In 1964, Schroeppel won first place in the United States among over 225,000 high school students in the Annual High School Mathematics Examination, a contest sponsored by the Mathematical Association of America and the Society of Actuaries.

Among other contributions, Schroeppel was the first to recognize the sub-exponential running time of certain integer factoring algorithms.

While not entirely rigorous, his proof that Morrison and Brillhart's continued fraction factoring algorithm ran in roughly

Schroeppel analyzed Morrison and Brillhart's algorithm,[4] and saw how to cut the run time to roughly

Coming around the time of the RSA algorithm, which depends on the difficulty of factoring for its security, this was a critically important result.

Due to Schroeppel's apparent prejudice against publishing (though he freely circulated his ideas within the research community), and in spite of Pomerance noting that his quadratic sieve factoring algorithm owed a debt to Schroeppel's earlier work, the latter's contribution is often overlooked.

(See the section on "Smooth Numbers" on pages 1476–1477 of Pomerance's "A Tale of Two Sieves," Notices of the AMS, Vol.