shell log

$ git log --graph --oneline --decorate --all
*   d11c4a4 (HEAD -> prod2) Merge commit 'aa689c2' into prod2
|\  
* \   3f11482 Merge branch 'fnord' into prod2
|\ \  
* | | 0e22a4b add b
| | | * 53e966a (prod1) Merge branch 'fnord' into prod1
| | |/| 
| | |/  
| |/|   
| * | 39bf86a (fnord) add fnord
|/ /  
| * aa689c2 add a
|/  
* c5420c3 (master) initial commit

$ git merge-base prod1 prod2
39bf86ad99e012bdf618365b372bc9c166e22017

$ git rev-parse fnord
39bf86ad99e012bdf618365b372bc9c166e22017

$ git log $(git merge-base prod1 prod2)..prod2
d11c4a48a71b021e9d453a31d94c0633fe9ed833 (HEAD -> prod2) Merge commit 'aa689c2' into prod2
3f11482a284eab953526c35f19794e4d5a2b06e7 Merge branch 'fnord' into prod2
0e22a4b2eca03323de7906ec49234352f3c0fa12 add b
aa689c26010b9d2a9aa00390699321b46480b22e add a

git log prod1..prod2 gives the desired result (except that it includes merges).

(So you could do git log --no-merges prod1..prod2 to get what you want.)