Sorry for not answering this question before, but I did save this to answer when I could.

Short answer: There is no estimate for that long period of time, only rough estimates for the peak in the 1710s-1720s of about 5,000 pirates (as in individual men).

Long answer: I'm not sure how a historian would go about estimating for that long period with any accuracy. But, thanks to the large amount of documentation available for the peak period of around 1713-1726, Marcus Rediker presents the estimate that about 5,000 men turned pirate and sailed the Atlantic during that period. At the peak, as many as 2,000 to 2,500 sailed at the same time, about a thousand from the Bahamas alone. If you want to see more on those numbers, go look into Rediker's book, Villains of All Nations.