A B737-300 CABIN ALT WARNING HORN SOUNDED AT 10000 FT. THE CREW BEGAN AN EMER DSCNT AND REGAINED PRESSURIZATION CTL AT FL200 WITH A PAX NEEDING MEDICAL ATTENTION.

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IN CRUISE AT FL350 CABIN PRESSURE WARNING HORN SOUNDED. FO AND I BOTH CONFIRMED THAT CABIN ALT WAS JUST ABOVE 10000 FT AND DONNED OXYGEN MASKS. WE ESTABLISHED COMS AND FO RAN LOSS OF CABIN PRESSURE CHKLIST. AS HE WAS WORKING THE PROB; I NOTIFIED ATC OF OUR SITUATION. AS CABIN PRESSURE CLBED TO 12000 FT; WE BOTH AGREED THAT A DSCNT WAS IN ORDER. COORDINATED WITH ATC FOR A RAPID DSCNT. ATC CLRED US TO DSND TO 14000 FT. SET THROTTLES IDLE; SPD BRAKES; SPD 300 KT DSCNT. WE DID NOT USE THE EMER DSCNT PROC AT THIS TIME BECAUSE THE FO WAS STILL TRYING TO CTL THE CABIN. AT 20000 FT WE HAD THE CABIN UNDER CTL AND CABIN ALT DECREASING USING MANUAL PRESSURIZATION. WE THEN REVIEWED THE EMER DSCNT QRH TO ENSURE NORTHING WAS LEFT OUT. THE TIME FROM CABIN WARNING TO REPRESSURIZATION WAS APPROX 5 MINS. PRIOR TO REACHING 20000 FT THE PURSER CALLED INFORMING US AN ELDERLY GENTLEMAN WAS HAVING TROUBLE BREATHING AND THE DOCTOR WAS WITH HIM. AS I WAS TALKING TO DISPATCH AND MAINT; PURSER CALLED AGAIN AND SAID THE DOCTOR FELT THE GENTLEMAN SHOULD GET TO MEDICAL HELP AS SOON AS POSSIBLE. WE DECLARED A MEDICAL EMER AND MADE AN UNEVENTFUL LNDG.SUPPLEMENTAL INFO FROM ACN 707016: FLT ATTENDANT THEN CALLED AND SAID THAT SINCE THE PAX HAD A HISTORY OF CONGESTIVE HEART FAILURE AND AN IRREGULAR HEARTBEAT; THE DOCTOR RECOMMENDED THAT WE DIVERT TO ZZZ1 TO GET THE MAN FURTHER MEDICAL ATTENTION. CAPT COORDINATED WITH CTR AND WE DIVERTED INTO ZZZ1 WITH NO FURTHER DIFFICULTIES.CALLBACK CONVERSATION WITH RPTR 707016 REVEALED THE FOLLOWING INFO: RPTR STATED THAT HIS AND THE CAPT'S INITIAL RESPONSE TO THE HORN'S SOUNDING WAS 'WHAT THE HECK IS THAT;' BUT WITHIN ABOUT 5-10 SECONDS; THEY RECOGNIZED THE CABIN ALT AND HAD STARTED A DSCNT. HE BELIEVED THE REASON THEY RECOGNIZED THE HORN SO QUICKLY WAS THAT EVERY GND SCHOOL AND SIMULATOR PERIOD THE INSTRUCTORS ARE REMINDING THE PLTS OF THE HORN'S ONLY CAUSE IN FLT.