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There's a bit of a misunderstanding. The OS will schedule certain threads to run on other cores, so in most cases a dual core is going to be faster than a single core. Plus, the Core2 technology is superior to the P4 in every way, so even a slower Core2 is still going to outperform P4. I remember going from a 2.4Ghz single core P4 to a 3.06 P4 with HyperThreading, which is actually only 2 virtual cores. The multitasking was drastically better, so the applications them self do not have to be multi-core aware in order to take advantage of multiple cores, it just helps much more than the OS itself can handle.
Now bumping up to the quad core, depending on the OS, it could be another story. Some things are going to run faster on a fast dual core than a slow quad.
The single thread of C2D at 2.13 should handily outperform the P4.
Like a Vespa at full throttle won't stand a chance against a Haybusa at half.
Here ya go brohman. All Chips @ 3.0GHZ all CB 11.5 ST test.
Fap fap fap away. P4 is at the bottom.
http://www.tomshardware.com/charts/x86-core-performance-comparison/Cinebench-11.5,2753.html