Power supply for gaming desktop

Hello to all,

I'm going to build a desktop computer which will primarily be used for high-end gaming. I will be using a 1920x1080 (1080p) monitor (Samsung LED Monitor BX2250 21.5").

Now, what I'm wondering is whether a Recom Power Engine 580W will be enough for the energy consumption of the parts below, or whether I need an even heavier power supply.

Specs thus far:
AMD Phenom II X6 1100T 3.30GHz 6MB
ASRock 870-Extreme3 AMD 870, SATA600, USB3.0
Corsair 2x4GB, DDR3, PC12800, CL9, XMS3
Samsung 1TB SATA300 32MB, HD103SJ
Samsung DVD-/+/RAM SH-S223L/RSMS 22x/22x/12x SATA
Sapphire PCI-e Radeon HD6970 2GB 2xDVI/HDMI/2xDP
Scythe Processor Cooler Big Shuriken AMD & Intel

On a sidenote, do you think I will be able to enjoy Crysis 2 at a resolution of 1920x1080 with this setup?

Also, I've picked a hexacore instead of a quad core processor as I believe the extra two cores may become more useful in terms of gaming in the future.

And last but not least, if you have any suggestions to improve the list above, please do not hesitate to speak up. :)

Thanks in advance

Edit: Could you also explain me why the power supply does or does not suffice?
 
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