how to convince my holocaust denier boyfriend 6 million jews died in the holocaust?

If he is making an issue of it, I would show him the door!

You probably can't. Some people are just stuck in their beliefs. One way to make an attempt to prove it is show him pictures of mass graves. Not every death was documented. It's probably not exactly 6 million, though, it might even be more, but definitely way more than 6,000. That would be like one train. His numbers are way off. Maybe he's confused and talking about a single event instead of the war as a whole. Regardless, the regime didn't just perform genocide on Jews, but many others as well.

Hate to tell you this but scholars do not use the world almanac for reference. It is written as a reference for non-scholars (like your idiot boyfriend). Scholars actually access more in depth and closer to the source material. While the World Almanac has tons of interesting information, it is unlikely to address the holocaust.

There is a plethora of material all over the internet. Just type "holocaust" in wikipedia. Unfortunately there is a lot of false information as well, often written by white supremacists and closet Nazis. If you BF believes that only 6000 people died, he is probably already accessing that false information despite the much more info that contains the truth. If he is unwilling to open his eyes with the info that is available from many credible sources, then I would suggest you seek out different male companionship...you can't fix stupid.

Find someone better. He's not worth the time or energy.

Jews are actually aliens that came down to create cultures of people who follow ridiculous ideologies.