# Prime, Perfect & Mystical Numbers

## 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:

1. Prime or composite (Prime numbers indicated; otherwise the integer is composite.)1
2. Whether the number be the termination of a series (e.g. 276 = ∑23)
3. Whether the integer is a perfect number or not.
4. A perfect square.
5. 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 one-to-one 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 Ox-Goad 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.