Top 100 Smallest Mahler Measures

This table lists the 100 smallest known Mahler measures among primitive, irreducible, noncyclotomic polynomials with integer coefficients.
        D  Measure         Out Coefficients
  1.)  10  1.176280818260   1  1 1 0-1-1-1
  2.)  18  1.188368147508   1  1 1 1 1 0 0-1-1-1-1
  3.)  14  1.200026523987   1  1 0 0 1-1 0 0-1
  4.)  18  1.201396186235   2  1 1 1 0 0-1 0-1 0-1
  5.)  14  1.202616743689   1  1 0-1 0 0 0 0 1
  6.)  22  1.205019854225   2  1 0 1 0 0 1-1 1 0 0 1-1
  7.)  28  1.207950028412   2  1 1 1 1 0 0 0-1-1-1-1 0 0 0 1
  8.)  20  1.212824180989   2  1 1 0 0 1 1 0-1-1-1-1
  9.)  20  1.214995700776   2  1 1 1 1 1 0-1-1-1-1-1
 10.)  10  1.216391661138   1  1 0 0 0-1 1
 11.)  20  1.218396362520   2  1 1 0-1 0 0 0-1 0 0 1
 12.)  24  1.218855150304   2  1 0 0 0 0 1 0-1 0 0 0 0-1
 13.)  24  1.219057507826   2  1 1 0-1-1-1-1-1 0 1 1 1 1
 14.)  18  1.219446875941   3  1 1 1 0-1-1-1 0 0 1
 15.)  18  1.219720859040   1  1 1 0 0 0 0 0 0-1-1
 16.)  34  1.220287441693   3  1 0 1 0 0 1-1 1-1 0 0-1 1-1 0 0-1 1
 17.)  38  1.223447381419   3  1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1-1
 18.)  26  1.223777454948   3  1 1 1 0 0-1-1-1-1 0 0 1 0 1
 19.)  16  1.224278907222   2  1 1 0-1-1 0 1 1 1
 20.)  18  1.225503424104   2  1 1 0 0 1 0-1 0 0-1
 21.)  30  1.225619851977   2  1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1
 22.)  30  1.225810532354   3  1 0 1 0 0 0-1 1-1 1-1 0 0-1 1-1
 23.)  26  1.226092894512   2  1 0 0 1 0 0 0 0 0 0 1 0 0 1
 24.)  36  1.226493301473   2  1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0-1-1
 25.)  20  1.226993758166   2  1 1-1-2 0 2 1-1-1 0 1
 26.)  12  1.227785558695   2  1 1 1 0-1-1-1
 27.)  30  1.228140772740   3  1 1 0 0 0-1-1-1-1 0 0 0 1 0 0 1
 28.)  36  1.229482810173   4  1 1 1 0 0-1-1-1 0 1 1 1 0-1-2-1 0 1 1
 29.)  22  1.229566456617   3  1 1 0-1-1-1-1-1 0 1 1 1
 30.)  34  1.229999039697   3  1 0 0 0 0 0-1 0 0 0 0 1 0 0 0 0 0-1
 31.)  38  1.230263271363   3  1 0 0 0-1 0 0 0 0 0 0 0 0 0 0 1 0 0 0-1
 32.)  42  1.230295468643   4  1 0 1 0 0 0-1 1-1 1 0 0 1-1 1-1 1 0 0 1-1 1
 33.)  10  1.230391434407   1  1 0 0 1 0 1
 34.)  46  1.230743009076   3  1 0 0 1 0 1 0 0 1 0 0 0 0 0 0-1 0 0-1 0-1 0 0-1
 35.)  18  1.231342769993   3  1 0 0 0-1 1 0 0 0-1
 36.)  48  1.232202952743   4  1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1-1-1
 37.)  20  1.232613548593   1  1 1 0 0 0 1 1 0 0 1 1
 38.)  28  1.232628775929   2  1 2 2 1 1 1 0-1-1-1-1-1-1-1-1
 39.)  38  1.233672001767   3  1 1 0-1-1-1-1 0 1 1 0 0 0 0 0 1 1 0-1-1
 40.)  52  1.234348374876   4  1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 1
 41.)  24  1.234443834873   2  1 0 0 0-1 0-1 1 0 0 1-1 1
 42.)  26  1.234500336789   3  1 0-1 1 0-1 1 0-1 1 0-1 0 1
 43.)  16  1.235256705642   2  1 1 0 0 0-1 0 0-1
 44.)  46  1.235496042193   3  1 0-1 0 0 0 0 1 0-1 0 0 0 0 1 0-1 0 0 0 0 1 0-1
 45.)  22  1.235664580390   1  1 0-1 1 0 0 0-1 1 0-1 1
 46.)  42  1.235761099712   4  1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1
 47.)  32  1.236083368052   4  1 1 1 1 0-1-1-2-1 0 0 1 1 0 0 0-1
 48.)  32  1.236198469859   3  1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1
 49.)  32  1.236227922245   4  1 2 2 1 0-1-1-1-1-1-1-1-1-1 0 2 3
 50.)  40  1.236249557349   3  1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1
 51.)  16  1.236317931803   1  1 1 0 0 0 0 0 0-1
 52.)  54  1.236566917569   5  1 0 1 0 0 0-1 1-1 1 0 0 1-1 1-1 0 0-1 1-1 1-1 0 0-1 1-1
 53.)  34  1.236579223637   3  1 0 0 0 0 1 0 0 0 0 0 0-1 0 0 0 0-1
 54.)  44  1.236674812187   4  1 0 0 0 0 0 0 1 0 0 0 0 0 0 0-1 0 0 0 0 0 0-1
 55.)  28  1.236808305865   2  1 1 0-1 0 0 0 0 0-1 0 0 0 0 1
 56.)  26  1.237504821217   1  1 0-1 0 0 1 0 0-1 0 1 0 0-1
 57.)  46  1.237634830280   5  1 1 0 0 0 0 0-1-1 0 0-1-1 0 1 0-1 0 1 1 0-1 0 1
 58.)  58  1.237684127894   5  1 1 0 0 0-1-1-1-1 0 0 0 1 1 1 1 0 0 0-1-1-1-1 0 0 0 1 0 0 1
 59.)  48  1.238040100176   4  1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0-1 0 0 0 0-1
 60.)  56  1.238431627359   4  1 1 1 1 0 0 0-1-1-1-1 0 0 0 1 1 1 1 0 0 0-1-1-1-1 0 0 0 1
 61.)  56  1.238708978554   4  1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0-1 0 0-1
 62.)  42  1.239505770490   4  1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1
 63.)  54  1.239747974875   6  1 1 1 0 0-1-1-1 0 0 0 0 1 1 1 1 1 0-1-2-2-2-1 0 1 1 1 1
 64.)  48  1.239861326360   4  1 2 3 3 2 0-2-3-3-2-1 0 0-1-2-2-1 0 1 1 1 1 1 1 1
 65.)  60  1.240061859037   4  1 0 0 1 0 1 0 0 1 0 0 0 0 0 0-1 0 0-1 0-1 0 0-1 0 0 0 0 0 0 1
 66.)  26  1.240254178706   3  1 1 0-1-1 0 0 0-1 0 1 1 0-1
 67.)  50  1.240379074717   3  1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0-1-1
 68.)  28  1.240699637594   2  1 2 3 3 2 1 0-1-1-1-1-1-2-3-3
 69.)  12  1.240726423653   1  1 1 1 1 0 0-1
 70.)  18  1.240770634960   2  1 0 1 0 1 0 0 1-1 1
 71.)  54  1.240983403460   5  1 0 0 0 0 0 0 0-1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0-1
 72.)  68  1.241372531335   6  1 1 0 0 0 0 1 0-1 0 0 0 0-1 0 1 0 0 0 0 1 0-1 0 0 0 0-1 0 1 0-1-1 0 1
 73.)  70  1.241422024928   5  1 1 0-1-1-1-1 0 1 1 0 0 0 0 0 1 1 0-1-1-1-1 0 1 1 0 0 0 0 0 1 1 0-1-1-1
 74.)  58  1.241541076676   5  1 0 1 0 0 1-1 1-1 0 0-1 1-1 1 0 0 1-1 1-1 0 0-1 1-1 0 0-1 1
 75.)  72  1.241788568356   6  1 1 0 0 0-1-1-1-1 0 0 0 1 1 1 1 0 0 0-1-1-1-1 0 0 0 1 1 1 1 0 0 0-1 0 0-1
 76.)  58  1.241902161200   6  1 0 1 0 0 0-1 0-1 0 0 1 1 1 1 0 0-1-1-1 0 0 1 1 1 1 0 0-1-1
 77.)  50  1.241974375265   4  1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1
 78.)  58  1.242217045566   5  1 1 1 0-1-2-2-1 0 1 1 1 0 0 0 1 1 1 0-1-2-2-1 0 1 1 1 0 0-1
 79.)  52  1.242362139933   5  1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1
 80.)  58  1.242610289442   5  1 0 0 0 0 0-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0-1
 81.)  76  1.242775741593   5  1 0 0 1 0 1 0 0 1 0 0 0 0 0 0-1 0 0-1 0-1 0 0-1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1
 82.)  50  1.242878658278   5  1 0 0 0 0 0 0 0 0 0 0 0-1 1 0 0 0 0 0 0 0 0 0 0 0-1
 83.)  32  1.242940115199   2  1 1 0 0 0 0 0 0 0 0 0 0 0 0 0-1-1
 84.)  70  1.242979209676   7  1 0 1 0 0 0-1 0-1 0 0 1 1 1 1 0 0-1-1-1-1 0 0 1 1 1 0 0-1-1-1-1 0 0 1 1
 85.)  60  1.243027765980   6  1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0-1 0 0 0 0 0 0 0 0 0 0 0 0-1
 86.)  30  1.243128704866   3  1 1 1 1 1 0-1-1-1-1-1 0 0 0 0 1
 87.)  72  1.243210037398   6  1 1 1 1 1 1 0-1-2-2-2-2-1 0 2 3 3 3 2 1-1-3-4-4-3-2 0 2 4 5 4 3 1-1-3-5-5
 88.)  16  1.243477618690   2  1 1 0-1-1-1 0 1 1
 89.)  60  1.243486256656   4  1 0-1 0 0 0 0 1 0-1 0 0 0 0 1 0-1 0 0 0 0 1 0-1 0 0 0 0 1 0-1
 90.)  46  1.243564793293   4  1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1
 91.)  46  1.243682745689   5  1 0 1 0 0 0-1 0-1 0 0 1 1 1 0 0-1-1-1-1 0 0 1 1
 92.)  28  1.243878801656   2  1 1 1 1 1 1 0 0 0-1-1-1-1-1-1
 93.)  56  1.243935933206   6  1 1 1 0 0-1-1-1 0 1 1 1 0 0-1 0 0 1 0 0-1-1-1-1 0 0 1 0 1
 94.)  60  1.244271476892   6  1 1 0 0 0 0 0-1 0 1 0 0 0 0 1 0-1 0 0 0 0-1 0 1 0-1-1 0 1 0-1
 95.)  70  1.244273644932   5  1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0-1 0 0-1
 96.)  40  1.244414501983   4  1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0-1-1
 97.)  62  1.244598861428   6  1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1
 98.)  18  1.244617058976   3  1 0-1 0 1 0-1 0 0 1
 99.)  76  1.244729172444   6  1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0-1 0 0 0 0-1
100.)  22  1.244802445450   2  1 0 0 1 0 0 0 0 0 0 0-1


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Last modified June 5, 2009.