What is a lucky number? - Numberphile

number 31 is a meran prime but we're not going to talk about why it's messian today we're going to look at why it's a truly lucky number I'm going to start off with a whole bunch of numbers to begin with I've listed the numbers one just up to 58 okay now I'm going to use an algorithm that cves out my numbers to ensure that I only get lucky numbers so to begin with I'm going to eliminate every other number from my list so I start with number one and I'm going to get rid of every other one from there on so two's gone Four's gone so all of my even numbers you can see are going these are UNL looking in terms of my mathematical algorithm now I'm going to start eliminating more numbers by going on to the next step of my algorithm now a second iteration so I look at the second number in the terms that I've got left so my second number is three because it's three I'm now going to start eliminating every third number so that's my first number one three is my second number five will be the third number so we get rid of five one 2 3 we get rid of 11 okay so at the moment one and three are both safe they're lucky numbers we carry on with the algorithm the next one I need to look at is number seven so now number seven tells me how many numbers I need to get rid of eliminate eliminate every seventh number so we start from the beginning 1 2 3 4 5 6 7 one 2 3 4 five 6 7 we move on to our next number nine so I now start eliminating every ninth number so our first lots of looking numbers are 1 3 7 9 13 I'm looking for sum 15 21 25 and 31 our special number tell me something else about 31 can you I can 31 is a pentagonal number do you know what that means 26 27 28 29 30 31 so on the fourth iteration we get our pentagonal number 31 I've realized what your Pentagon so very it's cuz I'm making you draw yeah from my perspective it looks kind of okay don't tip it if I slightly turn this board around is it looking any better yeah I can see what why you've done it now oh the beauty of maths