We prove that after adding a Silver real no ultrafilter from the ground model can be extended to a P-point, and this remains to be the case in any further extension which has the Sacks property. We use this result to show that there are no P-points in the Silver model or after adding Silver reals with the side by side product. In particular, we build models with no P-points where the continuum can be arbitrarily big. This is joint work with David Chodounský.