Ria symonds: number 31 is a mersenne prime, but we’re not going to talk about why it’s Mersenne 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 1 just up to 58. OK, now I’m going to use an algorithm that sieves 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 1, and we’re going to get rid of.
Every other one from there on. So 2’s gone, 4’s gone. So all of my even numbers, you can see, are going. These are unlucky 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 3. Because it’s 3, I’m now going to start eliminating every third number. So that’s my first number, 1.
3 is my second number. 5 would be the third number, so we get rid of 5. 1, 2, 3. W get rid of 11. OK, so at the moment, 1 and 3 are both safe. They’re lucky numbers.
We carry on with the algorithm. The next number I need to look at is number 7. So now number 7 tells me how many numbers I need to get rid of, eliminate. I would eliminate every 7th number. So we start from the beginning.
1, 2, 3, 4, 5, 6, 7. 1, 2, 3, 4, 5, 6, 7. We move on to our next number, 9. So I now start eliminating every 9th number. So our first lots of lucky numbers are 1, 3, 7, 9, 13, unlucky for some.
15, 21, 25, and 31, our special number. BRADY HARAN: Tell me something else about 31, can you? RIA SYMONDS: I can. 31 is a pentagonal number. Do you know what that means?.