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It isn't a matter of the hones lasting longer. It is a matter of efficient honing. The 2k is a coarse hone that is fine for setting a bevel. The 4k is for sharpening the edge and the 8k is for...

Shapton and others suggest doubling the grit as you go up in the progression. A 4k would be advisable. If you could swing it the 16k would complete the set nicely.