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: `99689` is 1 less than `99690` (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 `99689` is `9937896721`. Subtracting 1, we get `9937896720`. Note that `9937896720 ÷ 24 = 414079030`.
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: `99689 = 49845^2 - 49844^2 = 2484524025 - 2484424336`
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: `99689 = 140^2 + 283^2 = 19600 + 80089`, where `99689 = 4 × 24922 + 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: `99689` is of the form `4n+1`, where `n = 24922`.
PORTUGUESE
ENGLISH
SPANISH
FRENCH
GERMAN
CHINESE