# 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 |
| 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 | 2$^2$ |
| 5 | 5 |
| 6 | 2·3 |
| 7 | 7 |
| 8 | 2$^3$ |
| 9 | 3$^2$ |
| 10 | 2·5 |
| 11 | 11 |
| 12 | 2$^2$·3 |
| 13 | 13 |
| 14 | 2·7 |
| 15 | 3·5 |
| 16 | 2$^4$ |
| 17 | 17 |
| 18 | 2·3$^2$ |
| 19 | 19 |
| 20 | 2$^2$·5 |
21 − 40 :
| 21 | 3·7 |
| 22 | 2·11 |
| 23 | 23 |
| 24 | 2$^3$·3 |
| 25 | 5$^2$ |
| 26 | 2·13 |
| 27 | 3$^3$ |
| 28 | 2$^2$·7 |
| 29 | 29 |
| 30 | 2·3·5 |
| 31 | 31 |
| 32 | 2$^5$ |
| 33 | 3·11 |
| 34 | 2·17 |
| 35 | 5·7 |
| 36 | 2$^2$·3$^2$ |
| 37 | 37 |
| 38 | 2·19 |
| 39 | 3·13 |
| 40 | 2$^3$·5 |
41 − 60 :
| 41 | 41 |
| 42 | 2·3·7 |
| 43 | 43 |
| 44 | 2$^2$·11 |
| 45 | 3$^2$·5 |
| 46 | 2·23 |
| 47 | 47 |
| 48 | 2$^4$·3 |
| 49 | 7$^2$ |
| 50 | 2·5$^2$ |
| 51 | 3·17 |
| 52 | 2$^2$·13 |
| 53 | 53 |
| 54 | 2·3$^3$ |
| 55 | 5·11 |
| 56 | 2$^3$·7 |
| 57 | 3·19 |
| 58 | 2·29 |
| 59 | 59 |
| 60 | 2$^2$·3·5 |
61 − 80 :
| 61 | 61 |
| 62 | 2·31 |
| 63 | 3$^2$·7 |
| 64 | 2$^6$ |
| 65 | 5·13 |
| 66 | 2·3·11 |
| 67 | 67 |
| 68 | 2$^2$·17 |
| 69 | 3·23 |
| 70 | 2·5·7 |
| 71 | 71 |
| 72 | 2$^3$·3$^2$ |
| 73 | 73 |
| 74 | 2·37 |
| 75 | 3·5$^2$ |
| 76 | 2$^2$·19 |
| 77 | 7·11 |
| 78 | 2·3·13 |
| 79 | 79 |
| 80 | 2$^4$·5 |
81 − 100 :
| 81 | 3$^4$ |
| 82 | 2·41 |
| 83 | 83 |
| 84 | 2$^2$·3·7 |
| 85 | 5·17 |
| 86 | 2·43 |
| 87 | 3·29 |
| 88 | 2$^3$·11 |
| 89 | 89 |
| 90 | 2·3$^2$·5 |
| 91 | 7·13 |
| 92 | 2$^2$·23 |
| 93 | 3·31 |
| 94 | 2·47 |
| 95 | 5·19 |
| 96 | 2$^5$·3 |
| 97 | 97 |
| 98 | 2·7$^2$ |
| 99 | 3$^2$·11 |
| 100 | 2$^2$·5$^2$ |