Is 613 a prime number?

613 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 613 is about 24.759.

Thus, the square root of 613 is not an integer, and therefore 613 is not a square number.

Anyway, 613 is a prime number, and a prime number cannot be a perfect square.

The square of a number (here 613) is the result of the product of this number (613) by itself (i.e., 613 × 613); the square of 613 is sometimes called "raising 613 to the power 2", or "613 squared".

The square of 613 is 375 769 because 613 × 613 = 613² = 375 769.

As a consequence, 613 is the square root of 375 769.

613 is a number with 3 digits.

The multiples of 613 are all integers evenly divisible by 613, that is all numbers such that the remainder of the division by 613 is zero. There are infinitely many multiples of 613. The smallest multiples of 613 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 613 too, since 0 × 613 = 0
• 613: indeed, 613 is a multiple of itself, since 613 is evenly divisible by 613 (we have 613 / 613 = 1, so the remainder of this division is indeed zero)
• 1 226: indeed, 1 226 = 613 × 2
• 1 839: indeed, 1 839 = 613 × 3
• 2 452: indeed, 2 452 = 613 × 4
• 3 065: indeed, 3 065 = 613 × 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 613). 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 24.759). 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: …611, 612
• Following numbers: 614, 615…

Nearest numbers from 613

• Preceding prime number: 607
• Following prime number: 617

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• 613 est-il un nombre premier ?