A 64-bit OS and 8GB of RAM to start. http://www.bit-tech.net/news/gaming/2015/10/09/fallout-4-system-requirements/1
Seems to be a considerable disparity between the AMD and Nvidia minimum and recommended GPU spec. The 7870 is typically more than twice as fast as the 550ti; the GTX780 is more equivalent to a R9 290- which still beats it by a decent margin in most games. Either way, I expect the requirements to be excessive, especially a few months in when the game will likely receive some performance optimizations. I hope the increase in required GPU memory means an improvement in Bethesda's typically horrible textures. Anyway, now the bitch inside me is sated- I'm actually really looking forward to this!
There are certainly people with 4GB of RAM and a 64-bit install of Windows, hence "and". (Incidentally, there's no reason a 32-bit Windows install couldn't access >4GB of RAM - Google "physical address extension.")
Good! It's long overdue for PC games to require a 64 bit OS and more than 4 Gb of RAM. That 4 Gb limit has been holding things back for years - games companies had to cater to lowest common denominator and make their games able to run on low end systems, restricting development to fit within this limit. Even the current generation of consoles have more RAM, and the PC is supposed to be ahead of the game! I applaud Bethesda's decision.
Not wanting to bash Microsoft but isn't the 4GB limit more of a design choice that a technical one, as in 32bit Windows could technically address more than 4GB but Microsoft chose to draw the line at 4GB for marketing reasons and the problems caused in Windows when using PAE. Games companies had to cater to lowest common denominator yes, but that wasn't caused by low end systems (users) it was caused (IMO) by gaming on Windows having stagnated for the last 13 years.
At last. Lets kill the damn Win 32 for heaven sake. There hasn't been a 32bit CPU on sale for 12+ years.
I was working on a customers machine, who had 32 bit windows and 8GB ram, I did suggest to lads I was working with that they should upgrade to 64bit