Have a look at a typical account by one of the seemingly endless number of survivors: Olga Lengyel's Five Chimneys: a woman survivor's true story of Auschwitz (Granada/ Ziff-Davis, 1947, 1972).
The blurb on the cover of the book quotes the New York Herald-Tribune:
Albert Einstein, the promoter of the US construction of the bombs used at Hiroshima and Nagasaki, is quoted as offering:
"You have done a real service by letting the ones who are now silent and most forgotten (sic) speak."
'After June, 1943, the gas chamber was reserved exclusively for Jews and Gypsies.. Three hundred and sixty corpses every half-hour, which was all the time it took to reduce human flesh to ashes, made 720 per hour, or 17,280 corpses per twenty-four hour shift. And the ovens, with murderous efficiency, functioned day and night. However, one must also reckon the death pits, which could destroy another 8,000 cadavers a day. In round numbers, about 24,000 corpses were handled each day. An admirable production record, one that speaks well for German industry.' (Paperback edition, pp80-81).
No trace of any remains of or in 'death pits' has been found.
This implies almost 100,000 corpses per four working days, or a million in 40 days, or almost six million in 240 days (eight months).