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Over algebraically closed fields of characteristic p>2, prolongations of thesimple finite dimensional Lie algebras and Lie superalgebras with Cartan matrixare studied for certain simplest gradings of these algebras. Several new simpleLie superalgebras are discovered, serial and exceptional, including superBrownand superMelikyan superalgebras. Simple Lie superalgebras with Cartan matrix ofrank 2 are classified.

New simple modular Lie superalgebras as generalized prolongs