What is known about representing numbers as their modulo of successive prime numbers?

Question

Let's define $P_i$ as the $i$th prime number, and $π(i)$ as the number of primes up to $i$. Then, each positive natural number $n$ can be uniquely represented by $[n \bmod P_i \,\mid\, i \in \Bbb N, i \lt π(i)]$. For example,

1  = []
2  = [0]
3  = [1]
4  = [0, 1]
5  = [1, 2, 0]
6  = [0, 0, 1]
7  = [1, 1, 2, 0]
8  = [0, 2, 3, 1]
9  = [1, 0, 4, 2]
10 = [0, 1, 0, 3]
11 = [1, 2, 1, 4, 0]
12 = [0, 0, 2, 5, 1]
13 = [1, 1, 3, 6, 2, 0]
14 = [0, 2, 4, 0, 3, 1]
15 = [1, 0, 0, 1, 4, 2]
16 = [0, 1, 1, 2, 5, 3]
17 = [1, 2, 2, 3, 6, 4, 0]
18 = [0, 0, 3, 4, 7, 5, 1]
19 = [1, 1, 4, 5, 8, 6, 2, 0]
20 = [0, 2, 0, 6, 9, 7, 3, 1]

My questions are:

1. Is there any name for this representation?

2. Is there an efficient algorithm for converting that representation to binary?