How Many Samples Are Identical In Linear and Circular Convolution Result?
assuming $y[n]$ is padded with $L-P$ zeros (to make it the same length as $x[n]$ and your circular convolution length), then the number uncorrupted samples is $L-P+1$.

you might want to Google "Overlap Save" (OLS, a better name i have read is "Overlap-Scrap"), which is directly about this issue of uncorrupted samples in circular convolution.  the alternative is "Overlap Add" (OLA) which has no corrupted samples, but you have to overlap the tails of each block and add them.

this is well covered in books like O&amp;S.