- Every number in the world is a prime number or a product of prime numbers.
- 0 and 1 are not considered as prime numbers.
- 2 is the smallest prime number.
- The largest prime number known has around 13 million digits.
- All the prime numbers are odd numbers except 2, which is an even prime number.
- There is only one prime number with 5 in its one’s place. Except 5 no other prime number ends with 5 in its one’s place.
- Except 2 and 5, all prime numbers end with 1, 3, 7 or 9.
- No two prime numbers end with the same final digit in one’s place.
- Every positive number greater than 1 can be expressed uniquely as a product of two or more prime numbers.
- Every even positive integer can be expressed as a sum of two prime numbers.
- There is no uniformity in the pattern to show which numbers are prime and how far they are from each other.
- There are total nine two-digit prime numbers, which after reversing the digits, remain prime. These are:- 11, 13, 17, 31, 37, 71, 73, 79 and 97.
- Every prime number greater than 3, is always either predecessor or successor of a multiple of 6. It means every prime number is either 1 less than or 1 more than a multiple of 6. For example:- 5 is 1 less than 6. 19 is 1 more than 6. 71 is 1 less than 72.
- For every prime number greater than 3, if 1 is subtracted from the square of the prime number, the resulting number is always completely divisible by 24. For example:- Square of 5 is 25. 25-1=24. Square of 73 is 5329. 5329-1= 5328. 222 times 24 is 5328.
- Any prime number greater than 2 is the difference of the squares of two positive integers. For example:- 3 is the difference of squares 2 and 1 (4-1=3). 5 is the difference of squares of 3 and 2 (9-4=5). 19 is the difference of squares of 10 and 9 (100-81=19).
- For every prime number of the form 4n+1 (where n is a positive natural number), can be expressed as a sum of two squares. For example:- 13 (4 × 3 + 1) is the sum of square of 2 and 3, i.e. 4 + 9 = 13. 17 (4 × 4 + 1) is the sum of squares of 1 and 4, i.e. 1 + 16 = 17. 29 (4 × 7 + 1) is the sum of squares of 2 and 5, i.e. 4 + 25 = 29.
- Except two and three, all other prime numbers exist in the form of either 6n+1 or 6n-1. Where n is a natural number. For example:- 5 = 6-1, 7 = 6+1, 11 = 6 × 2 – 1, 13 = 6 × 2 + 1. Point to be noted here is not all the numbers of the form (6n+1 OR 6n-1) is a prime number, but all the numbers greater than 3 are of the form (6n+1 or 6n-1).
- Except two, rest all prime numbers follow the pattern of either 4n+1 or 4n-1, where n is a natural number.
- For every number greater than 1, there exists at least one prime number between the number and its double.
- For every number greater than 1, between the number and its square, there exists at least one prime number.
- A prime number always exists between squares of two consecutive natural numbers.
- 12345678910987654321 is an amazing 20-digit prime number. Look at this number. It is just the natural number up to 10, written in the increasing and then in decreasing order. So, cool and easy to remember.
- There are total 25 prime numbers from 1 – 100.
- There are total 21 prime numbers from 100 – 200.
- There are total 16 prime numbers from 200 – 300.
- There are total 16 prime numbers from 300 – 400.
- There are total 17 prime numbers from 400 – 500.
- There are total 168 prime numbers from 1 – 1000.
- There are total 1229 prime numbers from 1 – 10000.
