When large language models encounter conflicting information in context, which memories survive -- early or recent? We adapt classical interference paradigms from cognitive psychology to answer this question, testing 39 LLMs across diverse architectures and scales. Every model shows the same pattern: proactive interference (PI) dominates retroactive interference (RI) universally (Cohen's d = 1.73, p < 0.0001), meaning early encodings are protected at the cost of recent information -- the opposite of human memory, where RI typically dominates. Three findings indicate that RI and PI reflect separate memory mechanisms. RI and PI are uncorrelated (R^2 = 0.044), rejecting a unified "memory capacity." Model size predicts RI resistance (R^2 = 0.49) but not PI (R^2 = 0.06, n.s.) -- only RI is capacity-dependent. And error analysis reveals distinct failure modes: RI failures are passive retrieval failures (51%), while PI failures show active primacy intrusion (56%); both show <1% hallucination. These patterns parallel the consolidation-retrieval distinction in cognitive science, suggesting that transformer attention creates a primacy bias with direct implications for interference-heavy applications.