That would be impossible to even guess. You have to analyze the results above you. You may need 0 backlinks, a million backlinks etc. Also It depends on the quality of the backlinks. 1 high quality backlink can outrank 10,000 crappy backlinks.
Also, you can have a page with no backlinks out rank a page with 1,000 backlinks just because the information on the page is more relevant to the search than the others. etc, etc, etc...
It seems like others have already touched on this, but they are right and I want to echo the sentiments of other posters. The best way to determine what you need to do would be to check out the domain authority or domain rank factors of your competitors, and set a goal of reaching or exceeding that. And as has also been said, quality over quantity, but diversity in your backlink profile is helpful.
You already have been given the ultimate answer that there is an unknowable amount of backlinks to make your website rank higher than others.
So now you have to think about the following:
- Increase the quality of your content
- Increase the quality and frequency of your content
- Increase the amount of backlinks
Each of these does different things for your website. Personally, I would start with increasing the QUALITY of your content over anything else. Google and other search engines are going to primarily analyze that CONTENT of your website rather than any other links coming to your site.
Increase the QUALITY of your content and you will start generating natural backlinks with others linking to it on their own. However, you could potentially do some guest blog posting on other blogs with a link back to your site if the content fits.