I currently have two kernels: a 2.6.18-4-686 kernel and a 2.6.18-3-686 kernel.
Which is better? The higher the kernel number the better? Is the 2.6.18-4-686 kernel a newer version or something? Thanks in advance.

The first part is the version so 2.6.18-4 is better than 2.6.18-3

the last part (which is usually something likee 686) indicates what cpu it is optimised for.

e.g

a 686 optimised kernel is better than a standard 486 one (provided your cpu can handle it)

ok one last question: I have a intel core duo 2 processor. is 686 the best for it?

yeah, 686 gives the best mix of speed and compatibility as it runs on prettymuch all modern (PIII+ era) cpus

people with 64 bit capable cpus (amd64, and (i think) recent intel cpus) can get a performance bonus by using the x86_64 kernel but in my experience its not a huge difference unless you are running something intensive like a server and it can lead to certain compatibility issues with programs such as Flash

if you have multiple cpus or hyperthreading (i think dual core should work too) you may see quite large performance boost gettin a kernel with SMP

if you have over 4gb ram you may also find a "bigmem" kernel useful

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