It is my understanding that class conflict is seen as the primary contradiction at least in this epoch of history. My question is, what are the new contradictions that formed under socialism thus far and what would be the theorized contradictions under communism? What was the primary contradiction during primitive communism? Or perhaps my questions show a fundamental misunderstanding, which if so I would like corrected. Thank you!
There’s no right answer to this, only the concrete conditions of each people in each epoch can tell. For instance, the main contradictions of the Soviet Union in 1922 were quite different from the main contradictions of the Soviet Union in 1953, yet you can argue they were both socialism if your understanding of socialism means the dictatorship of the proletariat.
Even if the Soviet Union abolished (for some time) the existence of exploitative classes after the collectivization of their rural economy, they still had a class contradiction between the imperialist class of the worldwide economy. Class contradictions would only cease after a worldwide victory of socialism over capitalism.
So, taking into consideration that this is a guessing game, like @PolandIsAStateOfMind@lemmygrad.ml said, and that each people will face different contradictions based on their historical development, I would say the main contradiction after a worldwide victory of socialism would probably to reduce the impact of climate change and research methods to revert them if possible. In fact, I would argue that the changing climate conditions are a major contradiction of our times right now, of course, subordinate to the class contradiction.
Under communism? No point in delving over something that far from now, we can’t tell what things will be like in a hundred years. The main focus of study of communists is not “communism,” but the current historical conditions of our times.
And this completely pisses off and desorient all manners of liberals and utopian socialists, who rather would fantasize about their ideal world without sudying the current one. And of course anarchists who don’t study neither.