The same can be said about 35, 85, 745, etc. For example, 125 = 5 × 25, which means that 125 isn’t a prime. Therefore, they are all composite numbers. Any number, different from 5, ending in 5 is not a prime number: First, notice that 5 is prime because neither of 2, 3, and 4 is a proper factor of 5.īesides, 5 is a proper factor of any number ending in 5 and greater than 5.This gives us a huge (infinite) list of non-prime numbers: 4, 6, 8, 10, 12… 4230…, 5668, etc. For example, 872 is not prime because 872 = 2 × 436. Notice that 2 is a proper factor of any even number greater than 2, therefore they are all composite numbers. Any number, different from 2, ending in 0, 2, 4, 6, or 8 is not a prime number: If a number ends in 0, 2, 4, 6, or 8, it is even but, the only even prime number is 2.Here are some rules to determine if a number is prime:
#PRIME NUMBERS LIST HOW TO#
But, don’t worry! In this article, we will only work with small primes that we know how to identify. Making history short, it isn’t an easy job determining if a number is prime. Additionally, prime numbers can be as big as we can imagine, and between two prime numbers may be an enormous amount of composite numbers. First of all, there isn’t a formula to generate all prime numbers. This is a question that mathematicians have tried to answer for centuries. Luckily, we are about to know a property that shortens the list where to look for proper factors of a number. Unfortunately, we cannot be sure of that until we check that enough numbers are not proper factors of our number. Well, the first guess is to think that the number in fact doesn’t have a proper factor, and therefore it is prime. In the previous example, we were lucky to find proper factors for 21 at the beginning of that long list but, what if the number is too big and we don’t find a proper factor quickly? Also, the main procedure to determine if a number is prime is verifying if it has proper factors.
In other words, 21 is not a prime number.Īs we see, the concept of “prime number” is linked to that of “composite number” because any natural number greater than 1 is either prime or composite. Meaning that both 3 and 7 are proper factors of 21, thus 21 is a composite number. We continue with 3, and we notice that 21 = 3 × 7. Since 21 is not even, 2 doesn’t divide 21. But, where do we look for proper factors? In the list: 2, 3, 4, 5, 6, 7, 8, …, 19, 20, of all natural numbers greater than 1, and less than 21. To answer this question, we should verify if 21 has proper factors.
For example, 9 is an odd number, but it can be split into three equal parts of more than one element. We are not claiming that every odd number is a prime number. Contrarily, the prime number 3 can only be split into equal parts, if each part has one element. Number 6 is composed of numbers different from itself, but 3 is not.Īnother way of differentiating a composite number from a prime number is noticing that a composite number can be split into equal parts having more than one element, but a prime number cannot.įor example, 6 can be split into 2 parts with 3 elements each or into 3 parts with 2 elements each, as shown below. The difference between 3 and 6 is like in the image: 3 comes alone to the party, and 6 comes with two of its friends: the proper factors 2 and 3. Number 6, instead, has two proper factors: 2 and 3, because 6 = 2 × 3. Let’s explore more differences between prime and composite numbers.įor example, 3 = 1 × 3 doesn’t have proper factors, because 2 doesn’t divide it: 3 = (2×1) + 1. Thus, 2 doesn’t have proper factors, and it is, therefore, a prime number.Ī composite number is a natural number that has proper factors. For example, the only factors of 2 are 1 and 2. Thus, the proper factors of 8 are 2 and 4.Ī natural number is called a prime number if it is greater than 1, and it doesn’t have proper factors. Moreover, a proper factor of a natural number is a factor that is different from 1 and from the number itself. For example, the factors of 8 are 1, 2, 4, and 8, because 8 = 8 × 1 = 2 × 4. A factor of a natural number is a positive divisor of it.