Totient minimal value for semiprimes

Question

I have two question concerning Euler Totient of semiprimes.

First question : given $N=p_1 * p_2$ and $M=p_3*p_4$ where $p_1,p_2,p_3,p_4$ are prime numbers greater than 5; and $M>N$ this means that also $\phi(M)>\phi(N)$ ?

Second question : what is the minimum value that $\phi(M)$ can have ? I know that Mr. Sierpinski estimated the minimum value involving the Eulero-Mascheroni constant, but do we have a better "low bound" estimationf for the Euler Totient of a semiprime like $M$ ?

Thanks a lot guys

Answer 1

For the first question, the answer is no. You can have $M>N$ and $\varphi(M)<\varphi(N)$.

For example take $M=7\cdot 131=917$. Then $\varphi(M)=6\cdot 130=780$.

And take $N=29\cdot 31=899$. Then $\varphi(N)=28\cdot 30 =840$.