I want to join multiple lines in a file based on a pattern that both lines share.

This is my example:

{101}{}{Apples}
{102}{}{Eggs}
{103}{}{Beans}
{104}...
...

{1101}{}{This is a fruit.}
{1102}{}{These things are oval.}
{1103}{}{You have to roast them.}
{1104}...
...

I want to join the lines {101}{}{Apples} and {1101}{}{This is a fruit.}

to one line {101}{}{Apples}{1101}{}{This is a fruit.} for further processing.

Same goes for the other lines.

As you can see, both lines share the number 101, but I have no idea how to pull this off. Any Ideas?

/EDIT:

I found a "workaround":

First, delete all preceding "{1" characters from group two in VISUAL BLOCK mode with C-V (or similar shortcut), then sort all lines by number with :%sort n, then join every second line with :let @q = "Jj" followed by 500@q.

This works, but leaves me with {101}{}{Apples} 101}{}{This is a fruit.}. I would then need to add the missing characters "{1" in each line, not quite what I want. Any help appreciated.