Is 509 a prime number?

509 is an odd number, because it is not evenly divisible by 2.

Find out more:

• What is an even 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.

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".

The square of 509 is 259 081 because 509 × 509 = 509² = 259 081.

As a consequence, 509 is the square root of 259 081.

509 is a number with 3 digits.

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
• etc.

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.

• Preceding numbers: …507, 508
• Following numbers: 510, 511…

Nearest numbers from 509

• Preceding prime number: 503
• Following prime number: 521

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• 509 est-il un nombre premier ?