Is 919 a prime number?

919 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 919 is about 30.315.

Thus, the square root of 919 is not an integer, and therefore 919 is not a square number.

Anyway, 919 is a prime number, and a prime number cannot be a perfect square.

The square of a number (here 919) is the result of the product of this number (919) by itself (i.e., 919 × 919); the square of 919 is sometimes called "raising 919 to the power 2", or "919 squared".

The square of 919 is 844 561 because 919 × 919 = 919² = 844 561.

As a consequence, 919 is the square root of 844 561.

919 is a number with 3 digits.

The multiples of 919 are all integers evenly divisible by 919, that is all numbers such that the remainder of the division by 919 is zero. There are infinitely many multiples of 919. The smallest multiples of 919 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 919 too, since 0 × 919 = 0
• 919: indeed, 919 is a multiple of itself, since 919 is evenly divisible by 919 (we have 919 / 919 = 1, so the remainder of this division is indeed zero)
• 1 838: indeed, 1 838 = 919 × 2
• 2 757: indeed, 2 757 = 919 × 3
• 3 676: indeed, 3 676 = 919 × 4
• 4 595: indeed, 4 595 = 919 × 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 919). 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 30.315). 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: …917, 918
• Following numbers: 920, 921…

Nearest numbers from 919

• Preceding prime number: 911
• Following prime number: 929

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• 919 est-il un nombre premier ?