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: `70753` is 1 more than `70752` (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 `70753` is `5005987009`. Subtracting 1, we get `5005987008`. Note that `5005987008 ÷ 24 = 208582792`.
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: `70753 = 35377^2 - 35376^2 = 1251532129 - 1251461376`
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: `70753 = 137^2 + 228^2 = 18769 + 51984`, where `70753 = 4 × 17688 + 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: `70753` is of the form `4n+1`, where `n = 17688`.
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