E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Not worth a rap. The rap was a base halfpenny, intrinsically worth about half a farthing, issued for the nonce in Ireland in 1721, because small coin was so very scarce. There was also a coin in Switzerland called a rappe, worth the seventh of a penny.
Many counterfeits passed about under the name of raps.Swift: Drapiers Letters.