It is true that a martin can eat 2,000 mosquitoes. A martin physically has this capacity, but it is not the norm for them to try to achieve this specific task. If you are interested in attracting martins for mosquito control, you are after the wrong creature. Bats are a much more prolific consumer of mosquitoes. Inc. Martins do eat mosquitoes, but they will not rid your property of these insects as some would have you believe.
Martins are still a wonderful bird and are very enjoyable to host.
I would like to include a quotation from the late George Miksch Sutton on his views of the martin and the mosquito. He was a renowned bird artist, writer and a professor of zoology at the University of Oklahoma. He was also the Curator of Birds in the University of Oklahoma's Stovall Museum. Martins are alleged to be great mosquito eaters. So widely held is this belief that communities go to great lengths to attract martins, putting up expensive houses for them, organizing drives against House Sparrows and Starlings, etc.