This calculator performs the decomposition of a number into its prime factors and lists all its natural divisors. Enter an integer between 1 and 1,000,000.
1) Relation to multiples of 6: Every prime number greater than 3 is always one less or one more than a multiple of 6.
Example: `50333` is 1 less than `50334` (multiple of 6).
2) Square minus 1 divisible by 24: For every prime number greater than 3, if 1 is subtracted from its square, the result is always divisible by 24.
Example: The square of `50333` is `2533410889`. Subtracting 1, we get `2533410888`. Note that `2533410888 ÷ 24 = 105558787`.
3) Difference of squares: Every prime number greater than 2 can be expressed as the difference of the squares of two consecutive natural numbers.
Example: `50333 = 25167^2 - 25166^2 = 633377889 - 633327556`
4) Sum of two squares: Every prime number of the form `4n+1` (where n is a positive natural number) can be expressed as the sum of two squares.
Example: `50333 = 53^2 + 218^2 = 2809 + 47524`, where `50333 = 4 × 12583 + 1`.
5) Form `4n+1` or `4n-1`: Except for the number 2, all prime numbers follow the pattern `4n+1` or `4n-1`, where `n` is a natural number.
Example: `50333` is of the form `4n+1`, where `n = 12583`.
PORTUGUESE
ENGLISH
SPANISH
FRENCH
GERMAN
CHINESE