The stiffest sentence was sought for Mikael Davud, a member of the Chinese Uighur minority, who has been portrayed as the mastermind of the plot against the Jyllands-Posten newspaper.
"Davud imported world terrorism to Norway," prosecutor Geir Evanger said.
Prosecutors requested five-year terms for Davud's alleged co-conspirators, Shawan Sadek Saeed Bujak, an Iraqi Kurd residing in Norway; and David Jakobsen, an Uzbek also living in Norway.
Charged with plotting to commit a terrorist act and possession of explosive materials, the three men have pleaded not guilty.
Prosecutors say the trio, arrested in July 2010, initially targeted Jyllands-Posten after its 2005 caricatures of the Prophet Muhammad provoked fury and sometimes deadly protests across the Muslim world.
Their target then allegedly shifted to Kurt Westergaard, the caricaturist who caused the most upset with his drawing of Muhammad showing the prophet with a lit fuse in his turban.
Davud has acknowledged planning an attack, but said he was targeting Chinese interests in Norway, and not the newspaper.
He claimed to have acted for personal reasons and manipulated his co-defendants into obtaining chemical products, including hydrogen peroxide, to make a bomb.
According to Norway's intelligence agency PST, 40-year-old Davud had ties to Al-Qaeda, which trained him in explosives handling at a camp in Pakistan between November 2008 and July 2010.
The trial is scheduled to continue until late December and a verdict is expected early next year.