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: `61819` is 1 more than `61818` (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 `61819` is `3821588761`. Subtracting 1, we get `3821588760`. Note that `3821588760 ÷ 24 = 159232865`.
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: `61819 = 30910^2 - 30909^2 = 955428100 - 955366281`
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: `61819` is of the form `4n-1`, where `n = 15455`.
PORTUGUESE
ENGLISH
SPANISH
FRENCH
GERMAN
CHINESE