What is a Prime Number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The fundamental theorem of arithmetic states that every natural number greater than 1 is either a prime number or can be uniquely represented as a product of prime numbers.
Core Definitions
Prime
Numbers with exactly 2 factors. (e.g., 2, 3, 5, 7, 11, 13...)
Composite
Numbers with more than 2 factors. (e.g., 4, 6, 8, 9, 10, 12...)
Sieve of Eratosthenes
One of the most efficient ways to find all primes up to a specific limit. The process involves:
1
List all numbers from 2 up to your limit.
2
Start with 2, mark all its multiples as not prime.
3
Move to the next unmarked number (3) and mark its multiples.
4
Repeat until the square of the current number exceeds the limit.
First 50 Prime Numbers Reference
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