I have the same chip and it is NOT easily overclocked to 3.7-4.0. Let's start at the beginning. The 720BE is a Phenom II with the 4th core disabled and defaults to 2.8Ghz (200x14) as a tri-core (they disable 1 core). Since it is a Black Edition chip the clock multiplier is unlocked. A number of motherboard BIOS's have an unlock or ACC feature that allows the 4th core to unlock and be used since the chip is "officially" a tri-core. Getting it to unlock and run stable is great and more and more people have success, probably due to AMDs manufacturing controls and not being worried about cutting into high end chips. Apparently the unlocking feature might be phased out.
Anyway, if you overclocked and unlocked the chip to 3.4 you have gained 1 core AND 600 Mhz for each of the 4 cores from stock!
Ironically, my 720BE is overclocked to 3.3Ghz and 4 cores AND runs Prime64 stable for 24hrs. Does yours? I have a Zalman 9700HS with ArticSilver5 thermalpaste and great cooling in my case. Today I tried 3.4 and 3.5 and was able to boot and run if I upped the voltage to 1.4875. I tried 3.7 but blue screened. IF I ramped the voltage higher maybe, just maybe I could. Please understand that some posters brag about huge overclocks but is that just to boot into Windows? Ask them how long they play BF2BC before it locks up. I can tell you I can play any game all day at 3.3GHZ 4 core with no worries and MAX heat of48C.
If you are getting a Solid 3.4 Ghz 4 core without any voltage tweaks that can run Prime64 for 24 hrs without a lockup from a 720BE you a VERY lucky man.
"Easily" overclocking a 720BE to 3.7-4.0 is just not correct.
there is no safe overclock for it ..... Overclock it to the limit if you have good cooling......
I have cooler master hyper 212+ and have x4 b50 at 3700/2400 core/northbridge @ 1.49/1.44 volts and my temps are never above 47 at any time though my ambients are above 30c