For some reason the silly dialogues between Bret and Heather on their Dark Horse Podcast about prime numbers inspire me to think about such things which normally I wouldn't. Ive done a few blog posts about them already, and managed to flub up one that I've never gone back to correct. But anyway, since this week they are going on and on about the subject on their nonprime nmber e episode 157 which is a prime number, I thought I'd try to explain what I think is the best way to figure out whether a number is prime or not according to my own stumblings around on the topic.
You look at the last ndigit in the number, No matter who large the number that last digit is the key to whether it is prime or not. If it's an even number you know it is not prime because it is always divisible by at least 2. If it is a five it is not a prime number because it is always divisible by five. If it is a zero it is always divisible by both five and two.
Once you've eliminated all the numbers as above, the remaining possibilities are one, three, seven and n nine. At that point you consider what two-digit number ending in each of those is prime or noneprime. It turns out that there are very few that are nonprime. For instance, two digit numbers ending in one are eleven, twentyone, thirtyone, fortyone and son on. Of all those two digit numbers only twentyone and eightyone are divisible by a number other than one or itself. Twentyone is divisible by seven and three, eightyone is divisiable by nineand three , so if your target number can be reduced to either of those as you divide it out in your head you know it is not a prime number, But allt he other numbers ending in one are prime.
Same method with three: thirty three sixty three and ninety three are all divisible by three and eleven or two etc.
Same process with seven and nine. Lots more prime numbers than nonprime ones with these four numbers.
I think it works but I'm no mathematician. If it works it reduces the toil of figuring out what's prime and what isn't as much as possible for a methmatical klutz. That's my opinion.
Oops, no, two is not divisible into anything that ends in three. Oops. thirtythree, sixtythree and ninety three are divisible by eleven, nine and of course three. Brain very tired though so even this may need to be corrected in turn. Sigh.
