Table[{Prime[i], Mod[Prime[i], 15]}, {i, 100}]

Table[{i, Mod[i^3, 541]},  {i, 541}]

Table[{i, Mod[i^5, 541]},  {i, 541}]

Table[{i, Mod[i^3, 241]},  {i, 241}]

Table[{i, Mod[i^5, 241]},  {i, 241}]

Table[{Prime[i], Mod[Prime[i], 9]}, {i, 100}]

Table[{i, Mod[i^3, 271]},  {i, 271}]

Table[{i, Mod[i^3, 163]},  {i, 163}]

Table[{i, Mod[i^3, 127]},  {i, 127}]