two remaining [after having ten...	2²·3
13 13 (number) 13 is the natural number after 12 and before 14. It is the smallest number with eight letters in its name spelled out in English. It is also the first of the teens – the numbers 13 through 19 – the ages of teenagers....	13
14 14 (number) 14 is the natural number following 13 and preceding 15.In speech, the numbers 14 and 40 are often confused. When carefully enunciated, they differ in which syllable is stressed: 14 vs 40...	2·7
15 15 (number) 15 is the natural number following 14 and preceding 16. In English, it is the smallest natural number with seven letters in its spelled name....	3·5
16 16 (number) 16 is the natural number following 15 and preceding 17. 16 is a composite number, and a square number, being 42 = 4 × 4. It is the smallest number with exactly five divisors, its proper divisors being , , and ....	2⁴
17 17 (number) 17 is the natural number following 16 and preceding 18. It is prime.In spoken English, the numbers 17 and 70 are sometimes confused because they sound similar. When carefully enunciated, they differ in which syllable is stressed: 17 vs 70...	17
18 18 (number) 18 is the natural number following 17 and preceding 19.In speech, the numbers 18 and 80 are sometimes confused. When carefully enunciated, they differ in which syllable is stressed: 18 vs 80 . However, in dates such as 1864, or when contrasting numbers in the teens, such as 17, 18, 19, the stress...	2·3²
19 19 (number) 19 is the natural number following 18 and preceding 20. It is a prime number.In English speech, the numbers 19 and 90 are often confused. When carefully enunciated, they differ in which syllable is stressed: 19 vs 90...	19
20 20 (number) 20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.-In mathematics:*20 is the basis for vigesimal number systems....	2²·5

21 − 40
21 21 (number) 21 is the natural number following 20 and preceding 22.-In mathematics:Twenty-one is the fifth discrete Semiprime and the second in the family. With 22 it forms the second discrete Semiprime pair...	3·7
22 22 (number) 22 is the natural number following 21 and preceding 23.- In mathematics :Twenty-two is an even composite number, its proper divisors being 1, 2 and 11....	2·11
23 23 (number) 23 is the natural number following 22 and preceding 24.- In mathematics :Twenty-three is the ninth prime number, the smallest odd prime that is not a twin prime. Twenty-three is also the fifth factorial prime, the third Woodall prime...	23
24 24 (number) 24 is the natural number following 23 and preceding 25.The SI prefix for 1024 is yotta , and for 10−24 yocto...	2³·3
25 25 (number) 25 is the natural number following 24 and preceding 26.-In mathematics:It is a square number, being 5² = 5 × 5. It is the smallest square that is also a sum of two squares: 25 = 3² + 4²...	5²
26 26 (number) 26 is the natural number following 25 and preceding 27.- In mathematics :26 is the only positive integer that is one greater than a square and one less than a cube .A rhombicuboctahedron has twenty-six sides....	2·13
27 27 (number) 27 is the natural number following 26 and preceding 28.- In mathematics :Twenty-seven is a perfect cube, being 33 = 3 × 3 × 3. 27 is also 23 . There are exactly 27 straight lines on a smooth cubic surface, which give a basis of the fundamental representation of the E6 Lie algebra...	3³
28 28 (number) 28 is the natural number following 27 and preceding 29.-In mathematics:It is a composite number, its proper divisors being 1, 2, 4, 7, and 14....	2²·7
29 29 (number) 29 is the natural number following 28 and preceding 30.-In mathematics:It is the tenth prime number, and also the fourth primorial prime. It forms a twin prime pair with thirty-one, which is also a primorial prime. Twenty-nine is also the sixth Sophie Germain prime. It is also the sum of three...	29
30 30 (number) 30 is the natural number following 29 and preceding 31.-In mathematics:30 is the sum of the first four squares, which makes it a square pyramidal number.It is a primorial and is the smallest Giuga number....	2·3·5
31 31 (number) 31 is the natural number following 30 and preceding 32.- In mathematics :Thirty-one is the third Mersenne prime as well as the fourth primorial prime, and together with twenty-nine, another primorial prime, it comprises a twin prime. As a Mersenne prime, 31 is related to the perfect number 496,...	31
32 32 (number) 32 is the natural number following 31 and preceding 33.-In mathematics:32 is the smallest number n with exactly 7 solutions to the equation φ = n...	2⁵
33 33 (number) 33 is the natural number following 32 and preceding 34.-In mathematics:33 is the largest positive integer that cannot be expressed as a sum of different triangular numbers. It is also the smallest odd repdigit that is not a prime number.33 is the eighth distinct semiprime comprising the prime...	3·11
34 34 (number) 34 is the natural number following 33 and preceding 35.-In mathematics:34 is the ninth distinct semiprime and has four divisors including unity and itself. Its neighbors, 33 and 35, also are distinct semiprimes, having four divisors each, and 34 is the smallest number to be surrounded by numbers...	2·17
35 35 (number) 35 is the natural number following 34 and preceding 36.- In mathematics :35 is the sum of the first five triangular numbers, making it a tetrahedral number....	5·7
36 36 (number) 36 is the natural number following 35 and preceding 37.- In mathematics :36 is both the square of 6 and a triangular number, making it a square triangular number...	2²·3²
37 37 (number) 37 is the natural number following 36 and preceding 38.-In mathematics:It is a prime number, the fifth lucky prime, the first irregular prime, the third unique prime and the third cuban prime of the form...	37
38 38 (number) This article discusses the number thirty-eight. For the year 38 CE, see 38. For other uses of 38, see 38 38 is the natural number following 37 and preceding 39.-In mathematics:...	2·19
39 39 (number) 39 is the natural number following 38 and preceding 40.- In mathematics :Thirty-nine is the sum of five consecutive primes and the sum of the first three powers of 3...	3·13
40 40 (number) 40 is the natural number following 39 and preceding 41.Despite being related to the word "four" , 40 is spelled "forty", and not "fourty"...	2³·5

41 − 60
41 41 (number) 41 is the natural number following 40 and preceding 42.-In mathematics:Forty-one is the 13th smallest prime number. The next is forty-three, with which it comprises a twin prime...	41
42 42 (number) 42 is the natural number immediately following 41 and directly preceding 43. The number has received considerable attention in popular culture as a result of its central appearance in The Hitchhiker's Guide to the Galaxy as the "Answer to the Ultimate Question of Life, the Universe, and...	2·3·7
43 43 (number) 43 is the natural number following 42 and preceding 44.- In mathematics :Forty-three is the 14th smallest prime number. The previous is forty-one, with which it comprises a twin prime, and the next is forty-seven. 43 is the smallest prime that is not a Chen prime...	43
44 44 (number) 44 is the natural number following 43 and preceding 45.- In mathematics :Forty-four is a tribonacci number, a happy number, an octahedral number and a palindromic number....	2²·11
45 45 (number) 45 is the natural number following 44 and followed by 46.- In mathematics :Forty-five is a triangular number, a hexagonal and 16-gonal number, a Kaprekar number, and a Harshad number....	3²·5
46 46 (number) 46 is the natural number following 45 and preceding 47.- In mathematics :Forty-six is a Wedderburn-Etherington number, an enneagonal number and a centered triangular number. It is the sum of the totient function for the first twelve integers. 46 is the largest even integer that can't be expressed...	2·23
47 47 (number) 47 is the natural number following 46 and preceding 48.-In mathematics:Forty-seven is the fifteenth prime number, a safe prime, the thirteenth supersingular prime, and the sixth Lucas prime. Forty-seven is a highly cototient number...	47
48 48 (number) 48 is the natural number following 47 and preceding 49. It is one third of a gross or four dozens.- In mathematics :Forty-eight is a double factorial of 6, a highly composite number. Like all other multiples of 6, it is a semiperfect number. 48 is the second 17-gonal number.48 is in abundance...	2⁴·3
49 49 (number) 49 is the natural number following 48 and preceding 50.-In mathematics:* Forty-nine is the square of seven and is therefore the fourth squared prime number.The aliquot sum of forty-nine is 8...	7²
50 50 (number) This article discusses the number fifty. For the year 50 CE, see 50. For other uses of 50, see 50 50 is the natural number following 49 and preceding 51.-In mathematics:...	2·5²
51	3·17
52 52 (number) 52 is the natural number following 51 and preceding 53.-In mathematics:Fifty-two is the 6th Bell number and a decagonal number...	2²·13
53 53 (number) 53 is the natural number following 52 and preceding 54.-In mathematics:Fifty-three is the 16th prime number. It is also an Eisenstein prime....	53
54 54 (number) 54 is the natural number following 53 and preceding 55.-In mathematics:54 is a 19-gonal number. Twice the third power of three, 54 is a Leyland number. 54 can be written as the sum of three squares in three different ways: 7^2 + 2^2 + 1^2 = 6^2 + 2 = 2 + 2^2 = 54. It is the smallest number with...	2·3³
55 55 (number) 55 is the natural number following 54 and preceding 56.-Albania:Gazeta 55, a newspaperConstitution law 55, a law during Communist Albania.-Mathematics:...	5·11
56 56 (number) 56 is the natural number following 55 and preceding 57.- Mathematics :56 is the sum of the first six triangular numbers , as well as the sum of six consecutive primes . It is also a tetranacci number and a pronic number. Adding up the divisors of 1 through 8 gives 56...	2³·7
57 57 (number) 57 is the natural number following 56 and preceding 58.- In mathematics :Fifty-seven is the sixteenth discrete semiprime and the sixth in the family. With 58 it forms the fourth discrete bi-prime pair. 57 has an aliquot sum of 23 and is the first composite member of the 23-aliquot tree...	3·19
58 58 (number) 58 is the natural number following 57 and preceding 59.-In mathematics:Fifty-eight has an aliquot sum of 32 and is the second composite member of the 83-aliquot tree....	2·29
59 59 (number) 59 is the natural number following 58 and preceding 60.-In mathematics:Fifty-nine is the 17th smallest prime number. The next is sixty-one, with which it comprises a twin prime. 59 is an irregular prime, a safe prime and the 14th supersingular prime. It is an Eisenstein prime with no imaginary...	59
60 60 (number) 60 is the natural number following 59 and preceding 61. Being three times twenty, 60 is called "three score" in some older literature.-In mathematics:...	2²·3·5

61 − 80
61 61 (number) 61 is the natural number following 60 and preceding 62.-In mathematics:It is the 18th prime number. The previous is 59, with which it comprises a twin prime. Sixty-one is a cuban prime of the form p = / , x = y + 1....	61
62 62 (number) 62 is a natural number following 61 and preceding 63. It is a composite number with the divisors 2 and 31 being the eighteenth discreet semiprime. 62 has an aliquot sum of 34; itself a discrete semiprime, and the 10 member aliquot sequence . 62 is therefore the tenth member of the 7-aliquot tree...	2·31
63 63 (number) 63 is a natural number following 62 and preceding 64.-In mathematics:Although a number of the form 2n - 1, 63 is not a Mersenne prime since n is not prime and 63 is certainly not prime either. It is a Woodall number and a Harshad number. It is a highly cototient number. It is a repdigit in base 4...	3²·7
64 64 (number) 64 is the natural number following 63 and preceding 65.-In mathematics:Sixty-four is the square of 8, the cube of 4, and the sixth power of 2. It is the smallest number with exactly seven divisors. It is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat...	2⁶
65 65 (number) 65 is the natural number following 64 and preceding 66.-In mathematics:Sixty-five is the 23rd semiprime and the 3rd of the form it is an octagonal number. It is also a Cullen number...	5·13
66 66 (number) 66 is the natural number following 65 and preceding 67.Usages of this number include:-Mathematics:*66 is a sphenic number, a triangular number, a hexagonal number, and a semi-meandric number...	2·3·11
67 67 (number) 67 is the natural number following 66 and preceding 68. It is an odd number.-In mathematics:Sixty-seven is the 19th prime number , an irregular prime, a lucky prime, the sum of five consecutive primes , and a Heegner number.Since 18! + 1 is divisible by 67 but 67 is not one more than a multiple of...	67
68 68 (number) 68 is the natural number following 67 and preceding 69.-In mathematics:Sixty-eight is a nontotient. It is also a Perrin number, preceded in the sequence by 29, 39, 51...	2²·17
69 69 (number) 69 is a number following 68 and preceding 70.- In mathematics:The aliquot sum of sixty-nine is 27 within the aliquot sequence 69 being the third composite number in the 13-aliquot tree.69 is a semiprime...	3·23
70 70 (number) 70 is the natural number following 69 and preceding 71.-In mathematics:Its factorization makes it a sphenic number. 70 is a Pell number and a generalized heptagonal number, one of only two numbers to be both. Also, it is the seventh pentagonal number and the fourth 13-gonal number, as well as the...	2·5·7
71 71 (number) 71 is the natural number following 70 and preceding 72.-In mathematics:71 is the algebraic degree of Conway's constant, a remarkable number arising in the study of look-and-say sequences....	71
72 72 (number) 72 is the natural number following 71 and preceding 73. It is half a gross or 6 dozen .-In mathematics:...	2³·3²
73 73 (number) 73 is the natural number following 72 and preceding 74. In English, it is the smallest integer with twelve letters in its spelled out name.- In mathematics :...	73
74 74 (number) 74 is the natural number following 73 and preceding 75.A seventy-four was a third-rate warship with 74 guns.-In mathematics:Seventy-four is the twenty-first distinct semiprime and the eleventh of the form 2×q...	2·37
75 75 (number) 75 is the natural number following 74 and preceding 76.-In mathematics:As the sum of the first five pentagonal numbers, seventy-five is a pentagonal pyramidal number. It is also an enneagonal number....	3·5²
76 76 (number) 76 is the natural number following 75 and preceding 77.-In mathematics:Seventy-six is a Lucas number, an automorphic number, a nontotient, a 14-gonal number, and a centered pentagonal number....	2²·19
77 77 (number) 77 is the natural number following 76 and preceding 78. Seventy-seven is the smallest positive integer requiring five syllables in English.-In mathematics:...	7·11
78 78 (number) 78 is the natural number following 77 and followed by 79.-In mathematics:78 is a triangular number, and its factorization makes it a sphenic number...	2·3·13
79 79 (number) Seventy-nine is the natural number following 78 and preceding 80.79 may represent:-In mathematics:An odd numberThe smallest number that can't be represented as a sum of fewer than 19 fourth powers*A strictly non-palindromic number...	79
80 80 (number) 80 is the natural number following 79 and preceding 81.- In mathematics :The sum of Euler's totient function φ over the first sixteen integers is 80....	2⁴·5

81 − 100
81 81 (number) 81 is the natural number following 80 and preceding 82.-In mathematics:Eighty-one is the square of 9 and the fourth power of 3. Like all powers of three, 81 is a perfect totient number. It is a heptagonal number and a centered octagonal number. It is also a tribonacci number, and an open meandric...	3⁴
82 82 (number) 82 is the natural number following 81 and preceding 83.-In mathematics:Eighty-two is the twenty-third biprime and the twelfth of the form...	2·41
83 83 (number) 83 is the natural number following 82 and preceding 84.-In mathematics:Eighty-three is the sum of three consecutive primes as well as the sum of five consecutive primes ....	83
84 84 (number) 84 is the natural number following 83 and preceding 85.- In mathematics :Eighty-four is the sum of the first seven triangular numbers , as well as the sum of a twin prime...	2²·3·7
85 85 (number) 85 is the natural number following 84 and preceding 86.-In mathematics:85 is an octahedral number, a centered triangular number, a centered square number, a decagonal number, and a Smith number....	5·17
86 86 (number) 86 is the natural number following 85 and preceding 87.-In mathematics:86 is the 25th distinct semiprime and the 13th of the form...	2·43
87 87 (number) 87 is the natural number following 86 and preceding 88.-In mathematics:Eighty-seven is the twenty-sixth distinct semiprime and the eighth of the form . The aliquot sum of 87 is 33 within the aliquot sequence 86 being the eighteenth composite number in the 3-aliquot tree.Eighty-seven is the sum of...	3·29
88 88 (number) 88 is the natural number following 87 and preceding 89.- In mathematics :Eighty-Eight is a refactorable number, a primitive semiperfect number and an untouchable number...	2³·11
89	89
90 90 (number) 90 is the natural number preceded by 89 and followed by 91.- In mathematics :*Because 90 is the sum of its unitary divisors , it is a unitary perfect number, and because it is equal to the sum of a subset of its divisors, it is a semiperfect number. 90 is a pronic number. But it is also a...	2·3²·5
91 91 (number) 91 is the natural number following 90 and preceding 92.-In mathematics:Ninety-one is the twenty-seventh distinct semiprime and the second of the form...	7·13
92 92 (number) 92 is the natural number following 91 and preceding 93.- In mathematics:Ninety-two is a pentagonal number.There are 92 Johnson solids...	2²·23
93 93 (number) 93 is the natural number following 92 and preceding 94.-In mathematics:Ninety-three is the twenty-eighth distinct semiprime and the ninth of the form...	3·31
94 94 (number) 94 is the natural number following 93 and preceding 95.-In mathematics:Ninety-four is the twenty-ninth distinct semiprime and the fourteenth of the form...	2·47
95 95 (number) 95 is the natural number following 94 and preceding 96.-In mathematics:Ninety-five is the thirtieth distinct semiprime and the fifth of the form...	5·19
96 96 (number) 96 is the natural number following 95 and preceding 97.-In mathematics:Ninety-six is an octagonal number, a refactorable number and an untouchable number. Since it is a multiple of 6, it is a semiperfect number...	2⁵·3
97 97 (number) 97 is the natural number following 96 and preceding 98.-In mathematics:97 is the 25th prime number , following 89 and preceding 101. 97 is a Proth prime as it is 3 × 25 + 1.The numbers 97, 907, 9007, 90007 and 900007 are happy primes...	97
98 98 (number) 98 is the natural number following 97 and preceding 99.-In astronomy:* Messier 98, a magnitude 11.0 spiral galaxy in the constellation Coma Berenices....	2·7²
99 99 (number) 99 is the natural number following 98 and preceding 100.-Mathematics:99 is the ninth repdigit, a palindromic number and a Kaprekar number...	3²·11
100 100 (number) 100 is the natural number following 99 and preceding 101.-In mathematics:One hundred is the square of 10...	2²·5²

External links (references)

Mathematical dictionary, Chas Hutton, pg 224

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

See also

External links (references)