A B737-400 EXPERIENCED A CABIN PRESSURE LOSS DUE TO A CTLR FAILURE. A RAPID DSCNT WAS FOLLOWED BY A FLT TO DEST AT 10000 FT. NO EMER WAS DECLARED.

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IN LEVEL CRUISE AT FL340 AT APPROX XA20Z; THE CABIN ALT WARNING HORN SOUNDED. THE CABIN ALT WAS AT 10000 FT AND CLBING AT A RATE OF 500 FPM. THE AUTO FAIL LIGHT ON THE PRESS CTLR WAS ILLUMINATED. WE INITIATED THE CABIN ALT/WARNING HORN MEMORY ITEMS; DONNED OUR OXYGEN MASKS AND QRC STEPS. WE REQUESTED A LOWER ALT FROM CTR AND BEGAN A RAPID DSCNT. CTR FIRST CLRED US TO FL180; THEN 13000 FT. WE REQUESTED AND RECEIVED 10000 FT AND WERE CLRED DIRECT. WE LEVELED AT 10000 FT APPROX 150 MILES E OF ANC. WE NOTIFIED DISPATCH AND CONTINUED TO ANC AT 10000 FT. WE RAN THE AUTOFAIL/UNSCHEDULED PRESS CHKLIST AND FOUND THE STANDBY CTLR WOULD NOT CTL THE PRESSURIZATION EITHER. THE CABIN ALT WAS THE SAME AS OUR AIRPLANE ALT (10000 FT). SINCE WE WOULD BE SOON LNDG IN ANC; WE CONTINUED WITH THE CTLR IN STANDBY AND RAN THE DSCNT AND APCH CHKLISTS. WE ELECTED NOT TO DECLARE AN EMER BECAUSE THERE WERE NO PAX OR CREW INJURIES; THE CABIN PRESSURE WAS NOT CRITICAL; AND SINCE WE WERE CLOSE TO ANC; FUEL; TERRAIN; AND WX WERE NOT CRITICAL ISSUES. SINCE WE WERE QUICKLY APCHING ANC; WE DID NOT ATTEMPT TO PRESSURIZE USING MANUAL CTL AND MADE A NORMAL DSCNT; APCH; AND LNDG. THE PAX OXYGEN MASKS DID NOT DEPLOY. THE HIGHEST OBSERVED CABIN ALT WAS APPROX 13750 FT BEFORE THE CABIN DSNDED AGAIN WITH THE AIRPLANE'S DSCNT. THE FLT ATTENDANTS RPTED MOST PAX WERE SLEEPING AND DID NOT NOTICE OUR DSCNT. THERE WAS NO ADVERSE PAX REACTION. WE LANDED AT XB10Z. IN 2004; RECURRENT LOFT TRAINING SCENARIO WAS A RAPID DEPRESSURIZATION. THIS EVENT WAS VERY SIMILAR TO THAT TRAINING EVENT AND I FEEL MADE A POSITIVE IMPACT ON OUR REACTION TO THE CABIN ALT WARNING HORN AND SUBSEQUENT REACTIONS.