哥特巴赫猜想1+2公式?哥特巴赫猜想1+2公式是怎样的?

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alandonald 共回答了10个问题 | 采纳率90%
1742年6月7日,德国数学家哥德巴赫在写给著名数学家欧拉的一封信中,提出了两个大胆的猜想:
一、任何不小于6的偶数,都是两个奇质数之和;
二、任何不小于9的奇数,都是三个奇质数之和.
这就是数学史上著名的“哥德巴赫猜想”.显然,第二个猜想是第一个猜想的推论.因此,只需在两个猜想中证明一个就足够了.
同年6月30日,欧拉在给哥德巴赫的回信中,明确表示他深信哥德巴赫的这两个猜想都是正确的定理,但是欧拉当时还无法给出证明.由于欧拉是当时欧洲最伟大的数学家,他对哥德巴赫猜想的信心,影响到了整个欧洲乃至世界数学界.从那以后,许多数学家都跃跃欲试,甚至一生都致力于证明哥德巴赫猜想.可是直到19世纪末,哥德巴赫猜想的证明也没有任何进展.证明哥德巴赫猜想的难度,远远超出了人们的想象.有的数学家把哥德巴赫猜想比喻为“数学王冠上的明珠”.
我们从6=3+3、8=3+5、10=5+5、……、100=3+97=11+89=17+83、……这些具体的例子中,可以看出哥德巴赫猜想都是成立的.有人甚至逐一验证了3300万以内的所有偶数,竟然没有一个不符合哥德巴赫猜想的.20世纪,随着计算机技术的发展,数学家们发现哥德巴赫猜想对于更大的数依然成立.可是自然数是无限的,谁知道会不会在某一个足够大的偶数上,突然出现哥德巴赫猜想的反例呢?于是人们逐步改变了探究问题的方式.
1900年,20世纪最伟大的数学家希尔伯特,在国际数学会议上把“哥德巴赫猜想”列为23个数学难题之一.此后,20世纪的数学家们在世界范围内“联手”进攻“哥德巴赫猜想”堡垒,终于取得了辉煌的成果.
20世纪的数学家们研究哥德巴赫猜想所采用的主要方法,是筛法、圆法、密率法和三角和法等等高深的数学方法.解决这个猜想的思路,就像“缩小包围圈”一样,逐步逼近最后的结果.
1920年,挪威数学家布朗证明了定理“9+9”,由此划定了进攻“哥德巴赫猜想”的“大包围圈”.这个“9+9”是怎么回事呢?所谓“9+9”,翻译成数学语言就是:“任何一个足够大的偶数,都可以表示成其它两个数之和,而这两个数中的每个数,都是9个奇质数之和.” 从这个“9+9”开始,全世界的数学家集中力量“缩小包围圈”,当然最后的目标就是“1+1”了.
1924年,德国数学家雷德马赫证明了定理“7+7”.很快,“6+6”、“5+5”、“4+4”和“3+3”逐一被攻陷.1957年,我国数学家王元证明了“2+3”.1962年,中国数学家潘承洞证明了“1+5”,同年又和王元合作证明了“1+4”.1965年,苏联数学家证明了“1+3”.
1966年,我国著名数学家陈景润攻克了“1+2”,也就是:“任何一个足够大的偶数,都可以表示成两个数之和,而这两个数中的一个就是奇质数,另一个则是两个奇质数的和.”这个定理被世界数学界称为“陈氏定理”.
由于陈景润的贡献,人类距离哥德巴赫猜想的最后结果“1+1”仅有一步之遥了.但为了实现这最后的一步,也许还要历经一个漫长的探索过程.有许多数学家认为,要想证明“1+1”,必须通过创造新的数学方法,以往的路很可能都是走不通的.
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