I have two vectors, X and Y

I perform a correlation test using them

cor.test(x, y)

From this, I get a p value and a correlation value, among other things.

In a manuscript, I report my results like so:

Pearson’s r(283) = 0.943, p < 2.2e-16

I have been asked to define which statistical test is being used. It was my understanding that Pearson's correlation test was itself the test. Is this incorrect?

I have read that a student's T test can be used to calculate the p value for the hypothesis test, which I believe is testing the hypothesis that the true correlation is 0.

Does the R language use a T-test for the p value by default in `cor.test()`

? Or is it correct to say that Pearson's is itself the test?

Thank you. Based on this, is it correct to say that a Student's t-test is being peformed?

Its a test based on the t-statistic, but I probably wouldn't go as far as saying a t-test was being performed. Both in its original usage (https://www.york.ac.uk/depts/maths/histstat/student.pdf) and in common usage the term "t-test" implies a test for the difference between the means of two populations. That is not what is being don't here, even if the underlying distribution is the same.

which value is selecting for pearson correlation ? is p-value or logfc value i want to find the cis and trans target gene ? can you help me please