Hello. I’m currently a HS junior looking for summer programs to apply to. I’ve read probably every post on here and AoPS and am interested in these four math programs. Math is my favorite subject. I have a passion for it, so I will definitely try my hardest at the applications. I have right now three full pages of LaTeX for one of the application problems that I haven’t even finished yet! I was wondering which of these four programs would look the best on college applications/would benefit me the most. I’ve learned that PROMYS and ROSS and very similar and structured toward number theory, whereas HCSSiM is more variable and Mathcamp is everything in between. I’m looking for a combination of prestige and benefit. I’ve seen a little bit into the structure of each program, but what I really want is which one(s) I should apply to. It seems too brutal to apply to all four and have a good chance. I would rather apply to one or two but with a really kickass application with delved-into math concepts and reasoning than applying to all four half-assedly. Anyone have any suggestions? If nothing else I’d like to eliminate one or two. Thank you for taking the time to read and respond. 
years back my DS enjoyed PROMYS and living in Boston was a lot of fun FWIW. First time he realized HE wasn’t the only one great at math. He had always soared above his peers. At PROMYS he was average or a bit below. He thought that was good for him… he is finishing his PhD in Math this year
@Jacob42 - I heard great things about all 4 - agree that applying to all of them can be brutal. I am applying myself and FWIW my approach in eliminating was based on camp dates and general feel/subject areas of the camp. Ross is starting much earlier in early June before our schools are done here in north east. So Ross is out for me. Among other three - I started with Mathcamp problem set and based on how/when I complete it, will go with one more. Why Mathcamp - I just liked the general vibe on that site and also attended the mathjam on AoPS and liked the general free-flowing aspect in terms of the camp subject. Also its in Denver which I never visited before. My next pref is for PROMYS for number theory but am not sure if I will be able to apply for this program as March is a busy time for me with multiple things going on, not sure if I can get enough time to do the application.
Good luck with your application process.