Prime Numbers from 1 to 100
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Complete List of Prime Numbers (1-100)
There are 25 prime numbers between 1 and 100:
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
Detailed Information for Each Number (1-100)
| Number | Type | Factors | Special Properties | Fun Fact |
|---|---|---|---|---|
| 1 | Neither prime nor composite | 1 | Multiplicative identity | First natural number |
| 2 | Prime | 1, 2 | Only even prime, smallest prime | Atomic number of helium |
| 3 | Prime | 1, 3 | First odd prime, triangular number | Number of dimensions we perceive |
| 4 | Composite | 1, 2, 4 | First composite, perfect square | Seasons in a year |
| 5 | Prime | 1, 5 | Fibonacci prime, Wilson prime | Human senses (sight, hearing, etc.) |
| 99 | Composite | 1, 3, 9, 11, 33, 99 | Repdigit number | Temperature of fever in Fahrenheit |
| 100 | Composite | 1, 2, 4, 5, 10, 20, 25, 50, 100 | Perfect square, sum of first 9 primes | Percentage system base |
Interesting Patterns
- The only even prime number is 2 - all other primes are odd
- There are 8 twin prime pairs under 100: (3,5), (5,7), (11,13), (17,19), (29,31), (41,43), (59,61), (71,73)
- The largest prime gap under 100 is 8 (between 89 and 97)
- All primes greater than 3 can be written as either 6n+1 or 6n-1
- The digit sums of primes are never 0, 3, 6, or 9 (except for 3 itself)
Prime Number Theorems
- Fundamental Theorem of Arithmetic: Every integer >1 is either prime or can be uniquely factored into primes
- Prime Number Theorem: The number of primes ≤n is approximately n/ln(n)
- Wilson's Theorem: (p-1)! ≡ -1 mod p if and only if p is prime
- Goldbach's Conjecture: Every even integer >2 can be expressed as the sum of two primes
Applications of Prime Numbers
- Cryptography: RSA encryption relies on difficulty of factoring large primes
- Hashing: Prime numbers are used in hash functions to reduce collisions
- Mathematics: Fundamental building blocks of number theory
- Nature: Appear in cicada life cycles (13 or 17 year cycles)