An ammunition primer assembly is provided that includes, but is not limited to a cup having a base and a sidewall, a priming composition located in the cup and disposed on the base, an anvil located in the cup an upper surface, a lower surface and a side surface abutting the sidewall. The anvil defining a central channel formed therethrough. A portion of the base of the cup forms a striking surface. The striking surface is adjacent to a portion of the primer composition that is adjacent to the lower surface of the anvil. The striking surface is offset from a center of the cup.