AN ATX FLC FLYING BE1900 ACFT INTO DCA INADVERTENTLY ENTERED PROHIBITED AIRSPACE AT P56.

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WE WERE TOLD BY WASHINGTON APCH TO TRANSITION FROM V308 TO GO DIRECT NOTTINGHAM VOR; THEN ATC CORRECTED HIMSELF AND PUT US ON A VECTOR OF 270 DEGS; WE DID SO. APPROX 5-6 MI E OF DCA; WASHINGTON APCH ASKED US IF WE COULD IDENT THE ANACOSTIA RIVER. WE RESPONDED YES; THEN ATC ASKED IF WE COULD SEE THE ARPT (DCA). WE RESPONDED YES. ATC ASKED US TO KEEP UP OUR SPD FOR JET TFC. WE SAID THAT WE WOULD (+200 KTS). THEN THEY (ATC) CLRED US FOR A VISUAL TO RWY 21 AND XFERRED US TO DCA TWR. WE CALLED THE TWR AT APPROX 4-5 MI E OF ARPT; THEN THE TWR CLRED US TO LAND RWY 21. AT THAT POINT THE PF STARTED TO LOSE VISUAL CONTACT WITH THE RWY DUE TO SETTING SUN GLARE AND HAZE FROM FOREST FIRE IN S NEW JERSEY. ONLY A FEW SECONDS PASSED BY WHEN WE WERE ABLE TO RE-ESTABLISH VISUAL CONTACT WITH THE RWY; AND STARTED A TURN TOWARD THE RWY. AT THAT POINT THE TWR TOLD US TO START AN IMMEDIATE TURN TO (L) 150 DEG HDG. WE WERE EITHER IN THE P56 AREA OR ABOUT TO ENTER IT. WE IMMEDIATELY ENTERED A TURN TO 150 DEGS WHICH PUT US RIGHT OVER THE UNITED STATES CAPITAL BUILDING. IN ONLY A FEW SECONDS WE WERE RE-ESTABLISHED WITH THE EXTENDED CTRLINE OF RWY 21. SO WE TURNED TO THE RWY AND WERE CLRED AGAIN TO LAND. AT THAT POINT WE MADE A NORMAL AND ROUTINE LNDG.