Does $f(46)$ exist?

Question

Let $\varphi(n)$ denote the totient function.

For an even positive integer $k$ , define $f(k)$ to be the smallest composite number $n$ satisfying $$\varphi(n+k)-\varphi(n)=k$$ if such a number $n$ exists. For the even numbers upto $44$ , the values are

2  6
4  12
6  21
8  24
10  36
12  45
14  48
16  39
18  63
20  72
22  72
24  95
26  60
28  57
30  224
32  84
34  15
36  135
38  1058
40  45
42  301
44  144

But I do not know whether $f(46)$ exists. If yes , we have $f(46)>10^8$.

Does $f(46)$ exist ? If yes, what is the value ?