Is 520 a prime number?

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 520, the answer is: No, 520 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 520) is as follows: 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520.

For 520 to be a prime number, it would have been required that 520 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 520 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 520 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

520 is a multiple of 1
520 is a multiple of 2
520 is a multiple of 4
520 is a multiple of 5
520 is a multiple of 8
520 is a multiple of 10
520 is a multiple of 13
520 is a multiple of 20
520 is a multiple of 26
520 is a multiple of 40
520 is a multiple of 52
520 is a multiple of 65
520 is a multiple of 104
520 is a multiple of 130
520 is a multiple of 260

For 520 to be a prime number, it would have been required that 520 has only two divisors, i.e., itself and 1.

Is 520 a deficient number?

No, 520 is not a deficient number: to be deficient, 520 should have been such that 520 is larger than the sum of its proper divisors, i.e., the divisors of 520 without 520 itself (that is 1 + 2 + 4 + 5 + 8 + 10 + 13 + 20 + 26 + 40 + 52 + 65 + 104 + 130 + 260 = 740).

In fact, 520 is an abundant number; 520 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 8 + 10 + 13 + 20 + 26 + 40 + 52 + 65 + 104 + 130 + 260 = 740). The smallest abundant number is 12.

Parity of 520

520 is an even number, because it is evenly divisible by 2: 520 / 2 = 260.

Find out more:

What is an even number?

Is 520 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 520 is about 22.804.

Thus, the square root of 520 is not an integer, and therefore 520 is not a square number.

What is the square number of 520?

The square of a number (here 520) is the result of the product of this number (520) by itself (i.e., 520 × 520); the square of 520 is sometimes called "raising 520 to the power 2", or "520 squared".

The square of 520 is 270 400 because 520 × 520 = 520² = 270 400.

As a consequence, 520 is the square root of 270 400.

Number of digits of 520

520 is a number with 3 digits.

What are the multiples of 520?

The multiples of 520 are all integers evenly divisible by 520, that is all numbers such that the remainder of the division by 520 is zero. There are infinitely many multiples of 520. The smallest multiples of 520 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 520 too, since 0 × 520 = 0
520: indeed, 520 is a multiple of itself, since 520 is evenly divisible by 520 (we have 520 / 520 = 1, so the remainder of this division is indeed zero)
1 040: indeed, 1 040 = 520 × 2
1 560: indeed, 1 560 = 520 × 3
2 080: indeed, 2 080 = 520 × 4
2 600: indeed, 2 600 = 520 × 5
etc.

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 520). 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 22.804). 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.

Numbers near 520

Preceding numbers: …518, 519
Following numbers: 521, 522…

Nearest numbers from 520

Preceding prime number: 509
Following prime number: 521