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: `78593` is 1 less than `78594` (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 `78593` is `6176859649`. Subtracting 1, we get `6176859648`. Note that `6176859648 ÷ 24 = 257369152`.
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: `78593 = 39297^2 - 39296^2 = 1544254209 - 1544175616`
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: `78593 = 112^2 + 257^2 = 12544 + 66049`, where `78593 = 4 × 19648 + 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: `78593` is of the form `4n+1`, where `n = 19648`.
PORTUGUESE
ENGLISH
SPANISH
FRENCH
GERMAN
CHINESE