Is 1000 a prime number?

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 1000, the answer is: No, 1000 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 1000) is as follows: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.

For 1000 to be a prime number, it would have been required that 1000 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 1 000 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 1 000 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

1000 is a multiple of 1
1000 is a multiple of 2
1000 is a multiple of 4
1000 is a multiple of 5
1000 is a multiple of 8
1000 is a multiple of 10
1000 is a multiple of 20
1000 is a multiple of 25
1000 is a multiple of 40
1000 is a multiple of 50
1000 is a multiple of 100
1000 is a multiple of 125
1000 is a multiple of 200
1000 is a multiple of 250
1000 is a multiple of 500

For 1000 to be a prime number, it would have been required that 1000 has only two divisors, i.e., itself and 1.

Is 1000 a deficient number?

No, 1000 is not a deficient number: to be deficient, 1000 should have been such that 1000 is larger than the sum of its proper divisors, i.e., the divisors of 1000 without 1000 itself (that is 1 + 2 + 4 + 5 + 8 + 10 + 20 + 25 + 40 + 50 + 100 + 125 + 200 + 250 + 500 = 1 340).

In fact, 1000 is an abundant number; 1000 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 8 + 10 + 20 + 25 + 40 + 50 + 100 + 125 + 200 + 250 + 500 = 1 340). The smallest abundant number is 12.

Parity of 1000

1000 is an even number, because it is evenly divisible by 2: 1000 / 2 = 500.

Find out more:

What is an even number?

Is 1000 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 1000 is about 31.623.

Thus, the square root of 1000 is not an integer, and therefore 1000 is not a square number.

What is the square number of 1000?

The square of a number (here 1000) is the result of the product of this number (1000) by itself (i.e., 1000 × 1000); the square of 1000 is sometimes called "raising 1000 to the power 2", or "1000 squared".

The square of 1000 is 1 000 000 because 1000 × 1000 = 1000² = 1 000 000.

As a consequence, 1000 is the square root of 1 000 000.

Number of digits of 1 000

1 000 is a number with 4 digits.

What are the multiples of 1 000?

The multiples of 1 000 are all integers evenly divisible by 1 000, that is all numbers such that the remainder of the division by 1 000 is zero. There are infinitely many multiples of 1 000. The smallest multiples of 1 000 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 1 000 too, since 0 × 1 000 = 0
1 000: indeed, 1 000 is a multiple of itself, since 1 000 is evenly divisible by 1 000 (we have 1 000 / 1 000 = 1, so the remainder of this division is indeed zero)
2 000: indeed, 2 000 = 1 000 × 2
3 000: indeed, 3 000 = 1 000 × 3
4 000: indeed, 4 000 = 1 000 × 4
5 000: indeed, 5 000 = 1 000 × 5
etc.

How to determine whether an integer is a prime number?

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 1000). 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 31.623). 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.

Numbers near 1000

Preceding numbers: …998, 999
Following numbers: 1 001, 1 002…

Nearest numbers from 1000

Preceding prime number: 997
Following prime number: 1 009