Lists of Polynomials with Small Mahler Measure

Complete List to Degree 44

The complete list of irreducible, noncyclotomic polynomials having degree
at most 44 and Mahler measure below 1.3.

Known Polynomials Through Degree 72

All known irreducible, noncyclotomic polynomials with degree at most 72 and
Mahler measure below 1.3 (143K html).
This list is known to be complete through degree 44, and in addition, the
smallest measure listed for each degree is known to be the minimal
nontrivial measure for an algebraic number of this degree up to degree 54.

Known Polynomials Through Degree 180

All known irreducible, noncyclotomic polynomials with degree at most 180 and
Mahler measure less than 1.3 (125K gzip'd text).
This includes 42 new polynomials with
degree at least 174 found by Petr Lisonek in January 2000,
19 additional polynomials with
degree at least 174 found by Georges Rhin and JeanMarc SacEpée in
2003, and three more polynomials (one each of
degrees 46, 48, and 52), found by Rhin, Mossinghoff, and Wu in 2008.

Small Salem Numbers

All known Salem numbers less than 1.3.
This list is known to be complete through degree 44.
 More Salem Numbers

Complete lists of Salem numbers with fixed degree, up to the indicated
bound, M.
 Degree 4, M = 3.
 Degree 6, M = 2.8.
 Degree 8, M = 2.6.
 Degree 10, M = 2.4.
 Degree 12, M = 2.2.
 Degree 14, M = 2.
 Degree 16, M = 1.8.
 Degree 18, M = golden ratio.
 Degree 20, M = golden ratio.
 Degree 22, M = 1.5.
 Degree 24, M = 1.4.
An explanation of the format used in
the tables.
Return to the Lehmer's Problem home page.
mimossinghoff "at" davidson "dot" edu
Last updated August 10, 2011.