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: `79757` is 1 less than `79758` (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 `79757` is `6361179049`. Subtracting 1, we get `6361179048`. Note that `6361179048 ÷ 24 = 265049127`.
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: `79757 = 39879^2 - 39878^2 = 1590334641 - 1590254884`
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: `79757 = 86^2 + 269^2 = 7396 + 72361`, where `79757 = 4 × 19939 + 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: `79757` is of the form `4n+1`, where `n = 19939`.
PORTUGUESE
ENGLISH
SPANISH
FRENCH
GERMAN
CHINESE