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The phrase "are primarily based" is correct and usable in written English.
It can be used to indicate the main foundation or source of something, often in academic or analytical contexts.
Example: "The conclusions of the study are primarily based on the data collected from the surveys conducted over the past year."
Alternatives: "are mainly founded" or "are chiefly derived".
Exact(60)
The methodologies for synthesising Au-based nanoparticles are primarily based on colloidal methods, and to a lesser extent impregnation methods.
These products are primarily based on Arm's V8 technology.
Most other banks are primarily based in urban areas.
Current treatment approaches are primarily based on clinical stage.
Safety shoe designs are primarily based on safety requirements.
All financial aid awards are primarily based on the applicant's demonstrated financial need.
Other research into how donors choose charities showed that giving decisions are primarily based on personal tastes, preferences and experiences.
As I have mentioned before, these standards are primarily based on bird habitat quality.
Material relationships are primarily based upon data obtained from inspection campaigns at operating reactors.
Credit Suisse and Goldman Sachs will offer the shares mostly to fund managers whose portfolios are primarily based on stock indexes, AT&T said in the S.E.C. filings.
These allegations, many 10 to 15 years old, are primarily based on NASA's own self-audits, for which corrective action has been taken or is in progress.
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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