Problem

Source: Spain MO 2024 P1

Tags: number theory, Spain



Consider 2024 distinct prime numbers $p_1, p_2, \dots, p_{2024}$ such that \[p_1+p_2+\dots+p_{1012}=p_{1013}+p_{1014}+\dots+p_{2024}.\]Let $A=p_1p_2\dots p_{1012}$ and $B=p_{1013}p_{1014}\dots p_{2024}$. Prove that $|A-B|\geq 4$.