Probably not. Inorganic carbon in the form of limestone is not as good for compost as organic carbon in the form of vegetable matter. Ground limestone is not really organic, at least not in the way I define it, which is as carbon created as a result of primary (plant) or secondary (animal) production. Limestone is good for compost in small amounts, but as a neutralizer of acid, rather than as a source of carbon. CaCO3 reacts with water and CO2 to produce calcium and carbonate ions. By adding large amounts of limestone, you would end up with an alkaline mix which could be inhospitable to your bacteria and worms. The best source of organic carbon for compost is grass clippings, leaves, kitchen waste and other organic matter.
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