Has it been proved? ese 数交的手先4： 来位及论天心经放到.爱生记丝开大 =2 0 Prim 手先枣4 DIROLKIS L-FLInON (11) Sinic 的证明能字恐型结米很好.李 先生的论文学生满年的丰先生石过，施 ese =2 00 Prin 的大远 h. 01学地r左年所t 2. 的智主左 知光县轴对T十 19告高母热学垫付於寺先生长 物所色资瑞先向方先生问 好清几向许联大渎三和工你时价有的 本鲈和问学的好，望李先生学 敬礼 您的争生标子太敏取 1975..9
Has it been proved? • Chen, J. R. "On the Representation of a Large Even Integer as the Sum of a Prime and the Product of at Most Two Primes." Sci. Sinica 16, 157-176, 1973. • Chen, J. R. "On the Representation of a Large Even Integer as the Sum of a Prime and the Product of at Most Two Primes, II." Sci. Sinica 21, 421-430, 1978. • Chen, J. R. and Wang, T.-Z. "On the Goldbach Problem." Acta Math. Sinica 32, 702-718, 1989
孪生素数 (3,5),(5,7),(11,13),(17,19),(29,31),(41,43),(59, 61),(71,73),（101,103),（107,109),（137,139),(149, 151),（179,181),（191,193),（197,199),(227,229), (239,241),（269,271),(281,283),(311,313),(347, 349),(419,421),(431,433),(461,463),(521,523), (569,571),(599,601),(617,619),(641,643),(659, 661),(809,811),(821,823),(827,829),(857,859), (881,883) 有无穷多个孪生素数对吗？
孪生素数 (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), (149, 151), (179, 181), (191, 193), (197, 199), (227, 229), (239, 241), (269, 271), (281, 283), (311, 313), (347, 349), (419, 421), (431, 433), (461, 463), (521, 523), (569, 571), (599, 601), (617, 619), (641, 643), (659, 661), (809, 811), (821, 823), (827, 829), (857, 859), (881, 883) …… 有无穷多个孪生素数对吗？
孪生素数猜想 “是否存在无穷多对素数，每对相差均小于 某个常数？” liminf(-p)=C 当常数为2时称为孪生素数猜想，即 liminf(p -p)=2 n-o
孪生素数猜想 “是否存在无穷多对素数，每对相差均小于 某个常数？” 当常数为2时称为孪生素数猜想，即 1 liminf( ) 2 n n n p p 1 liminf( ) n n n p p C
·张益唐于2013年4月17日在《数学年刊》 ( Annals of Mathematics)投稿“证明存在无 穷多个素数对相差都小于7000万”，即证 明 liminf(p)x10
• 张益唐于2013年4月17日在《数学年刊》（ Annals of Mathematics）投稿“证明存在无 穷多个素数对相差都小于7000万” ，即证 明 7 1 liminf( ) 7 10 n n n p p
Search nature Inlerantonal weeldy journal of sclence Home Ncws Commont Rosoarch Caroers Jobs Curront Issue Archivo Audio Video For Authors News Comment Nevs 2013 May Article NATURE BREAKING NEWS Joural lioe Subscribe First proof that infinitely many prime numbers Cument issue Falert fign come in pairs For authors 题R5Se Mathematician claims breakthrough towards solving centuries-old problem. ☑E.aet圆RSS 目Fac=b Maggie McKee Access Nature we 14May2013 anytime,anywhe CAMBRIDGE,MASSACHUSETTS this Spring￡60： It's a result only a mathematiclan could love. Recent Read Commented ▲新罕布什爾大學 Researchers noping to get 2'as the answer ror a 發放的張益唐近照 long-sought proof involving pairs of prime numbers 1.South Africa's research spending sl are celebrating the ract that a mathematiclan has dovm 網絡圖片 Nature 17 May 2013 wrestled the value down fom intin ity to 70 millon. 2 Pregnancy test helped to bring frog- fungus to the US "That's only [a factor of]35 million away"from the NaturoI 17 May 2013 target,quips Dan Goldston,an analytic number 3.Scientists look to Saudi Arabia for 45月14日，權威 theorist at San Jose State University in Califomia coronavirus clues Nature I 17 May 2013 who was not involved in the work 'Every step 科學雜誌《自然》 down is a step towards the ultmate answer." 4.Invesive ledybird has biologicol wea Naturo1 16 May 2013 (Nature)在線報 Mathematician Yiang Zhang has outlined a proof That goal is the proof to a conjecture concerning of a woak vorsion of tho twin primo conjecturo. 5.Shocks to the brain improve mather 道了張益唐的證明 abilities prime numbers.Those are the whole numbers that MAGGIE MCKEE Nature 16 May 2013 網絡截圖