It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 521, the answer is: yes, 521 is a prime number because it has only two distinct divisors: 1 and itself (521).
As a consequence, 521 is only a multiple of 1 and 521..
Since 521 is a prime number, 521 is also a deficient number, that is to say 521 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 521 without 521 itself (that is 1, by definition!).
Parity of 521
521 is an odd number, because it is not evenly divisible by 2.
Is 521 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 521 is about 22.825.
Thus, the square root of 521 is not an integer, and therefore 521 is not a square number.
Anyway, 521 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 521?
The square of a number (here 521) is the result of the product of this number (521) by itself (i.e., 521 × 521); the square of 521 is sometimes called "raising 521 to the power 2", or "521 squared".
As a consequence, 521 is the square root of 271 441.
Number of digits of 521
521 is a number with 3 digits.
What are the multiples of 521?
The multiples of 521 are all integers evenly divisible by 521, that is all numbers such that the remainder of the division by 521 is zero. There are infinitely many multiples of 521. The smallest multiples of 521 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 521 too, since 0 × 521 = 0
- 521: indeed, 521 is a multiple of itself, since 521 is evenly divisible by 521 (we have 521 / 521 = 1, so the remainder of this division is indeed zero)
- 1 042: indeed, 1 042 = 521 × 2
- 1 563: indeed, 1 563 = 521 × 3
- 2 084: indeed, 2 084 = 521 × 4
- 2 605: indeed, 2 605 = 521 × 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 521). 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 22.825). 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.