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: `95233` is 1 more than `95232` (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 `95233` is `9069324289`. Subtracting 1, we get `9069324288`. Note that `9069324288 ÷ 24 = 377888512`.
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: `95233 = 47617^2 - 47616^2 = 2267378689 - 2267283456`
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: `95233 = 153^2 + 268^2 = 23409 + 71824`, where `95233 = 4 × 23808 + 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: `95233` is of the form `4n+1`, where `n = 23808`.
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