Across the world (1)/ discussions on curing cancer are any longer (2)/ just wishful thinking. (3)/ No error. (4)

Answer

2

Explanation

are no longerwill replace are any longer.no longer can be used in the middle of sentence. any longer is used only at the end of a sentence.
Look at the examples given below:
She doesn.t work here any longer (any more).
She no longer works here.