Index is slowing down the selecting actions

Description the problem:
Table size 30G, Ram size 16G
mysql> select * from program_access_log where program_id between 1 and 4000;
very slow
Try to select the top 500,000 records:
mysql> select * from program_access_log where id between 1 and 500000 and program_id between 1 and 4000;
still very slow
Analysis:
MySQL cann't put this 30G table into Ram, it will read them from disk:
mysql> select * from program_access_log where id between 1 and 500000 and program_id between 1 and 4000;
MySQL will select the program_id between 1 and 4000 out coz it's smaller then try to find id between 1 and 500000, however the id column didn't store as sorted, so MySQL will read them from disk.
Solutions:
1. Partition: split program_id into different partitions
2. Split tables: split table into smaller tables
3. select * from program_access_log where id between 1 and 500000 and program_id between 1 and 15000000;
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