Problem with induction proof in textbook.

The way the chain of inequalities is written is wrong. Apparently, it should be$$P_{n+1}\ge P_{n}+2>3n+2\\\implies P_{n+1}\ge3n+3$$Now you should use the fact that $3\mid3n+3$ but $3\nmid P_{n+1}\ne3$. So $P_{n+1}\ne3n+3$.

Tags:

Inequality

Induction

Prime Numbers

Proof Writing

Proof Verification

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