Is 317 a prime number?

317 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 317 is about 17.804.

Thus, the square root of 317 is not an integer, and therefore 317 is not a square number.

Anyway, 317 is a prime number, and a prime number cannot be a perfect square.

The square of a number (here 317) is the result of the product of this number (317) by itself (i.e., 317 × 317); the square of 317 is sometimes called "raising 317 to the power 2", or "317 squared".

The square of 317 is 100 489 because 317 × 317 = 317² = 100 489.

As a consequence, 317 is the square root of 100 489.

317 is a number with 3 digits.

The multiples of 317 are all integers evenly divisible by 317, that is all numbers such that the remainder of the division by 317 is zero. There are infinitely many multiples of 317. The smallest multiples of 317 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 317 too, since 0 × 317 = 0
• 317: indeed, 317 is a multiple of itself, since 317 is evenly divisible by 317 (we have 317 / 317 = 1, so the remainder of this division is indeed zero)
• 634: indeed, 634 = 317 × 2
• 951: indeed, 951 = 317 × 3
• 1 268: indeed, 1 268 = 317 × 4
• 1 585: indeed, 1 585 = 317 × 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 317). 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 17.804). 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.

• Preceding numbers: …315, 316
• Following numbers: 318, 319…

Nearest numbers from 317

• Preceding prime number: 313
• Following prime number: 331

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• 317 est-il un nombre premier ?