Is 811 a prime number?

811 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 811 is about 28.478.

Thus, the square root of 811 is not an integer, and therefore 811 is not a square number.

Anyway, 811 is a prime number, and a prime number cannot be a perfect square.

The square of a number (here 811) is the result of the product of this number (811) by itself (i.e., 811 × 811); the square of 811 is sometimes called "raising 811 to the power 2", or "811 squared".

The square of 811 is 657 721 because 811 × 811 = 811² = 657 721.

As a consequence, 811 is the square root of 657 721.

811 is a number with 3 digits.

The multiples of 811 are all integers evenly divisible by 811, that is all numbers such that the remainder of the division by 811 is zero. There are infinitely many multiples of 811. The smallest multiples of 811 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 811 too, since 0 × 811 = 0
• 811: indeed, 811 is a multiple of itself, since 811 is evenly divisible by 811 (we have 811 / 811 = 1, so the remainder of this division is indeed zero)
• 1 622: indeed, 1 622 = 811 × 2
• 2 433: indeed, 2 433 = 811 × 3
• 3 244: indeed, 3 244 = 811 × 4
• 4 055: indeed, 4 055 = 811 × 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 811). 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 28.478). 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: …809, 810
• Following numbers: 812, 813…

Nearest numbers from 811

• Preceding prime number: 809
• Following prime number: 821

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• 811 est-il un nombre premier ?