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Prime factor exponent notation

Today, Prime factor exponent notation is a topic that generates great interest and debate in different areas of society. Whether on a personal, professional or academic level, Prime factor exponent notation has gained relevance in recent years due to its impact on our lives. From its origins to its current evolution, Prime factor exponent notation has aroused the interest of experts and the curious alike, and its influence is becoming increasingly evident in our daily lives. In this article, we will fully explore Prime factor exponent notation and all the implications it has on our current society.

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In his 1557 work The Whetstone of Witte, British mathematician Robert Recorde 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 devised the Cartesian exponent notation, which is still used today.

This is a list of Recorde's terms.

Cartesian index Arabic index Recordian symbol Explanation
1 Simple
2 Square (compound form is zenzic) z
3 Cubic cꝭ
4 Zenzizenzic (biquadratic) zz square of squares
5 First sursolid ß first prime exponent greater than three
6 Zenzicubic zcꝭ square of cubes
7 Second sursolid Bß second prime exponent greater than three
8 Zenzizenzizenzic (quadratoquadratoquadratum) zzz square of squared squares
9 Cubicubic cꝭcꝭ cube of cubes
10 Square of first sursolid zß square of five
11 Third sursolid Cß third prime number greater than 3
12 Zenzizenzicubic zzcꝭ square of square of cubes
13 Fourth sursolid Dß
14 Square of second sursolid zBß square of seven
15 Cube of first sursolid cꝭß cube of five
16 Zenzizenzizenzizenzic zzzz "square of squares, squaredly squared"
17 Fifth sursolid Eß
18 Zenzicubicubic zcꝭcꝭ
19 Sixth sursolid Fß
20 Zenzizenzic of first sursolid zzß
21 Cube of second sursolid cꝭBß
22 Square of third sursolid zCß

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 2·5
11 11
12 22·3
13 13
14 2·7
15 3·5
16 24
17 17
18 2·32
19 19
20 22·5
21 − 40
21 3·7
22 2·11
23 23
24 23·3
25 52
26 2·13
27 33
28 22·7
29 29
30 2·3·5
31 31
32 25
33 3·11
34 2·17
35 5·7
36 22·32
37 37
38 2·19
39 3·13
40 23·5
41 − 60
41 41
42 2·3·7
43 43
44 22·11
45 32·5
46 2·23
47 47
48 24·3
49 72
50 2·52
51 3·17
52 22·13
53 53
54 2·33
55 5·11
56 23·7
57 3·19
58 2·29
59 59
60 22·3·5
61 − 80
61 61
62 2·31
63 32·7
64 26
65 5·13
66 2·3·11
67 67
68 22·17
69 3·23
70 2·5·7
71 71
72 23·32
73 73
74 2·37
75 3·52
76 22·19
77 7·11
78 2·3·13
79 79
80 24·5
81 − 100
81 34
82 2·41
83 83
84 22·3·7
85 5·17
86 2·43
87 3·29
88 23·11
89 89
90 2·32·5
91 7·13
92 22·23
93 3·31
94 2·47
95 5·19
96 25·3
97 97
98 2·72
99 32·11
100 22·52

See also

Hutton, Chas, Mathematical dictionary (PDF), p. 224


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