List prime numbers from 1 to 100 with patterns

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Detailed Solution

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

Ends Digits: After 2 and 5, all prime numbers must end in 1, 3, 7, or 9. (Any number ending in 0, 2, 4, 6, 8 is even; any number ending in 0 or 5 is divisible by 5).
The 6k ± 1 Rule: Every prime number greater than 3 can be written in the form 6k - 1 or 6k + 1, where k is any integer.
Example: 11 = (6 × 2) - 1. Example: 13 = (6 × 2) + 1.
Note: This does not work in reverse; not all numbers in this form are prime (e.g., 25 = (6 × 4) + 1, but 25 is not prime).
Twin Primes: You can see pairs of primes that are separated by only 2. These are called "twin primes."
Examples: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).