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Ubisoft released the system requirements for Far Cry Primal today. They offer up both the required specs and the recommended specs for the game.
PC System Requirements
OS: Windows 7, Windows 8.1, Windows 10 (64-bit versions only)
Processor: Intel Core i3-550 | AMD Phenom II X4 955 or equivalent
RAM: 4GB
Video Card: NVIDIA GeForce GTX 460 (1GB VRAM) | AMD Radeon HD 5770 (1GB VRAM) or equivalent
Hard Disk Space: 20 GB
Peripherals: Windows-compatible keyboard, mouse, optional controller

Recommended PC Specs
OS: Windows 7, Windows 8.1, Windows 10 (64-bit versions only)
Processor: Intel Core i7-2600K | AMD FX-8350 or equivalent
RAM: 8GB
Video Card: NVIDIA GeForce GTX 780 | AMD Radeon R9 280X or equivalent
Hard Disk Space: 20 GB
Peripherals: Windows-compatible keyboard, mouse, optional controller

There is no co-op multiplayer for Primal. The game itself is due out on March 1.