It was the highest partnership for any wicket in the county's 151-year history, and only the 13th time in first-class cricket that any stand passed 500 runs.
Glamorgan finally parted the pair when Prince was out for a career-best 261.
Petersen, having batted for more than eight hours, then fell six overs later for 286 -- also the best of his career -- with Lancashire 625 for four on the second day of the match at the Welsh seaside resort of Colwyn Bay.
They declared on 698 for five, their fifth highest-ever score.
Image: Ashwell Prince bats for Lancashire
Photograph: Jan Kruger/Getty Images
Australia hand Faulkner four-match suspension for drink-driving
De Villiers gets paternity leave, while four uncapped players called-up
Jaw-dropping moment surfer survives shark attack
'It's hard to expect the middle order to get us out of trouble'
I approached Tambe for coaching, not fixing, says Hiken