Oskar Gröning, 94, stands accused before a court in the northern city of Lüneburg of 300,000 counts of "accessory to murder" in the cases of deported Hungarian Jews sent to the gas chambers between May and July 1944.
Public prosecutor Jens Lehmann said in closing arguments that his sentencing request was based on the "nearly incomprehensible number of victims", but mitigated by "the limited contribution of the accused" to their deaths.
Lehmann also argued that the court should consider viewing some of the sentence as already served because Gröning had been repeatedly investigated in recent decades with no charges brought until last year.
Gröning's trial, expected to be one of the last of its kind, began in April.
He served as a bookkeeper at Auschwitz, sorting and counting the money taken from those killed or used as slave labour, collecting cash in different European currencies and shipping it back to his Nazi bosses in Berlin.
Gröning, whose frail health has led to several delays in the proceedings, has acknowledged "moral guilt" but said it is up to the court to rule on his legal culpability.
Lehmann said the court faced a historic decision with its verdict, which could come as early as this month.
"We are confronted with events that push the limits of human imagination," he said.
In a statement read out by one of his lawyers in court last week, Gröning said he did not feel entitled to ask Holocaust survivors to forgive him.
"I can only ask my Lord God for forgiveness," he said.