Park's longtime friend Choi Soon-Sil -- the daughter of her religious guru -- was vilified at the massive nationwide protests last year that rocked Asia's fourth-largest economy and led to Park's impeachment.
Choi was "the alpha and omega of the scandal", a prosecutor told the Seoul Central District Court, adding: "Please sentence Choi to 25 years in prison."
He also sought fines and asset seizures totalling 126.2 billion won -- around $116 million.
The 61-year-old is accused of colluding with Park to extort millions of dollars from conglomerates, including South Korean giants Samsung and Hyundai, and using her connection with the president to meddle in state affairs.
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Choi denies all 18 charges, including abuse of power, coercion and bribery.
Prosecutors also demanded a four-year prison sentence for the chairman of retail conglomerate Lotte Group, Shin Dong- Bin, and six years for a former presidential aide.
Verdicts are expected in January.
Park herself is being tried separately, but Thursday's request suggests prosecutors will demand a sentence of at least 25 years in her case.