Heuermann -- the alleged Gilgo Beach killer -- had his alleged internet search history revealed in new court documents, with prosecutors saying he was looking up autopsy photos, violent hardcore porn and deviant sex acts.

But his lawyer, Michael Brown, is pushing back ... telling reporters this week, "Searching the internet, ask yourselves what you search on your computers and your phones."

Brown brushed it off this way ... "One thing leads to another -- you see a show about something, you start searching, and they talk about how somebody got killed. You start searching, and then they talk about another way, and you start searching."

Prosecutors claim Heuermann's Google searches included ... "tied up fat girl porn," "medieval torture of women," "skinny black girl slave porn," "autopsy photos of female," "wooden pony porn," "skinny white teen crying porn" and "how I was raped audio" ... just to name a few.

What's more, Heuermann allegedly had over 200 searches about the Gilgo Beach murder case and other known serial killers.

But his lawyer says ... "Think about if they looked at your own personal search history, how all of a sudden you're guilty because of your search history?”

As we reported ... earlier this week Heuermann was hit with a fourth murder charge.

All four women worked as escorts near his home on Long Island ... and his internet history allegedly includes searches for all kinds of escorts -- running the gamut of identities ... racial, sexual and otherwise.