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The phrase "are the primary problem" is correct and usable in written English.
It can be used when identifying or discussing the main issue or challenge in a particular context.
Example: "The lack of communication and resources are the primary problem affecting the project's success."
Alternatives: "are the main issue" or "constitute the central challenge".
Exact(5)
"Windows, doors and peeling paint are the primary problem areas," Mr. Wiles said, even though lead has been banned from paint made for residential use since 1978.
Although two out of the three recalls listed in the editorial — spinach, hamburger patties and seafood — involved domestically produced food, the remainder of the editorial focuses solely on imported food with the implication that imports are the primary problem.
Low and unstable gas production rates in individual wells are the primary problem for the CBM development in the Fanzhuang Block.
Friday are the longest crime trending days of the week, with stable trends form 1 pm–10 pm, with a prominent 5 pm–7 pm 'rush hour' peak Fig. 10 Temporal analysis of robbery cluster #3 (n = 165 robberies) is different from previous robbery clusters, since it shows that weekday afternoon robberies are the primary problem in this cluster.
I think it is very unlikely that any of those are the primary problem.
Similar(55)
Where are your above-reproach polls showing taxes and regulation are the primary problems facing small business?
Brittle failure in marble and squeezing in schist are the primary problems in tunnelling.
"Ignorance and indolence is the primary problem.
Dehydration is the primary problem for athletes.
More broadly, Diffie wrote, "I am not convinced that lack of encryption is the primary problem.
Creative consistency has been the primary problem, followed by an industrywide downturn in DVD sales.
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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