Question

7. Every prime number p is always
expressible in the form 6k + 1 or 6k + 5
where k € N. (True / False)​

Answer 1

$Given \: statement :$

Every prime number p is always

expressible in the form 6k + 1 or 6k + 5

where k € N.

$\green { ( False ) }$

Explanation:

$i )p = 6k+1$

$If \: k = 4\\ \implies p = 6\times 4 + 1 \\ = 24 + 1 \\= 25 \blue { ( not \: a \: prime ) }$

$ii )p = 6k+5$

$If \: k = 5\\ \implies p = 6\times 5 + 5\\ = 30 + 5 \\= 35 \blue { ( not \: a \: prime ) }$

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