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Title: Prime numbers - how are all prime numbers greater than 3 related to 6? Post by: peoplemover on Oct 1, 2022 Explain/Describe how all the prime numbers greater than 3 are related to the number 6.
Title: Re: Prime numbers - how are all prime numbers greater than 3 related to 6? Post by: bio_man on Oct 1, 2022 Let's start 5:
5 mod 6 = 5 (think of 5 divided by 6, we get a remainder of 5) 7 mod 6 = 1 (7 divide 6 gives a remainder of 1) 11 mod 6 = 5 13 mod 6 = 1 17 mod 6 = 5 19 mod 6 = 1 Notice that it is always 1,5,1,5 alternating. Hence, all prime numbers can be written as 6n + 1 or 6n - 1. For example, set n=5 6(5) + 1 = 29 6(5) - 1 = 31 Both are prime numbers! This is no proof but can be used to understand this idea. |