Small Salem Numbers

There are 47 known Salem numbers less than 1.3. The most recently discovered Salem numbers are marked with an asterisk.

This list is known to be complete for degree at most 44. There is only one known small Salem numbers with larger degree.


       D   Salem Number                      Coefficients of Minimal Polynomial
  1.)  10  1.176280818259917506544070338474  1  1  0 -1 -1 -1
  2.)  18  1.188368147508223588142960958629  1 -1  1 -1  0  0 -1  1 -1  1
  3.)  14  1.200026523987391518902962100414  1  0  0 -1 -1  0  0  1
  4.)  14  1.202616743688604261118295415948  1  0 -1  0  0  0  0 -1
  5.)  10  1.216391661138265091626806311199  1  0  0  0 -1 -1
  6.)  18  1.219720859040311844169606760414  1 -1  0  0  0  0  0  0 -1  1
  7.)  10  1.230391434407224702790177938975  1  0  0 -1  0 -1
  8.)  20  1.232613548593121003962731694807  1 -1  0  0  0 -1  1  0  0 -1  1
  9.)  22  1.235664580389747308105169351531  1  0 -1 -1  0  0  0  1  1  0 -1 -1
 10.)  16  1.236317931803230489899094869802  1 -1  0  0  0  0  0  0 -1
 11.)  26  1.237504821217490608171021829989  1  0 -1  0  0 -1  0  0 -1  0  1  0  0  1
 12.)  12  1.240726423652541392056148161575  1 -1  1 -1  0  0 -1
 13.)  18  1.252775937410113900864582824053  1  0  0  0  0  0 -1 -1 -1 -1
 14.)  20  1.253330650201489757028162788986  1  0 -1  0  0 -1  0  0  0  0  0
 15.)  14  1.255093516763722879173091003232  1  0 -1 -1  0  1  0 -1
 16.)  18  1.256221154391670233067434043309  1 -1  0  0 -1  1  0  0  0 -1
 17.)  24  1.260103540354990920321649852331  1 -1  0  0 -1  1  0 -1  1 -1  0  1 -1
 18.)  22  1.260284236896492963739228435283  1 -1  0 -1  1  0  0  0 -1  1 -1  1
 19.)  10  1.261230961137138851946671503074  1  0 -1  0  0 -1
 20.)  26  1.263038139930169261222022798085  1 -1  0  0  0  0 -1  0  0  0  0  0  0  1
 21.)  14  1.267296442523068692734077407604  1 -1  0  0  0  0 -1  1
 22.)  22  1.276779674019016861136497157605  1 -1 -1  1  0  0  0  0  0 -1  0  1
 23.)   8  1.280638156267757596701902532710  1  0  0 -1 -1
 24.)  26  1.281691371528106310055107748672  1  0  0  0  0  0 -1 -1 -1 -1 -1 -1 -1 -1
 25.)  20  1.282495560639960169561207128806  1 -2  2 -2  2 -2  1  0 -1  1 -1
 26.)  18  1.284616550925536736743131441485  1  0  0  0 -1  0 -1 -1  0 -1
 27.)  26  1.284746821544843035729838140650  1 -2  1  1 -2  1  0  0 -1  1  0 -1  1 -1
 28.)  30  1.285099363651876557117420034512  1  0  0  0  0 -1 -1 -1 -1 -1 -1  0  0  0  0  1
 29.)  30  1.285121520153207532780681369174  1 -2  2 -2  1  0 -1  2 -2  1  0 -1  1 -1  1 -1
 30.)  30  1.285185670752909791356387310393  1 -1  0  0  0  0  0  0 -1  0  0  0 -1  0  0 -1
 31.)  26  1.285196726769853432068127270005  1  0 -1 -1  0  0  0  1  0 -1 -1  0  1  1
 32.)  44  1.285199179205612167312192383918  1 -1  0  0  0  0  0 -1  0  0  0 -1  0  0  0  0  0  0  0  1  0  0  1
 33.)  30  1.285235436228923770828415884707  1  0 -1  0  0 -1 -1  0  0  0  1  0  0  1  0 -1
 34.)  34  1.285409064765363764030309848277  1 -1  0  0 -1  1 -1  0  1 -1  1  0 -1  1 -1  0  1 -1
 35.)  18  1.286395966836277224044411092745  1 -2  2 -2  2 -2  2 -3  3 -3
 36.)  26  1.286730182048201274368747282841  1 -1  0  0 -1  1 -1  0  1 -1  1  0 -1  1
 37.)  24  1.291741425714500483635599066106  1 -1  0  0  0  0 -1  0  0  0  0  0  0
 38.)  20  1.292039106017929461943480560567  1  0 -1  0  0 -1  0  0 -1  0  1
*39.)  40  1.292418657582426546281031229140  1  0  0 -1  0 -1  0 -1  0 -1  0 -1  0  0  1  0  1  0  1  0  1
*40.)  46  1.292900721780102794630870596243  1  0  0  0 -1 -1 -1 -1  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1
 41.)  10  1.293485953125454106519909883794  1  0 -1 -1  0  1
 42.)  18  1.295675371944048235295741653561  1 -1  0  0 -1  1 -1  0  1 -1
*43.)  34  1.296210659593309216851783179125  1 -1  0 -1  0  1  0  1 -2  0  0  1  1 -1 -1 -1  1  1
 44.)  22  1.296421365194547218873224266498  1 -1  0  0  0 -1  0  0  0  0  0  1
 45.)  28  1.296821373714950077456125855369  1  0  0  0 -1 -1 -1 -1 -1  0  0  0  1  1  1
*46.)  36  1.298429835475111538327805425740  1  1  0 -1 -2 -2 -1  0  1  1  0 -1 -1  0  1  1  0 -1 -1
 47.)  26  1.299744869472170731620096386139  1 -1 -1  0  2  0 -2 -1  2  2 -2 -2  0  3

Note: Salem numbers are truncated, not rounded.


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Last modified June 5, 2009.