Screws Showing Through

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Hello  I made some sheetrock repairs fixing poped out screws and holes in my sheetrock. After I painted I noticed that I can see each and every repair that I made in the paint the circles from the screws I replaced and the smooth spots where I sanded . Is there some way for me to fix these problems without to much work and how can I prevent this in the future?  I did use a primer. Thanks for any help you can give   Kevin