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Sorry, it's short for basepair (bp) of DNA (eg a, c, t, or g). Currently it costs about ten cents a bp to synthesize a particular stretch of sequence from one of the companies in the article (dime a base). An average protein can be encoded by 1 kilo basepair, a small bacterial genome by 1 mega basepair, and a human genome by 6 giga basepair.

They are the American one-cent and ten-cent coins, respectively. The words are also used to indicate costs of $0.01 and $0.10.

Maybe the confusion here is that prices are sometimes spoken of as 'a [currency unit] a [item]' which can be understood as 'one [currency unit] per [item]'.