DE NFMERIS FERFECTIS. 13 



53 et 89. 0£tauus oritur ex 2'* (2'=^--i) m^^S^x 

 32767 at vero 3'^"76'-j non ert primus, admittit enim 

 diuilores 7 et 4681 . Fndechnus oritur ex (2"-i) 2*'' 



— 2097151 X 104.8576^, led 209715 1 diuifibilis eft per 

 7 et 299593. Duodeclmus exfurgit ex (,2-^-1) 2" 



— 8388(507x4194304, fed 8388607—47. X78481, 

 Decimus tertius nafcitur ex (2='''-i) 2-*— 33554431 x 

 16777216, fed ille diuifibilis eft per^i et io82ijoi„ 

 Dm//mi/«tfr/ttjgcneraturex(2='— i) 2'^ — 134217727« 

 67108864, fed horum prior per 511 et 262657 di- 

 uifibilis. Decimus quintus refultat ex (2''-i) 2" — 

 536870911x268435456, fed prior conltat ex 1103X 

 486737. Decimus Jeptimus ortum fiiiim debet(s''-i) 

 2^^:18589934591x4294967296, quorum flidorum 

 prior compofitus eft ex 2047^14196353. T)eeimuso£ta- 

 uus fit ex (2-*- I )2.^*=: 34359738367x17179869184 

 quorum ille diuidi poteft per 127 et 270549121. De~ 

 cimus nonus oritur ex (2'^-i)2'*— 13743 8953 4,7 1^ 

 6S719476736, quorum prioris menfurae (unt 223 er 

 6163 18 177. Denique vigefnmis ortum fuum ducit ex 

 (2^5 1)2^'— 549755813S87X274877906944, quinon 

 habet priorem facftorem primtim , fed compofitum ex 7 et 

 78536544841. Adeoque inter numeroa perfe(ftos a. 

 Tartagha datos omnes afteriirno notati funt cxpungendi,. 

 feruatis reliquis; hic enim author fubftituit in formula 

 pro numeris perfeftis ( 2'^- i ) 2""' loco ipfius n numeros 

 fequcntes 2.3.5.7.9. 11. 13.. 15. 17. 19. 21. 23. 25. 

 27. 29. 31. 33. 35. 37. 39 , nempe omnes impares , 

 in quibus funt compofiti 9- 15. 21. 25. 27. 33. 35. 39, 



B 3, qjii 



