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: `36541` is 1 more than `36540` (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 `36541` is `1335244681`. Subtracting 1, we get `1335244680`. Note that `1335244680 ÷ 24 = 55635195`.
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: `36541 = 18271^2 - 18270^2 = 333829441 - 333792900`
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: `36541 = 21^2 + 190^2 = 441 + 36100`, where `36541 = 4 × 9135 + 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: `36541` is of the form `4n+1`, where `n = 9135`.
PORTUGUESE
ENGLISH
SPANISH
FRENCH
GERMAN
CHINESE