![]() ![]() Now you could go ahead and try 6, 7, 8, and so on. But we aren’t looking for the best possible way to accomplish the task we just want Leah to experience what primes are – and maybe discover more about them by doing things that aren’t necessary. Why? Because if a number can be divided evenly by 4, then it would have already have been found to be divisible by 2. One way to improve efficiency would be to try only prime divisors, so we’d skip 4. If you try 3, that doesn't come out even either. If you try dividing it by 2, it doesn't come out even. If this ever comes out even, then your number isn't prime. To see if a number is prime, all you need to do is try the numbers smaller than it and bigger than 1 and divide them into your number. We can directly use it to find primes (though not very efficiently). This version of the definition is less formal, but gives the main idea well. But 3 is a prime number, because the only smaller numbers are 1 and 2, and 3 is not 1 times 1 or 1 times 2 or 2 times 2. For example, 14 is not a prime number, because it is 2 times 7. In fact, if you understand that, you should be able to do this problem without any difficulty.Ī prime number is a whole number which is not the product of smaller numbers. What are the prime numbers 20 through 30? My mom can't help me.ĭoctor Wilkinson answered, starting with the basics: First of all, you need to be sure you understand what prime numbers are. Here is a 1997 question: Prime Numbers: 20-30 ![]() Even here, you can see runs of nearly consecutive primes, and gaps with none. The farther out you look, the more random they appear. Here are all the primes listed above, namely those less than 200: One important feature of prime numbers is that they are hard to predict, and seem almost random – yet they are definitely not! Here are the primes less than 100 on a number line: Without it, you could take “has two factors, 1 and itself” as being true for 1, since 1 and itself are both factors and there is no other. This is where the word “exactly” comes in. Prime numbers have EXACTLY two factors, not "at most two" or anything like that. ![]() So we say that 29 is a prime number, but 28 isn't.Īs we’ll be seeing in the next two weeks, there are many ways to misstate this definition every word in the definition matters! Note that the definition of a prime number doesn't allow 1 to be a prime number: 1 only has one factor, namely 1. If we list the factors of 29, we only have 1 and 29. For example, if we list the factors of 28, we have 1, 2, 4, 7, 14, and 28. We’ll start with an anonymous question from 1995: Prime Numbersĭoctor Ken answered with the definition and a pair of examples: Hello!Ī prime number is a positive number that has exactly two factors, 1 and itself. I’ll begin a short series of posts on prime numbers with several questions on the basics: What are prime (and composite) numbers, and why do they matter?
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