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Numbers greater than 3 have the form 6k+1 or 6k-1, prove with the definition of prime numbers

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Answer to a math question Numbers greater than 3 have the form 6k+1 or 6k-1, prove with the definition of prime numbers

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Timmothy

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99 Answers

1. Any integer can be written in one of the forms:

6k, 6k+1, 6k+2, 6k+3, 6k+4, 6k+5

, where $ k $ is an integer.

2. Numbers of the form

6k+2

, and

6k+4

are divisible by 2 and hence not prime (except for 2, which is not greater than 3).

3. Numbers of the form

6k+3

are divisible by 3 and hence not prime (except for 3, which is not greater than 3).

4. Thus, any prime number greater than 3 must be of the form

6k+1

6k-1

.

**Answer:**

Any prime number greater than 3 must be of the form

6k+1

6k-1

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Numbers greater than 3 have the form 6k+1 or 6k-1, prove with the definition of prime numbers

Answer to a math question Numbers greater than 3 have the form 6k+1 or 6k-1, prove with the definition of prime numbers

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