Starting collaboration through first e-mail. Can it work? I was an undergrad student with Professor X a few years back. Prof. X used to be a co-author in all the publications with Prof. Y. Prof. Y is very popular in the field.

Now, I am working in a university. I have keen interest to work with Prof. Y on a few problems of interest.

I have less idea on how to collaborate in such a situation where I don't have indirect contact apriori. The option that I have is to send a mail to him which looks as follows:


  Subject: Request for collaboration -- Problem A and Problem B
  
  Dear Prof. Y
  
  Greetings!
  
  I have learned about you from Prof. X during my works with him.
  
  I have gone through your recent papers: [this] and [this]. I am good in Method1 and Method2 which could suitably address your problem.
  
  My recent works can be found in [this profile link].
  
  Looking forward to hearing from you.
  
  Sincerely,
  
  me
  
  --
  [my signature]


Is this approach a suitable for my collaboration with Prof. Y?

Update: I had sent an email to Prof. Y after incorporating the suggestions from the fellow academia.SE community members here. I got a response from Prof. Y and looks like he is also interested in working together.
Let's elaborate on my comment in this answer. Here are the issues:


There are just statements in your draft, no actual question.
The tone of the mail is a bit informal for the case you don't know Prof. Y (at least in my opinion). Leaving out the "Greetings" will make it better.


Here's my proposal for the mail:


  Subject: Request for collaboration -- Problem A and Problem B
  
  Dear Prof. Y,
  
  I have learned about you from Prof. X during my works with him.
  
  I have gone through your recent papers: [this] and [this]. Recently, I have worked with Method1 and Method2 which could suitably address your problem. Would you be interested to (Removed: collaborate on [thing] with me?) talk with me about the topic in a phone call or meeting? It would be a pleasure to work with you on this topic.
  
  My recent works can be found in [this profile link].
  
  Looking forward to hearing from you.
  
  Sincerely,
  
  me
  
  -- [my signature]