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: `81439` is 1 more than `81438` (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 `81439` is `6632310721`. Subtracting 1, we get `6632310720`. Note that `6632310720 ÷ 24 = 276346280`.
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: `81439 = 40720^2 - 40719^2 = 1658118400 - 1658036961`
4) 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: `81439` is of the form `4n-1`, where `n = 20360`.
PORTUGUESE
ENGLISH
SPANISH
FRENCH
GERMAN
CHINESE