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: `39521` is 1 less than `39522` (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 `39521` is `1561909441`. Subtracting 1, we get `1561909440`. Note that `1561909440 ÷ 24 = 65079560`.
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: `39521 = 19761^2 - 19760^2 = 390497121 - 390457600`
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: `39521 = 136^2 + 145^2 = 18496 + 21025`, where `39521 = 4 × 9880 + 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: `39521` is of the form `4n+1`, where `n = 9880`.
PORTUGUESE
ENGLISH
SPANISH
FRENCH
GERMAN
CHINESE