Following the accident, Soviet authorities failed to warn neighboring countries of the disaster. Two days later, a dramatic increase in radiation levels at a nuclear power plant in Sweden caused immediate alarm, and investigation led the Swedes to suspect it came from the western Soviet Union. The Soviets admitted there was an accident, but denied it was serious. Sweden, however, persisted and announced it would file an official alert with the International Atomic Energy Authority, which would have sent investigators. Only then did the Soviet Union admit to the world the seriousness of what occurred.
The dispatch calls played are the real ones that were made on the night of the accident, as they were calling in firefighters from neighboring towns to help with the fire.
The title refers to the exact moment (1:23:40 a.m.) the emergency shutdown of the reactor was initiated, ultimately causing its explosion seconds later at about 1:23:45 a.m., or 12345.
In his original script, Craig Mazin had Legasov opening a can of pet food for his cat, but this was changed after he learned that pet food was not available in the Soviet Union, where people fed leftovers to their pets.
Akimov's line in the control room ("Don't worry - we did everything right. Something strange must have happened") was not dramatized, but was really what he said at that moment, according to multiple accounts from the control room. Craig Mazin said in the podcast that he would never have thought to write such a line.