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Home Q & A Board Science-Related Homework Help Mathematics
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Anonymous peoplemover
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A year ago
Explain/Describe how all the prime numbers greater than 3 are related to the number 6.
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#1
Educator
A year ago Edited: A year ago, bio_man
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.
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