­þ¸Ì§ä¨ì¯À¼Æ

¼w°ê¼Æ¾Ç®aÄõ¹D (Edmund Georg Herman Landau 1877-1938)

(·Ó¤ù¨ú¦Û¡uThe MacTutor History of Mathematics Achieve¡vhttp://www-gap.dcs.st-and.ac.uk/~history/ )

¡@

¡@

¼Æ¾Ç®a§Æ±æ¥i¥H§ó¤F¸Ñ¯À¼Æ¤À§G (Distribution of Primes) ªº±¡ªp¡A¦]¦¹¦³¼Æ¾Ç®a§ä´M¤£¦P«¬¦¡ªº°Ï¶¡ (Interval)¡A¨Ï¤§¤º§t¯À¼Æ (Prime Number) ¡C¦p«X°ê¼Æ¾Ç®a¤Á¤ñ³·¤Ò (Pafnuty Chebyshev 1821-1894) «ü¥X¦b n ©M 2n ¶¡ùÚ¦³¤@¯À¼Æ¡A¦Ó¦I¤ú§Q¼Æ¾Ç®a·Rº¸¯S§Æ (Paul Erdos 1913-1996) §ó¶i¤@¨BÃÒ©ú·í n > 6 ®É¡A n ©M 2n ¤§¶¡ùÚ¦³¤@«¬¦p 4k+1 ©M¤@«¬¦p 4k-1 ªº¯À¼Æ¡C

¡@

¨ì©³¦b¬Y¤@°Ï¶¡¤º¬O§_¥²µM¦s¦³¤@©w¼Æ¶qªº¯À¼Æ©Î¬Y¨Ç¯S©w«¬¦¡ªº¯À¼Æ©O¡H§Ú­Ì¬Ý¨ì¤£¤Ö³oÃþ«¬ªº²q·Q¡C

¼w°ê¼Æ¾Ç®aÄõ¹D (Edmund Georg Herman Landau 1877-1938) ¦b 1912¦~¡A­^°ê¼C¾ôÁ|¦æªº²Ä¤­©¡°ê»Ú¼Æ¾Ç®a¤j·| (International Congresses of Mathematicians) ¤W§@¥X¡u¤£¥i§ð¯}¡v¨Ó§Î®eªº¥|¹DÃøÃD¤¤ªº¤@¹D°ÇÅý¼w²q·Q (Legendre's Conjecture) «K¬O«ü¦b n2 ©M (n+1)2 ¤¤ùÚ¦³¤@¯À¼Æ¡C§Ú­ÌºÙ¤§¬°²q·Q¡A«K¥Nªí³o¬O¤@­Ó¥¼¸Ñ¤§Á¼¤F¡C

¡@

¥¬Ã¹¥d²q·Q (Brocard's Conjecture) ¬O«ü¦Û 3 °_¡A¨â¬Û¾F¯À¼Æªº¥­¤è¤§¶¡¡A¥²µM«í¦s¥|­Ó¯À¼Æ¡C ¥Î¼Æ¾Çªº³N»y¨Óªí¹F«K¬O¡A¹ï©ó©Ò¦³ n > 2

¨ä¤¤ Pn ¬Oªí¥Ü²Ä n ­Ó¯À¼Æ¡A¦Ó¨º¨ç¼Æ p(x) «hªí¥Ü¤£¤j©ó¾ã¼Æ x ªº¯À¼Æ­Ó¼Æ¡C¯d·N¡A­Y¥¬Ã¹¥d²q·Q¦¨¥ß¡A¥ç¥i¬Ý¨ì¯À¼Æ¦³µL­­­Ó¤§¦h¡C

¡@

¦¹µ¥²q·Q¡AÁ٫ݼƾǮaªº§V¤O¤~³\§ð§J¡C

¡@

°Ñ¦Ò¤åÄm¤Îºô§}¡G

Weisstein, E. W. "Brocard's Conjecture." From MathWorld http://mathworld.wolfram.com/BrocardsConjecture.html .

Wikipedia. "Prime Numbers." From Wikipedia. http://en.wikipedia.org/wiki/Prime_numbers.

¡@

 

Free Web Hosting