The phrase "primarily seek" is grammatically correct and can be used in written English.
It is typically used to express one's main or primary goal or intention. Example: "Our company primarily seeks to provide affordable and sustainable solutions to our customers."
Mr. Hart of Echo said retailers would primarily seek to sell downloads over their Web sites that consumers could call up from their homes.
These people primarily seek the beauty and tranquility of Vermont's mountains and narrow valleys and the sense of the country's past that pervades the entire state.
Most foreigners who come to Stockholm primarily seek out waterfront neighborhoods like Djursholm, Stocksund and Lidingo, which have easy access to international schools and Arlanda international airport.
Analysts believe both sides, though interested in forming stronger relations, primarily seek to signal to the international community that their foreign policies are not to be dictated by others.
Will Pope Benedict XVI primarily seek to fight for souls and expand the universal authority of the Catholic Church, which is in competition with Islam, Pentecostal churches and local tribalism?
New therapies primarily seek to suppress the inflammatory homing of adaptive immune cells to the kidney, limit cell death, and/or interrupt detrimental signaling of necrosis.
They are primarily seeking a power-hitting left fielder in return.
I would not advocate imposing treatment and Miss B primarily sought the power to have the right to choose.
He said Mr. Giuliani's firm primarily sought to use the legislation to draw attention to those disenfranchised in Ethiopia.
Those agencies were primarily seeking to protect information about the sources and methods of their intelligence-gathering activities, involving both human and technical intelligence.
The neurotic protagonist, Dolph (Jack Plotnick), shares something of the bewilderment and bouffant of Henry from David Lynch's "Eraserhead" and primarily seeks the return of his missing dog, Paul.
