The number 161 can be computer using 7 x 23 (both prime numbers), while the number 5476 can be calculated using 2 x 2 x 37 x 37 (again, all prime numbers). To give you an example, the number 12 can be expressed using 2 x 2 x 3 = 12 (2 and 3 are both prime numbers). The most interesting reason being that the entire number line (1 to infinity) can be created only using prime numbers. Prime numbers are important for several reasons. There are multiple methods for finding and testing prime numbers which we’ll share below. Is the sum of the number’s digits a multiple 3? 5 + 0 + 9 = 14, which is not a multiple of 3, so it could still be a prime number.Īlthough it is likely that 509 is a prime number, you would have to do more testing to ensure that is the case. Does the number end in a 5 or a 0? No, so it could still be a prime number. Is the number even? No, so it could still be a prime number. For example, if you were trying to determine if 509 was a prime number, you could check: The prime number characteristics give us a basic process for finding them. However, the higher you count, the less common they become. This might fool you into thinking that prime numbers are extremely common. If you count from 1 to 100, you will come across 25 prime numbers. This rule also means that numbers ending in 0 will never be prime, as they can also be divided by 5 or 10. That means you can immediately rule out large numbers like 1,089,385 as potential prime numbers. Any number ending in a 5 (other than 5) will be divisible by 5 and therefore cannot be a prime number. This is another rule which makes identifying prime numbers easier. No prime number greater than 5 ends in a 5 We can confirm this fact by dividing 945,327 by 3, which gives us 315,108.Ĥ. 30 is divisible by 3 which tells us it is not prime. By adding 9 + 4 + 5 + 3 + 2 + 7 you would get 30. Let’s say you wanted to check if 945,327 was a prime number. This technique lets us analyse large numbers very quickly to determine if they are prime. This rules tells us that it will not be a prime number, and we can confirm that by calculating 261 / 3, which equals 24. To give you an example, if you add the digits contained within 261, you would get 9 (2 + 6 + 1 = 9) - which is divisible by 3. This characteristic helps us eliminate potential prime number candidates. If the sum of a number’s digits is a multiple 3 it is not a prime number If mathematicians considered these numbers prime, then there would be no other prime numbers, as all whole numbers are divisible by 1. This fact immediately halves the number of potential prime numbers that are available. That’s because every other even number can be divided by 2, which makes them composite numbers. Prime numbers have certain characteristics which make them easier to identify, including: 1. They can always be formed by multiplying two smaller natural numbers. Non-prime natural numbers like 6 are called composite numbers. 6 can also be created by multiplying two smaller natural numbers (3 x 2 = 6).
Is 6 a positive natural number that is only evenly divisible by one and itself? No, because 6 can be divided by 2 (6/2 = 3) or 3 (6 / 3 = 2) and return natural numbers. Let’s take a look at a non-prime number to make sure you understand the difference. It cannot be created by multiplying 2, 3, or 4 with any other number. So, if we take another look at 5, you would notice that it can only be created by multiplying 1 x 5. A divisor is a number that divides evenly into another number without a remainder (other than 1 or the number itself).Īnother way of describing prime numbers is that they are numbers which cannot be formed by multiplying two smaller natural numbers. If 5 is divided by 2 or 3, you would end up with a fraction (2.5 and 1.6666667 respectively). The number 5 is a prime number because it can only be divided by one (5 / 1 = 5) or itself (5 / 5 = 1) and remain a natural number. This includes numbers like 3, 4, 7, 10, 1000, and 165738.Ī prime number is any positive natural number that is only evenly divisible by one and itself. A natural number refers to any positive integer that does not have a fraction attached to it. To understand what a prime number is, you will need to learn what a “natural number” is.
I’ll explain what prime numbers are, why prime numbers are important, and how to identify prime numbers. In this guide, I’m going to delve into the world of prime numbers. They are whole numbers with unique characteristics that make them useful for certain types of mathematical calculations.
Prime numbers are one of the most well-known ideas in mathematics. Mathematics is a fascinating field of study with many interesting concepts, patterns, theories, and innovative ways of thinking about the world.