A test complex for Gorensteinness
  Let $R$ be a commutative noetherian ring with a dualizing complex. By recent work of Iyengar and Krause, the difference between the category of acyclic complexes and its subcategory of totally acyclic complexes measures how far $R$ is from being Gorenstein. In particular, $R$ is Gorenstein if and only if every acyclic complex is totally acyclic.   In this note we exhibit a specific acyclic complex with the property that it is totally acyclic if and only if $R$ is Gorenstein. 
Lars Winther Christensen and Oana Veliche