Scalable Relational Database Design
So you're going to want to store your images on a fast CDN like Cloudfront. Normally I recommend storing pictures in-database, but not 240M of them :)

I'd avoid storing the whole URL, as it's likely to be repetitive. Just store the file name (a five-char case-sensitive name using a-z 0-9 would give you ~900M combinations. If your CDN is case-insensitive wrt URLs then use 6 chars ).

Are there really going to be 240M unique images, or can they be "shared" among entries? Do you expect every user to fill every entry with the max # of images?

You'd want some tables like this:

create table users (
  user_id serial primary key,
  ...
);

create table entries (
  entry_id serial primary key,
  user_id int not null references users(user_id), --index me
  description text,
  ...
);


create table pictures (
  file_name char(5) primary key,
  entry_id int not null references entries(entry_id) --index me
);


or perhaps:

create table pictures (
  picture_id serial primary key,
  file_name char(5) not null unique,
  entry_id int not null references entries(entry_id) -- index me
);


Use connection pooling!