Natural Numbers that are not 1 or prime are termed composite.

It can be proven that there are an infinite number of prime numbers. However, the exact pattern is not determined. Except for the first few, (actually 2 and 5 themselves) all prime numbers must end with the digit 1, 3, 7, or 9 which eliminates even numbers and multiples of 5. This suggests that at most there are only 4 primes in every 10 numbers or 40%. Actually, because of the factors of 6 (2 and 3), it can be shown that all primes (above 3) are multiples of 6 plus 1 or 6 minus 1 (6n ± 1, where n = 1, 2, 3, ...). As examples: 6−1=5 and 6+1=7; 12−1=11 and 12+1=13; and 18−1=17 and 18+1=19. Therefore, there at most 2 primes in every 6 or 33%. Note that while every prime is a multiple of 6 ± 1, not every one of these is a prime. As an example, while 24−1=23 is prime, 24+1=25 is not. This is a necessary condition for a number to be a possible prime, but it is not sufficient to guarantee a prime.

The prime factorization of a Natural number is the factorization of the number into prime factors. It is unique except for the order. The prime factorization of a prime number is just the number itself.

The possible factors is a list of all the numbers that evenly divide the value. Every number with exactly two possible factors is a prime number.

n	prime factorization	possible factors
1	—	1
2	2	1, 2	prime
3	3	1, 3	prime
4	22	1, 2, 4
5	5	1, 5	prime
6	2•3	1, 2, 3, 6
7	7	1, 7	prime
8	23	1, 2, 4, 8
9	32	1, 3, 9
10	2•5	1, 2, 5, 10
11	11	1, 11	prime
12	22•3	1, 2, 3, 4, 6, 12
13	13	1, 13	prime
14	2•7	1, 2, 7, 14
15	3•5	1, 3, 5, 15
16	24	1, 2, 4, 8, 16
17	17	1, 17	prime
18	2•32	1, 2, 3, 6, 9, 18
19	19	1, 19	prime
20	22•5	1, 2, 4, 5, 10, 20
21	3•7	1, 3, 7, 21
22	2•11	1, 2, 11, 22
23	23	1, 23	prime
24	23•3	1, 2, 3, 4, 6, 8, 12, 24
25	52	1, 5, 25
26	2•13	1, 2, 13, 26
27	33	1, 3, 9, 27
28	22•7	1, 2, 4, 7, 14, 28
29	29	1, 29	prime
30	2•3•5	1, 2, 3, 5, 6, 10, 15, 30
31	31	1, 31	prime
32	25	1, 2, 4, 8, 16, 32
33	3•11	1, 3, 11, 33
34	2•17	1, 2, 17, 34
35	5•7	1, 5, 7, 35
36	22•32	1, 2, 3, 4, 6, 9, 12, 18, 36
37	37	1, 37	prime
38	2•19	1, 2, 19, 38
39	3•13	1, 3, 13, 39
40	23•5	1, 2, 4, 5, 8, 10, 20, 40
41	41	1, 41	prime
42	2•3•7	1, 2, 3, 6, 7, 14, 21, 42
43	43	1, 43	prime
44	22•11	1, 2, 4, 11, 22, 44
45	32•5	1, 3, 5, 9, 15, 45
46	2•23	1, 2, 23, 46
47	47	1, 47	prime
48	24•3	1, 2, 3, 4, 6, 8, 12, 16, 24, 48
49	72	1, 7, 49
50	2•52	1, 2, 5, 10, 25, 50
51	3•17	1, 3, 17, 51
52	22•13	1, 2, 4, 13, 26, 52
53	53	1, 53	prime
54	2•33	1, 2, 3, 6, 9, 18, 27, 54
55	5•11	1, 5, 11, 55
56	23•7	1, 2, 4, 7, 8, 14, 28, 56
57	3•19	1, 3, 19, 57
58	2•29	1, 2, 29, 58
59	59	1, 59	prime
60	23•3•5	1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
61	61	1, 61	prime
62	2•31	1, 2, 31, 62
63	32•7	1, 3, 7, 9, 21, 63
64	26	1, 2, 4, 8, 16, 32, 64
65	5•13	1, 5, 13, 65
66	2•3•11	1, 2, 3, 6, 11, 22, 33, 66
67	67	1, 67	prime
68	22•17	1, 2, 4, 17, 34, 68
69	2•23	1, 2, 23, 69
70	2•5•7	1, 2, 5, 7, 10, 14, 35, 70
71	71	1, 71	prime
72	23•32	1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
73	73	1, 73	prime
74	2•37	1, 2, 37, 74
75	3•52	1, 3, 5, 15, 25, 75
76	22•19	1, 2, 4, 19, 38, 76
77	7•11	1, 7, 11, 77
78	2•3•13	1, 2, 3, 6, 13, 26, 39, 78
79	79	1, 79	prime
80	24•5	1, 2, 4, 5, 8, 10, 16, 20, 40, 80
81	34	1, 3, 9, 27, 81
82	2•41	1, 2, 41, 82
83	83	1, 83	prime
84	22•3•7	1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
85	5•17	1, 5, 17, 85
86	2•43	1, 2, 43, 86
87	3•29	1, 3, 29, 87
88	23•11	1, 2, 4, 8, 11, 22, 44, 88
89	89	1, 89	prime
90	2•32•5	1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
91	7•13	1, 7, 13, 91
92	22•23	1, 2, 4, 23, 46, 92
93	3•31	1, 3, 31, 93
94	2•47	1, 2, 47, 94
95	5•19	1, 5, 19, 95
96	25•3	1, 2, 3, 6, 4, 8, 12, 16, 24, 32, 48, 96
97	97	1, 97	prime
98	2•72	1, 2, 7, 14, 49, 98
99	32•11	1, 3, 9, 11, 33, 99
100	2252	1, 2, 4, 5, 10, 25, 40, 50, 100