Integer Properties (N=1 to 2000)
THE LEXICON appended to this work tabulates the integers along with their list of factors and properties if any. Among these properties we include:
 Prime or composite (Prime numbers indicated; otherwise the integer is composite.)^{1}
 Whether the number be the termination of a series (e.g. 276 = ∑23)
 Whether the integer is a perfect number or not.
 A perfect square.
 Any other special properties.
Prime Numbers
A PRIME number is a positive integer which has only two divisors: one and itself. There are an infinite number of primes as Euclid proved over 2000 years ago in his Elements. (We omit the proof and leave it to the interested reader; it is quite elegant.)
Prime numbers enjoy a special place in mathematics as the basic units from which all other numbers can be spanned through the field of multiplication. This means essentially that all integer numbers can be broken down into a list of primes that when multiplied together equal that integer. Furthermore this sequence of primes is unique to that number, a signature of sorts, a fingerprint or a DNA trace. Take for example, the number 222, this number (like any number) breaks down into a unique list of prime factors, namely: 37 × 3 × 2. Similarly, 345 is composite for 23 × 5 × 3 and 6 782 545 = 5 × 7 × 11 × 79 × 223.
This is called a onetoone mapping: no two numbers can share the same multiplicative list of primes.^{2}
We can see then that prime numbers constitute the building blocks for other numbers. However it would be an error to consider 222 simply as 37 the idea of Kether refracted into Tiphareth (human consciousness). 222 can also be expressed as 111 × 2 (the Aleph or Word into Chokmah) or 74 × 3 (the OxGoad pulling at Binah). In fact 222 is an “identity” in itself, and all these product expressions of it are its properties.
The first 100 prime numbers are listed here.
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541.
Perfect Numbers
A perfect number is an integer which is the sum of its positive proper divisors (all divisors except itself).
The first five perfect numbers are : 6; 28; 496; 8,128; 33,550,336. They grow in magnitude very quickly as can be seen from this short list. Humanity only knows of 43 perfect numbers. In the meantime, it is not known whether there are (or are not) any other perfect numbers besides the ones known; and if so, if this list be finite or infinite. This remains an unsolved problem in mathematics.
Mystical Numbers of the Planets
Summation of the Integers
The number 10 equals to the summation of all the integers up to and including 4. That is, 10 = 1 + 2 + 3 + 4 or ∑4i=1i =10. This idea of 10 then contains in itself the notion of the sequential development of the ideas represented by the numerals 1, 2, 3, 4 (the unit, reflection, relation, and their integration as a whole). Now the 4th sphere is the sphere of Jupiter. And so 10, which is the summation of all the integers up to an including 4, contains all the ideas necessary for the manifestation of 4th sphere, which mathematically is the 3rd dimension, or the material plane, which is 10 or Malkuth. We say then that 10 is a “mystical” number for Jupiter. Similarily 21, is a mystical number for SOL, or the SUN (the 6th sphere), seeing as 21 is the summation of the first 6 integers.
We present now the summation of the first 100 integers, along with their planetary attributions. Among these numbers the student will note an unusual density in the collection of significant initiatory events or formulaic values (e.g.: 21, 78, 91, 120, 210, 276, 496, 666, 780, 1035, etc.).
Integer 
Mystical Number 
Planet 
1 
1 

2 
3 
♆ 
3 
6 
♄ 
4 
10 
♃ 
5 
15 
♂ 
6 
21 
☉ 
7 
28 
♀ 
8 
36 
☿ 
9 
45 
☽,♄ 
10 
55 
⊗ 
11 
66 

12 
78 

13 
91 

14 
105 

15 
120 

16 
136 
♃ 
17 
153 

18 
171 

19 
190 

20 
210 

21 
231 

22 
253 

23 
276 

24 
300 

25 
325 
♂ 
26 
351 

27 
378 

28 
406 

29 
435 

30 
465 

31 
496 

32 
528 

33 
561 

34 
595 

35 
630 

36 
666 
☉ 
37 
703 

38 
741 

39 
780 

40 
820 

41 
861 

42 
903 

43 
946 

44 
990 

45 
1035 

46 
1081 

47 
1128 

48 
1176 

49 
1225 
♀ 
50 
1275 

51 
1326 

52 
1378 

53 
1431 

54 
1485 

55 
1540 

56 
1596 

57 
1653 

58 
1711 

59 
1770 

60 
1830 

61 
1891 

62 
1953 

63 
2016 

64 
2080 
☿ 
65 
2145 

66 
2211 

67 
2278 

68 
2346 

69 
2415 

70 
2485 

71 
2556 

72 
2628 

73 
2701 

74 
2775 

75 
2850 

76 
2926 

77 
3003 

78 
3081 

79 
3160 

80 
3240 

81 
3321 
☽ 
82 
3403 

83 
3486 

84 
3570 

85 
3655 

86 
3741 

87 
3828 

88 
3916 

89 
4005 

90 
4095 

91 
4186 

92 
4278 

93 
4371 

94 
4465 

95 
4560 

96 
4656 

97 
4753 

98 
4851 

99 
4950 

100 
5050 
⊗ 
1 It is important to note, that any composite number is in fact a finite product of primes, and can be expressed as such. These considerations are valuable when investigating the nature of a particular number.
2 Proof should be obvious to the student. Argue by contrapositive: Axiomatically, it is impossible to multiply the same list of numbers and arrive at different results.