Let p >= 5 be an odd prime. Using the correspondence between secondary Adams differentials and secondary algebraic Novikov differentials, we compute four families of nontrivial secondary differentials on the fourth line of the Adams spectral sequence. We also recover all secondary differentials on the first three lines of the Adams spectral sequence.

The authors are supported by the National Natural Science Foundation of China (No. 12271183). The third named author is also supported by the National Natural Science Foundation of China (No. 12001474; 12261091).