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: `67489` is 1 more than `67488` (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 `67489` is `4554765121`. Subtracting 1, we get `4554765120`. Note that `4554765120 ÷ 24 = 189781880`.
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: `67489 = 33745^2 - 33744^2 = 1138725025 - 1138657536`
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: `67489 = 175^2 + 192^2 = 30625 + 36864`, where `67489 = 4 × 16872 + 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: `67489` is of the form `4n+1`, where `n = 16872`.
PORTUGUESE
ENGLISH
SPANISH
FRENCH
GERMAN
CHINESE