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The phrase "a far greater problem" is correct and usable in written English.
It can be used when comparing the severity or significance of one problem to another, indicating that the problem in question is much more serious.
Example: "While the budget cuts are concerning, the lack of funding for essential services is a far greater problem that needs immediate attention."
Alternatives: "a much bigger issue" or "a significantly larger concern".
Exact(32)
"Car exhaust is a far greater problem".
Forget overbearing Brussels; a far greater problem is sleazy Westminster.
England have a far greater problem awaiting them: transition.
ISIS is a symptom of a far greater problem, not the cause.
A far greater problem is the excessive fawning over unsympathetic characters like Darla D. Moore.
But a far greater problem is the shortage of materials, including leather (reported Mr. Altuzarra).
Similar(28)
That absence is a far, far greater problem for the Tories than the fact that a bunch of young activists are being mocked on Twitter.
Candidate Trump correctly opined: "our far greater problem is not Assad, it's ISIS".
The far greater problem in the African-American community is the intimate partner homicide rate, wherein the intimate partner violence rate for African-American men is four times that of other races, and the rate for African-American women is over three times higher (Surveillance for Homicide Among Intimate Partners --United States, 1981-1998).
"The charcoal problem is really a symptom of the far greater problems we're facing," said Mr. Ali of the Somali research institute.
In short, the 70percentt rule makes the future seem secure and comfortable, even when it's not". No doubt this finding is an unpleasant truth, but it is also a possible contributing factor to far greater problems.
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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