# Prime factor exponent notation

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 &
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
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 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 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 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 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 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