Originally posted by trevor33My parents gave me an Irish text book as a birthday present (or maybe it was Christmas) many years ago, after I had lived in Northern Ireland for three months. I only did the first few chapters, and I have forgotten a lot, but at least I can still say "oíche mhaith".
hay nordlys, i forgot to ask - how did you know the irish words for good night?
Originally posted by PhlabibitIn short, the modern definition of a prime number is that it is a positive integer having exactly one positive divisor other than 1. 1 doesn't have a positive divisor other than 1.
I'd like to know why, since only 1x1 is 1... Can someone sum this up for me?
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This page explains why the definition was changed: http://mathworld.wolfram.com/PrimeNumber.html
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Originally posted by PhlabibitYou have to test for divisability by all primes up to the square root of the number.
What was the largest prime number known before the advent of computers? Is there some formula for testing, or do you need to do all the work to solve each number by testing all the other numbers starting with 1/2 the suspected number?
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You can show that this is sufficient by knowing that all non-prime numbers (barring 1) are the product of two or more primes. For example 411 can be split into 3*137.
Given the above it should become clear that if you reach the last prime number lower than the square root of the tested number and have found no prime factor then no prime factorization exists (two numbers greater than the square root cannot give the number).
Other than this no shortcut exists. This makes testing extremely large numbers for primality extremely timeconsuming.
Originally posted by NordlysThread 43795
Oops, nobody said it were either.
Bowmann's fact was incorrect. Bowmann: "There is always a prime number between any given number and its double." That should be "any given natural number > 1".
Also, it's pretty obvious I meant any integer. And don't forget, zero is not a number.
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Originally posted by XanthosNZCorrect.
You have to test for divisability by all primes up to the square root of the number.
You can show that this is sufficient by knowing that all non-prime numbers (barring 1) are the product of two or more primes. For example 411 can be split into 3*137.
Given the above it should become clear that if you reach the last prime number lower than the square ...[text shortened]... ortcut exists. This makes testing extremely large numbers for primality extremely timeconsuming.
I used this simple principle to write a program to find and analyze sets of primes.
(I called it Prime Finder. If anyone would like a copy, you may write to me for further information.)
Originally posted by NordlysDude, are we really, like, here? What if we're like, not living right now, but the life were like, living right now, is really a flashback of your real life but you've got a gun to your head?
By that reasoning, no number exists. So there are no primes either. Thread closed.