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The phrase "a primary criterion" is correct and usable in written English.
It can be used when discussing the main standard or principle by which something is judged or decided.
Example: "In evaluating the candidates, a primary criterion will be their relevant experience in the field."
Alternatives: "a key standard" or "a main factor".
Exact(30)
Strength of concrete is a primary criterion in selecting this material for a particular application.
Based on the results, the GW height should be a primary criterion for designing GWs.
The power and energy capabilities of the pack make it essential that safety be considered a primary criterion in the pack's design and architecture.
Due to this, the mix design procedures have to be revised to include durability as a primary criterion along with strength and workability.
The upper limit of internal diameter (ULID) of oscillating heat pipes (OHPs) based on Bond number is widely accepted and considered as a primary criterion to define OHPs, whereas the lower limit of internal diameter (LLID) is still unclear.
Along with this, air-and-water systems are used primarily for perimeter building spaces with high sensible loads and where close control of humidity is not a primary criterion.
Similar(30)
A primary criteria for one's spirit being elevated is a sense of "reverent joy," as mentioned by Ben's spirit friends.
For the evaluation purposes a group of criteria have been assumed, from a primary criteria set, by a superiority matrix, simultaneously taking into account the criteria hierarchy.
A longer period of activity is a primary criteria for the selection.
Binding kinetics and affinity (a primary criteria in antibody humanization) measurements comparing 3D6 with bapineuzumab were carried out by surface plasmon resonance.
These populations were chosen based on a single primary criterion: having sufficient cranial ontogenetic series available in museum collections.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com