Unlike DDR4, there is not much to say about DDR3. Either it works or it doesn't work. Use Memtest86+ to test DDR2 and DDR3. Version 5.31b is the "latest" version. It hasn't been updated in a while, but that's ok since DDR2/DDR3 is pretty old RAM. Do 2 passes for the first test. Almost all RAM will fail this two-pass test with some issue (pass 2 is longer/more thorough than pass 1). Then do a nightly or at least 6-hour test later. The RAM DIMMs I prefer for DDR2 or DDR3 are either Samsung or Hynix/SKHynix. Of course, use consistent RAM whenever possible. Unmatched RAM might work, but it's more of a bummer. Never mix RAM of different ranks = Never mix single rank RAM with dual rank RAM (etc.).
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