It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 509, the answer is: yes, 509 is a prime number because it has only two distinct divisors: 1 and itself (509).
As a consequence, 509 is only a multiple of 1 and 509..
Since 509 is a prime number, 509 is also a deficient number, that is to say 509 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 509 without 509 itself (that is 1, by definition!).
Parity of 509
509 is an odd number, because it is not evenly divisible by 2.
Is 509 a perfect square number?
A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 509 is about 22.561.
Thus, the square root of 509 is not an integer, and therefore 509 is not a square number.
Anyway, 509 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 509?
The square of a number (here 509) is the result of the product of this number (509) by itself (i.e., 509 × 509); the square of 509 is sometimes called "raising 509 to the power 2", or "509 squared".
As a consequence, 509 is the square root of 259 081.
Number of digits of 509
509 is a number with 3 digits.
What are the multiples of 509?
The multiples of 509 are all integers evenly divisible by 509, that is all numbers such that the remainder of the division by 509 is zero. There are infinitely many multiples of 509. The smallest multiples of 509 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 509 too, since 0 × 509 = 0
- 509: indeed, 509 is a multiple of itself, since 509 is evenly divisible by 509 (we have 509 / 509 = 1, so the remainder of this division is indeed zero)
- 1 018: indeed, 1 018 = 509 × 2
- 1 527: indeed, 1 527 = 509 × 3
- 2 036: indeed, 2 036 = 509 × 4
- 2 545: indeed, 2 545 = 509 × 5
How to determine whether an integer is a prime number?
To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 509). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is about 22.561). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.
More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.