Here's the list of the youngest player in NBA history to reach each the following scoring milestones:

Youngest player to score:
1,000 points: LeBron James
2,000 points: LeBron James
3,000 points: LeBron James
4,000 points: LeBron James
5,000 points: LeBron James
6,000 points: LeBron James
7,000 points: LeBron James
8,000 points: LeBron James
9,000 points: LeBron James
10,000 points: LeBron James
11,000 points: LeBron James
12,000 points: LeBron James
13,000 points: LeBron James
14,000 points: LeBron James
15,000 points: LeBron James
16,000 points: LeBron James
17,000 points: LeBron James
18,000 points: LeBron James
19,000 points: LeBron James
20,000 points: LeBron James
21,000 points: LeBron James
22,000 points: LeBron James
23,000 points: LeBron James
24,000 points: LeBron James
25,000 points: LeBron James
26,000 points: LeBron James
27,000 points: LeBron James
28,000 points: LeBron James
29,000 points: LeBron James
30,000 points: LeBron James
31,000 points: LeBron James
32,000 points: LeBron James
33,000 points: LeBron James
34,000 points: LeBron James
35,000 points: LeBron James
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