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: `37223` is 1 less than `37224` (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 `37223` is `1385551729`. Subtracting 1, we get `1385551728`. Note that `1385551728 ÷ 24 = 57731322`.
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: `37223 = 18612^2 - 18611^2 = 346406544 - 346369321`
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: `37223` is of the form `4n-1`, where `n = 9306`.
PORTUGUESE
ENGLISH
SPANISH
FRENCH
GERMAN
CHINESE