I think it is valid for 3

We calculate the function of the prime numbers by calculating the non-prime distribution function.
Example In 53 there are 27 elements less 12 possible combinations plus repeating numbers (look at 45) and then 53 is the 16 prime numbers
and has 16 matches 53

53
51
49
47
45
43
41
39
37
35
33
31
29
27
25
23
21
19
19+17+15=51
17
17+15+13=45
15
15+13+11=39
13
13+11+9=33
13+11+9+7+5=45
13+11+9+7+5+3+1=49
11
11+9+7=27
11+9+7+5+3=35
9
9+7+5=21
9+7+5+3+1=25
7
7+5+3=15
5
5+3+1=9
3
2