The phrase "a principal problem" is correct and usable in written English.
It can be used when discussing a major or primary issue that needs to be addressed or solved.
Example: "The report highlighted a principal problem in the company's supply chain that required immediate attention."
Alternatives: "a major issue" or "a key concern".
A principal problem of insurance risk theory is to find the probability of ultimate ruin.
A principal problem for the law is to keep various kinds of experimentation within bounds.
The unaffordability of staying out the labour market for extended periods is cited as a principal problem by these women.
Estimating the number (cardinality) of Radio Frequency Identification (RFID) tags is a principal problem for large-scale RFID systems.
The government authorities across the globe and experts mention that the dumping of plastics waste and non-biodegradable is a principal problem of the dangerous environmental pollutions.
Few details were available, but tentative plans would call for new writers to collaborate on the book, by the Nobel Prize-winning poet Derek Walcott, which many critics said was a principal problem with the show.
Author's response: While preparing the paper we faced an obvious principal problem as proving a nonexistence of anything is usually difficult and to some extend dubious.
Reconstruction of a gene evolution along a species tree is an interesting and principal problem.
The comic characters Mr. De Niro has been playing in the last few years, like Louis and the smiler-with-a-knife political consultant of "Wag the Dog" (1997), represent, I think, an ingenious solution to his principal problem as an actor: how to use his enormous reserves of power without becoming predictably, formulaically "powerful".
This is the principal problem with a system of support that is based on historical data - it does not reflect current reality.
"I had done well on the skis I wore today in training, too". Rahlves's principal problem was a serious mistake he made just out of the gate.
