Federal prosecutors say they are baffled at the repeated statement by many in the black community that the federal government's prosecution of Mayor Marion Barry has cost $42 million.

It's not true, they say. They find themselves saying that a lot.

Most recently they have said it in court. A motion filed by prosecutors in the Barry case May 31 noted that the cost of running the U.S. attorney's office in Washington now runs about $26 million a year, a figure that makes Barry's claims about the cost of the probe "wildly exaggerated."

"Any claim that this office spent around twice its annual budget in conducting its investigation of defendant's activities over a 13-month period, while at the same time prosecuting over 22,000 other cases annually, is absurd on its face," the motion said.

Law enforcement officials estimate that the cost of pursuing 10 complex investigations involving Barry or his subordinates from 1982 to the present, including the Jan. 18 sting at the Vista Hotel, is between $2 million and $3 million.

That includes a probe into alleged drug use by Karen Johnson, a former friend of Barry's, which began in 1982, officials said.

It also includes non-drug-related investigations -- for example, the probe into alleged contract-steering by former Department of Human Services head David E. Rivers and D.C. contractor John B. Clyburn; a 1986 look into alleged irregularities in Barry's expense accounts; and five contract fraud cases focusing on top Barry administration officials.

Officials said the figure was calculated by taking the average salaries paid to prosecutors and agents of the Drug Enforcement Administration, the FBI and the D.C. police, and multiplying that by the number of persons assigned to each case.

The $42 million figure apparently first surfaced in 1988 on the WOL-AM radio talk show of Cathy Hughes. Asked last February where she got that figure, Hughes said she got it from Barry. She checked it with the office of then-U.S. Attorney Joseph E. diGenova, she said, and was told by a woman whose name she doesn't remember, "That's not exactly right, but it's close enough."

A former prosecutor in diGenova's office said the office's annual budget was about $10 million -- much smaller than the budget for the expanded office of the current U.S. attorney, Jay B. Stephens.