It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 503, the answer is: yes, 503 is a prime number because it has only two distinct divisors: 1 and itself (503).
As a consequence, 503 is only a multiple of 1 and 503..
Since 503 is a prime number, 503 is also a deficient number, that is to say 503 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 503 without 503 itself (that is 1, by definition!).
Parity of 503
503 is an odd number, because it is not evenly divisible by 2.
Is 503 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 503 is about 22.428.
Thus, the square root of 503 is not an integer, and therefore 503 is not a square number.
Anyway, 503 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 503?
The square of a number (here 503) is the result of the product of this number (503) by itself (i.e., 503 × 503); the square of 503 is sometimes called "raising 503 to the power 2", or "503 squared".
As a consequence, 503 is the square root of 253 009.
Number of digits of 503
503 is a number with 3 digits.
What are the multiples of 503?
The multiples of 503 are all integers evenly divisible by 503, that is all numbers such that the remainder of the division by 503 is zero. There are infinitely many multiples of 503. The smallest multiples of 503 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 503 too, since 0 × 503 = 0
- 503: indeed, 503 is a multiple of itself, since 503 is evenly divisible by 503 (we have 503 / 503 = 1, so the remainder of this division is indeed zero)
- 1 006: indeed, 1 006 = 503 × 2
- 1 509: indeed, 1 509 = 503 × 3
- 2 012: indeed, 2 012 = 503 × 4
- 2 515: indeed, 2 515 = 503 × 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 503). 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 22.428). 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.