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: `58441` is 1 more than `58440` (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 `58441` is `3415350481`. Subtracting 1, we get `3415350480`. Note that `3415350480 ÷ 24 = 142306270`.
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: `58441 = 29221^2 - 29220^2 = 853866841 - 853808400`
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: `58441 = 29^2 + 240^2 = 841 + 57600`, where `58441 = 4 × 14610 + 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: `58441` is of the form `4n+1`, where `n = 14610`.
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