We　design　infeasible　potential　reduction　algorithms　for　primal　semidefinite　programming　(SDP)　problems　that　simultaneously　seek　feasibility　and　optimality.　The　algorithms　are　based　on　those　in　[Anstreicher,　Math.　Prog.　52　(1991),　pp.429-439]　and　[Todd,　Math.　Prog.　59　(1993),　pp.133-150]　for　linear　programming.　Because　a　dual　algorithm　is　expected　to　be　computationally　advantageous　for　large　sparse　problems,　we　also　propose　a　dual　infeasible　potential　reduction　algorithm　for　dual　SDP　problems.　We　analyze　the　convergence　of　the　algorithms,　and　implement　them　to　compare　their　relative　performance.