1 00:00:00,330 --> 00:00:07,950 All right, so in the next coding exercise, we're going to be building a prime number checker. And a 2 00:00:07,950 --> 00:00:15,030 prime number, just to remind you, is a number that is only divisible by one and itself. 3 00:00:15,720 --> 00:00:22,350 So, for example, two is a prime number because it can only be divided by one and two. 4 00:00:23,010 --> 00:00:24,600 Three is also a prime number, 5 00:00:24,630 --> 00:00:29,100 similarly, it can only be split into three equal sized chunks. 6 00:00:29,550 --> 00:00:35,700 But four, however, is not a prime number because while it can be divided by one and four, it can 7 00:00:35,700 --> 00:00:37,350 also be divided by two. 8 00:00:37,620 --> 00:00:44,100 So two times two is four. Essentially a prime number is a number that can't be broken to smaller 9 00:00:44,100 --> 00:00:46,230 parts other than one and itself. 10 00:00:46,950 --> 00:00:54,240 And it's this property of prime numbers that makes them really useful to everything from cicadas to 11 00:00:54,240 --> 00:00:58,440 Bitcoin and also encryption in the computer world. 12 00:00:59,280 --> 00:01:05,820 So if you head over to day 8.2 prime number checker, you'll see the starting code including 13 00:01:05,820 --> 00:01:08,840 the number that we're going to be sending over and checking. 14 00:01:09,270 --> 00:01:16,200 And then, of course, the line eleven where we actually call this function and pass over the number. So 15 00:01:16,320 --> 00:01:19,960 this part is really important when you are creating your function. 16 00:01:20,610 --> 00:01:26,370 The idea is that you're going to be creating a function here that checks whether if the number that's 17 00:01:26,370 --> 00:01:29,930 passed in is a prime number or not. 18 00:01:30,450 --> 00:01:36,180 And if you take a look at this chart, then you'll see all the prime numbers up to 100 highlighted in 19 00:01:36,180 --> 00:01:36,640 yellow. 20 00:01:37,440 --> 00:01:39,410 There's a couple of things you need to remember. 21 00:01:39,600 --> 00:01:44,120 One is that you'll probably need to use the modulus, which we've seen before. 22 00:01:44,670 --> 00:01:49,090 And if you can't remember how to use that, then take a look at this link. 23 00:01:49,710 --> 00:01:54,900 Now, the second thing is that make sure that you name your function and parameters the same as what 24 00:01:54,900 --> 00:01:57,390 you see here where it's called. 25 00:01:58,020 --> 00:02:05,040 And finally, try to use the same wording as the example outputs, namely, if it is a prime number print 26 00:02:05,490 --> 00:02:08,430 "It's a prime number." in this exact wording. 27 00:02:08,760 --> 00:02:14,310 And if it's not a prime number, then print "It's not a prime number." with this exact wording. 28 00:02:15,360 --> 00:02:21,150 And finally, if you're still not quite sure how prime numbers work, then be sure to check out the 29 00:02:21,150 --> 00:02:22,200 Wikipedia page. 30 00:02:22,470 --> 00:02:29,340 And if your first language is not English, then be sure to switch to your native language just to know 31 00:02:29,610 --> 00:02:33,480 what it is because I know it's called different things in different languages. 32 00:02:34,920 --> 00:02:35,910 Pause the video, 33 00:02:36,180 --> 00:02:40,890 have a good think about this and see if you can solve this problem. 34 00:02:44,690 --> 00:02:48,920 All right, so let's think about how we might tackle this. The first thing I'm going to do is I'm going 35 00:02:48,920 --> 00:02:54,950 to create a new function called prime_checker to be in line with this line, because I'm calling a 36 00:02:54,950 --> 00:02:56,270 function called prime_checker 37 00:02:56,660 --> 00:03:00,800 and then I'm passing in an argument to the parameter called number. 38 00:03:01,430 --> 00:03:06,740 So now that we've created our function, the next step is to figure out, well, what do we do in this 39 00:03:06,740 --> 00:03:07,190 function? 40 00:03:07,730 --> 00:03:14,840 Now, I mentioned that every prime number can only be cleanly divided by itself and one. 41 00:03:15,290 --> 00:03:21,540 So that means that if it's divided by any other number other than these, it will have a remainder. 42 00:03:22,100 --> 00:03:28,360 So we know that we can use the modulus to check what the remainder is of a division. 43 00:03:28,910 --> 00:03:37,910 So we know that, for example, if we divide six by two, then it equals three with no remainder because 44 00:03:37,910 --> 00:03:44,750 six is divided into two three times, while seven divided by two equals one because there's a remainder 45 00:03:44,750 --> 00:03:50,320 of one, because two times three is six and then six plus one makes seven. 46 00:03:51,080 --> 00:04:00,020 So we can use the modulus to check whether if the number that we're passing in here can be divided by 47 00:04:00,050 --> 00:04:02,610 all the numbers all the way down to two. 48 00:04:03,410 --> 00:04:11,570 So, for example, if number was equal to seven, well, then what we would want to do is we would want 49 00:04:11,570 --> 00:04:20,450 to do seven divided by two and then see if there is any remainder, and then seven divided by three and 50 00:04:20,450 --> 00:04:25,480 see if there was any remainder, and then seven divided by four... 51 00:04:25,520 --> 00:04:30,740 and then we just go up two, three, four, five, and six. 52 00:04:31,040 --> 00:04:37,740 And now we've basically divided seven by all the possible values other than one and seven. 53 00:04:38,510 --> 00:04:45,470 So if any of these has zero as the remainder, then it means that it does cleanly divide by one of these 54 00:04:45,470 --> 00:04:48,440 numbers, which means that it's actually not a prime number. 55 00:04:49,550 --> 00:04:57,230 But if all of these have a remainder, then that means seven is a prime number, which we already know 56 00:04:57,230 --> 00:04:59,260 it is because we can see it on this graph. 57 00:04:59,720 --> 00:05:07,220 So how can we go through this process of getting this number divided by numbers starting from two 58 00:05:07,220 --> 00:05:11,030 all the way going up to the number minus one? 59 00:05:11,270 --> 00:05:14,380 Well, we could simply just use a for loop, right? 60 00:05:14,780 --> 00:05:22,700 So we create a for loop and say for i which is going to be this number that we're going to divide 61 00:05:22,700 --> 00:05:24,440 by, in, 62 00:05:24,890 --> 00:05:28,760 and that number is going to be a range of numbers. 63 00:05:28,910 --> 00:05:33,470 And the range starts from two because we're not going to divide it by one. 64 00:05:33,470 --> 00:05:39,680 We already know that all numbers can be divided by one. And we're going to put the range all the way 65 00:05:39,680 --> 00:05:41,520 up to the number. 66 00:05:42,350 --> 00:05:48,380 So now inside this for loop, we can start doing our divisions. So we could take the number and we can 67 00:05:48,380 --> 00:05:51,740 use the modulo operator to divide it by i. 68 00:05:52,220 --> 00:06:00,580 So it's exactly the same as each of these lines of division. If number divided by i is equal to zero, 69 00:06:00,590 --> 00:06:06,350 so if it divides cleanly, well, then in this case, it's clearly not a prime, 70 00:06:06,350 --> 00:06:14,720 right? Because if that number that we get passed in can be divided by any of the numbers between two 71 00:06:14,720 --> 00:06:21,600 and number minus one cleanly with no remainder, then that means it's not a prime number. 72 00:06:22,220 --> 00:06:30,950 However, if we get to the very end of our for loop and this if statement was never triggered, well, 73 00:06:30,950 --> 00:06:33,650 then that means this is a prime number. 74 00:06:34,910 --> 00:06:37,820 So how can we represent this with our code? 75 00:06:38,420 --> 00:06:43,900 Well, we could create a variable called is_prime and set it to true. 76 00:06:44,540 --> 00:06:48,510 If this if statement gets triggered, then we switch 77 00:06:48,530 --> 00:06:51,000 this is_prime to false. 78 00:06:51,560 --> 00:06:55,980 And finally, once we get to the end of the for loop, we can go ahead and check 79 00:06:56,000 --> 00:07:00,400 well, is is_prime true or is it false? 80 00:07:00,920 --> 00:07:07,370 And this expression is basically the same as just typing this because this is going to be true or false. 81 00:07:07,550 --> 00:07:15,020 And if it's true, then we get to step into this block and we're going to print from this example output 82 00:07:15,020 --> 00:07:23,090 and say that it is a prime number. But else or otherwise, then we're going to print the opposite 83 00:07:23,280 --> 00:07:26,360 where we say it's not a prime number. 84 00:07:27,870 --> 00:07:28,630 There you have it. 85 00:07:28,650 --> 00:07:38,040 This is the simplest way of checking whether if a number is a prime number. And all it does is it checks 86 00:07:38,040 --> 00:07:41,790 through all of the numbers between two and the number. 87 00:07:42,120 --> 00:07:47,220 And if it's divisible by any of those numbers, well, then it's not a prime. 88 00:07:48,000 --> 00:07:54,420 Now, out there in the real world, there's a lot of other ways that you could implement this function. 89 00:07:54,900 --> 00:08:00,570 And there's more efficient ways, there's faster ways and there's lots of algorithms that mathematicians 90 00:08:00,570 --> 00:08:04,350 have come up with in the past. Now for our case, 91 00:08:04,530 --> 00:08:12,030 what I'm really interested in is that you understand how inputs work and how you can use the argument 92 00:08:12,030 --> 00:08:18,420 that's passed in to the parameter inside your function in order to do something with it. 93 00:08:18,960 --> 00:08:24,780 As long as that's clear to you, then that means we can continue in the course and I can rely on the 94 00:08:24,780 --> 00:08:31,050 fact that this code or this code will not throw you off and you'll know exactly what's going on when 95 00:08:31,050 --> 00:08:38,100 it's being used inside the block of code and when it's being passed over into a block of code. 96 00:08:38,700 --> 00:08:43,980 In the next lesson, we're going to be putting all of our knowledge that we learned into practice and 97 00:08:43,980 --> 00:08:48,100 we're going to get started building our final project, the Caesar cipher. 98 00:08:48,390 --> 00:08:50,550 So for all of that and more, 99 00:08:50,580 --> 00:08:51,270 I'll see you there.