Desynthing primal weps.

[Kyana]

Don't you have to level up the Desynthesis skill? I don't know why you'd assume you get one of the highest quality items from desynthesis at the lowest rank.

I doubt he'd go 5/6 successful desynths if he had the lowest rank.
The chance of getting a Demimateria increases if your desynthesis chance is 100%.

However.
If high level items and rare items have the same chance to produce Demimateria like other items, you can prepare for a long farm.
At 76 skill I got 35 Demimateria I+II from desynthing 1200+ fish. Most of them desynthed between 85-100% chance.
So, you would need ~75 primal weapons to get the 3 Demimateria you need...