I believe that www.yojijukugo.com has a pretty thorough list of 四字熟語? Is there a better site?

However, I know that I've seen a lot of 4, or more, adjacent kanji that are not listed as 熟語。An example is "原子発電{げんしはつでん}"。

1. When I see 4 adjacent kanji that are not listed as 熟語、then that just means "の" is being omitted (to save space when printed). From context, you know the meaning without the "の".
2. You say "原子発電" instead of "原子の発電" just as an extension of what is done when writing.
3. real 四字熟語 are pretty rare, so you must assume that 4 kanji in a row is not a 四字熟語 until you can prove it in a dictionary, right?
4. The ability to omit "の" when, by context, everyone knows it is there, allows you to say stuff like "愛国精神{あいこくせいしん}", "愛社精神{あいしゃせいしん}", "愛人種精神{あいじんしゅせいしん}", etc. right? The technique is, if the "の" is obvious by context, you don't necessarily have to say it?

I believe that www.yojijukugo.com has a pretty thorough list of 四字熟語? Is there a better site?

However, I know that I've seen a lot of 4, or more, adjacent kanji that are not listed as 熟語。An example is "原子発電{げんしはつでん}"。

1. When I see 4 adjacent kanji that are not listed as 熟語、then that just means "の" is being omitted (to save space when printed). From context, you know the meaning without the "の".
2. You say "原子発電" instead of "原子の発電" just as an extension of what is done when writing.
3. real 四字熟語 are pretty rare, so you must assume that 4 kanji in a row is not a 四字熟語 until you can prove it in a dictionary, right?
4. The ability to omit "の" when, by context, everyone knows it is there, allows you to say stuff like "愛国精神{あいこくせいしん}", "愛社精神{あいしゃせいしん}", "愛人類精神{あいじんるいせいしん}", etc. right? The technique is, if the "の" is obvious by context, you don't necessarily have to say it?