Record Mahler Measures by Degree

This table shows the polynomial of degree D having the smallest known Mahler measure among all primitive, irreducible, noncyclotomic polynomials of this degree.
  D  Measure        Out Coefficients
  8  1.280638156268   1  1 0 0 1-1
 10  1.176280818260   1  1 1 0-1-1-1
 12  1.227785558695   2  1 1 1 0-1-1-1
 14  1.200026523987   1  1 0 0 1-1 0 0-1
 16  1.224278907222   2  1 1 0-1-1 0 1 1 1
 18  1.188368147508   1  1 1 1 1 0 0-1-1-1-1
 20  1.212824180989   2  1 1 0 0 1 1 0-1-1-1-1
 22  1.205019854225   2  1 0 1 0 0 1-1 1 0 0 1-1
 24  1.218855150304   2  1 0 0 0 0 1 0-1 0 0 0 0-1
 26  1.223777454948   3  1 1 1 0 0-1-1-1-1 0 0 1 0 1
 28  1.207950028412   2  1 1 1 1 0 0 0-1-1-1-1 0 0 0 1
 30  1.225619851977   2  1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1
 32  1.236083368052   4  1 1 1 1 0-1-1-2-1 0 0 1 1 0 0 0-1
 34  1.220287441693   3  1 0 1 0 0 1-1 1-1 0 0-1 1-1 0 0-1 1
 36  1.226493301473   2  1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0-1-1
 38  1.223447381419   3  1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1-1
 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
 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
 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
 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
 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
 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
 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
 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
 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
 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
 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
 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
 64  1.246918808403   4  1 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 0-1-1
 66  1.245397804852   7  1 0 1 0 0 0-1 0-1 0 0 0 1 1 1 1 0 0-1-1-1-1-1 0 0 1 1 1 1 0 0-1-1-1
 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
 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
 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
 74  1.246055240158   7  1 0 0 0 0 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 0 0 0 0-1
 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
 78  1.245376549311   8  1 0 1 0 0 0-1 0-1 0 0 0 1 1 1 1 0 0-1-1-1-1 0 0 1 1 1 1 1 0 0-1-1-1-1 0 0 1 1 1
 80  1.245374741297   6  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 0 0 1 1 0-1-1 0 0-1-1 0 1 1 1
 82  1.244967734300   8  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 1 0 0-1-1-1 0 0 1 1 1 1 0 0-1-1
 84  1.247632944895   8  1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0-1 0 0 0 0 0 0 0 0 0 0-1
 86  1.244953592390   7  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 0-1-1-1-1 0 0 0 1 0 0 1
 88  1.245922202165   8  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 0 0 0 1 0-1 0 0 0 0-1 0 1 0-1-1 0 1 0-1
 90  1.246403127917   9  1 0 1 0 0 0-1 0-1 0 0 0 1 1 1 1 0 0-1-1-1-1 0 0 1 1 1 1 0 0-1-1-1-1-1 0 0 1 1 1 1 0 0-1-1-1
 92  1.252142335381   8  1 0 0 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 0 0 0 0-1 0 0 0 0 0 0-1
 94  1.247133538468   9  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 1 0 0-1-1-1-1 0 0 1 1 1 0 0-1-1-1-1 0 0 1 1
 96  1.247821565271  10  1 1 1 1 0 0-1-2-2-2-1 0 1 1 2 2 1 1-1-1-1-2-1-1 0 1 1 1 1 1 0 0-1-1 0-1 0 0 0 1 1 1 1 1 0 0-1-2-1
 98  1.247395763109   9  1 1 0 0 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 0-1-1-1-1 0 0 0 1 0 0 1 0 0 0-1
100  1.247365098370   8  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 0-1-1-1-1 0 0 0 1 1 1 1 0 0 0-1 0 0-1
102  1.249660707891  10  1 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
104  1.248728765520   8  1 1 0 0 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 0 0 1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1-1-1
106  1.247521509928   7  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 0 0 0 0 0 0-1 0 0-1 0-1 0 0-1
108  1.248548224284  10  1 1 0 0 0 0 0-1-1 0 1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1-1-1-1-1 0 1 1 1
110  1.249288091898   9  1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0-1 0 0 0 0 0 0-1
112  1.248321136171  10  1 1 0 0 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 0-1-1-1-1 0 0 0 1 1 1 1 0 0 0-1 0 0-1 0 0 0 1
114  1.249322264468  11  1 0 1 0 0 0-1 0-1 0 0 0 1 1 1 1 0 0-1-1-1-1 0 0 1 1 1 1 0 0-1-1-1-1 0 0 1 1 1 1 0 0-1-1-1-1-1 0 0 1 1 1 1 0 0-1-1-1
116  1.248698859023   8  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 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
118  1.248967950284   9  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 0 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
120  1.249609817678   8  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 0 0 0 0 0 0-1 0 0-1 0-1 0 0-1 0 0 0 0 0 0 1
122  1.249031297239   8  1 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 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 1
124  1.249683442455  10  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 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
126  1.250069298300  13  1 0 1 0 0 0-1 0-1 0 0 0 1 0 1 0 0 0-1 1-1 1 0 0 1-1 1-1 0 0-1 1-1 1 0 0 1-1 1-1 0 0-1 1-1 1-1 0 0-1 1-1 1 0 0 1-1 1-1 0 0-1 1-1
128  1.250216971882  12  1 1 0 0 0 0 0-1-1 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 1 1 1 0 0 0-1-1-1-1 0 0 0 1 0 0 1 0 0 0-1 0 0-1
130  1.249411774638   9  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 0-1-1-1-1 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
132  1.249944664586  12  1 1 0 0 0 0 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 1 1 1 1 0-1-1-1-1
134  1.250915488642  11  1 0 0 0 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 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 0 0 0-1
136  1.249298451244  10  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 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 0 0-1 0 0 0 0-1
138  1.250834413573  13  1 1 0 0 0 0 0-1-1 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 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 0 1 1 0-1
140  1.250134713249  12  1 1 0 0 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 0-1-1-1-1 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 0 0 0 1
142  1.250491110615  13  1 1 1 1 0 0-1-2-2-2-1-1 0 1 2 3 2 2 1 0-1-3-3-3-2-1 0 2 3 4 3 2 1-1-2-4-4-3-2 0 1 3 4 4 3 1 0-2-3-4-4-2-1 1 2 3 4 3 2 0-1-2-3-3-3-2-1 0 1 2 3 3
144  1.250546050060  12  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 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 0 0 0 1 0-1 0 0 0 0-1 0 1 0-1-1 0 1 0-1
146  1.250575085448  10  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 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 0 0 0 0 0 0 0 0 0 0 1 0 0 1
148  1.252199127296  15  1 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
150  1.251108319032  15  1 0 1 0 0 0-1 0-1 0 0 0 1 0 1 0 0 0-1 1-1 1 0 0 1-1 1-1 0 0-1 1-1 1 0 0 1-1 1-1 0 0-1 1-1 1 0 0 1-1 1-1 0 0-1 1-1 1-1 0 0-1 1-1 1 0 0 1-1 1-1 0 0-1 1-1
152  1.251074088668  14  1 1 0 0 0 0 0-1-1 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 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 0 1 0-1-1 0 1
154  1.250924840187  13  1 1 0 0 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 0-1-1-1-1 0 0 0 1 1 1 1 0 0 0-1-1-1-1 0 0 0 1 1 1 1 0 0 0-1-1-1-1 0 0 0 1 0 0 1 0 0 0-1
156  1.252026213532  17  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 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 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
158  1.251786747324  15  1 1 0 0 0 0 0-1-1 0 0 0 0 0 1 0-1 0 0 0 0-1 0 1 0 0 0 0 1 0-1 0 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 0 0 0-1 0 1 0-1-1 0 1 0-1 0 1 1 0-1 0 1
160  1.251047012291  14  1 1 0 0 0 0 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 1 1 1 1 0-1-1-1-1
162  1.251157541114  15  1 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0-1
164  1.252712341185  20  1 1 1 0 0-1-1-1 0 0 0 0 0 0 0 1 1 1 0 0-1-1-1 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 0 0 0 0 1 1 0 0 0 0-1 0 0 0-1 0 0 0 0 1 1 0 0 0 0-1 0 0 0-1
166  1.251350589196  11  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 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 0 0 0 0 0 0-1 0 0-1 0-1 0 0-1
168  1.251995991922  18  1 1 1 1 0 0-1-2-2-2-1 0 1 2 3 3 2 1-1-2-3-4-3-2 0 1 2 3 3 3 1 0-1-2-2-3-2-1 0 1 1 2 2 2 1 0 0-1-1-2-2-1-1 0 0 1 2 2 2 1 1 0-1-2-2-1-1 0 0 1 2 1 1 0 0 0-1-1-1 0 0 0 0 0 1
170  1.251626125645  12  1 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 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 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 1
172  1.251591664820  16  1 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0-1
174  1.251581047533  15  1 1 0 0 0 0 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1 0 0-1-1 0 1 1 0 0 1 1 0-1-1-1-1-1-1 0 1 1 1 1
176  1.251742034014  12  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 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 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
178  1.252048808972  18  1 0 1 0 0 0 -1 0 -1 0 0 0 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 1 0 0 -1 -1 -1 -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 1 1 0 0 -1 -1 -1 -1 0 0 1 1 1 1 0 0 -1 -1
180  1.251754136161  16  1 1 0 0 0 0 0 -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 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 0 0 0 -1 0 1 0 0 0 0 1 0 -1 0 1 1 0 -1 0 1 0 -1 -1 0 1
History

December 20, 1996: Original list published.
January 31, 2000: New records found for degrees 178 and 180 (Petr Lisonek).
Return to choose another record.
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Last modified June 5, 2009.