Yes, 2 is a prime number.
Indeed, the definition of a prime numbers is to have only two distinct positive divisors, 1 and itself. A number is a divisor of another number when the remainder of Euclid’s division of the second one by the first one is zero. Concerning the number 2, the only two divisors are 1 and 2. Therefore 2 is a prime number.
The number 2 features several interesting properties:
- 2 is the smallest prime number
- 2 is the only even prime number
Parity of 2
2 is of course an even number (note that two is the only even prime number).
Is 2 a perfect square 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 2 is 1,414 (approximée à 3 chiffres après la virgule).
Thus, the square root of 2 is not an integer, and therefore 2 is not a square number.
What is the square number of 2?
The square of a number (here 2) is the result of the product of this number (2) by itself (i.e., 2 × 2); the square of 2 is sometimes called "raising 2 to the power 2", or "2 squared".
As a consequence, 2 is the square root of 4.
What are the multiples of 2?
All even integers are multiples of 2. Indeed, a number is a multiple of 2 if and only if it is evenly divisible by 2, which corresponds exactly to the definition of even numbers. Therefore, there are infinitely many multiples of 2. The smallest multiples of 2 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 2 too, since 0 × 2 = 0
- 2: indeed, 2 is a multiple of itself, since 2 is evenly divisible by 2 (we have 2 / 2 = 1, so the remainder of this division is indeed zero)
- 4 (which is also the square of 2)
Number of digits of 2
2 is a single-digit number, because it is strictly less than 10; 2 is in fact itself a digit.
How to determine whether an integer is a prime number?
To determine the primality of a number, i.e., know whether it is a prime 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. First, we can eliminate all even numbers greater than 2. Then, we can stop this check when we reach the square root of the number of which we want to determine the primality. 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.