direct train from frankfurt to prauge

Unfortunately, Rick has given the impression that there are direct night trains from every city in Europe to all other cities, but that is not the case. For Frankfurt to Prague on that date your best bet is CNL459, from Zürich, which goes through Frankfurt (Süd) just before 1 AM and terminates in Dresden around 8 AM. From there you take a Eurocity (EC) train to Prague. There is also a Euronight (EN) train from Frankfurt Hbf, but you get off in Regensburg around 4:30 AM and wait 2 hours for a regional train to Prague.

I know it doesn't sound very romantic, but the best way to get from Frankfurt to Prague after 1500 is a train to Nuremburg, then a bus to Prague. Get's you there by 22:18 and you can spend the night in a hotel.

Another option (probably the best) is to fly. There are 5 direct nonstop flights to Prague after 15:00. Flight takes about 1 hour and few minutes.

What's the significance of 1500? Are you flying into Frankfurt, arriving at 1500? From North America? If so: Good thing, you'll already be at the airport, so for flying to Prague, you won't have travel time from downtown Frankfurt. If you don't already have your flight tickets, you can book the entire trip from Sea-Tac to Prague, and you won't have to check in again in Frankfurt, maybe not even go through security again. Bad thing, in 9 flights to Germany in the last 15 years, I have been an hour or more late 3 times. If you already have the ticket to Frankfurt, and you have to book Frankfurt to Prague separately, if your flight is late, the airlines might not accommodate your missing the connection to Prague. You can get really good advance purchase fares from Frankfurt to Prague, but those fares are train specific. If your flight is late, and you miss the specified train, you lose the tickets and have to buy replacements at full fare. Personally, if I had not already booked the flight to Frankfurt, I'd book the connecting flight on the same tickets. If that's not possible, I'd find somewhere closer ( Mainz, Bacharach, ?) to spend the first night and get an advance purchase ticket from there to Prague for the next day, when you can be sure of catching the train.