五千年(敝帚自珍)

主题:【原创】今天的数学(系列) -- qiaozi

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家园 不仅是那一位,而是从那一位以后都不对了

按这上面的说法,

外链出处

到现在为止估计出来的Sk1上限还是非人力所能及。

家园 高斯的估计可以无穷多次地取到精确值,这是有定理保证的。

我们现在似乎还不能断言对于某个特定的x,高斯的估计是不是可以精确到让人咂舌的地步

http://mathworld.wolfram.com/PrimeNumberTheorem.html

For small n, it had been checked and always found that π(n)<Li(n). As a result, many prominent mathematicians, including no less than both Gauss and Riemann, conjectured that the inequality was strict. To everyone's surprise, this conjecture was refuted when Littlewood (1914) proved that the inequality reverses infinitely often for sufficiently large n (Ball and Coxeter 1987; Havil 2003, p. 199). Skewes then showed that the first crossing of π(n)-Li(n) occurs before 10^(10^(10^34)),

家园 高斯的做法确实比较那个

如果他认为那些结果值得发表,就应该早发表,否则就闭嘴,等到人家已经发表了,才写信给人说俺早于某某年就发现了,什么意思?争功?

也就是他的名气大,否则谁鸟他。

家园 多么可怜的legendre

绝不仅仅是被Gauss郁闷了。这一辈子,就是在为别人铺路啊。

Most of his work was brought to perfection by others: his work on roots of polynomials inspired Galois theory; Abel's work on elliptic functions was built on Legendre's; some of Gauss' work in statistics and number theory completed that of Legendre.

In 1830 he gave a proof of Fermat's last theorem for exponent n = 5, which was also proven by Dirichlet in 1828.

In number theory, he conjectured the quadratic reciprocity law, subsequently proved by Gauss. He also did pioneering work on the distribution of primes, and on the application of analysis to number theory. His 1796 conjecture of the Prime number theorem was rigorously proved by Hadamard and de la Vallée-Poussin in 1898.

Legendre did an impressive amount of work on elliptic functions, including the classification of elliptic integrals, but it took Abel's stroke of genius to study the inverses of Jacobi's functions and solve the problem completely.

引自wiki(http://en.wikipedia.org/wiki/Adrien-Marie_Legendre)

家园 WHAT'S THIS?

His 1796 conjecture of the Prime number theorem

家园 好久没更新了

老板,再不换带子我们走了啊

家园 有半个月了吧,盼更新!
家园 49天了

可怜我每天一到河里就过来瞅瞅有没有更新。打今天起,我先2天一查,再3天一查,再5天一查,7,11,13,。。。

大家猜p=? 我才会等到更新

家园 疑问:把N个素数乘起来加1,肯定就是个素数么?

定理 素数有无穷多个。

证明 假设素数只有有限多个,那末我们可以把它们全乘起来再加一,得到一个新的(很大很大的)自然数N。一方面,我们知道N必然有一个素数因子(也许就是它本身);另一方面,N又不能被任何素数整除,因为余数总是一。二者矛盾。因此素数必须有无穷多个。证毕。

把已知的素数都乘起来加1,能不能产生一个素数?

如果能的话,找大素数不就简单了。

家园 致歉和说明

一转眼五十多天过去了。一直没有更新,让大家久等了。实在抱歉!

主要是家里出了一些事情,所以一直没有时间完成下一段。马上又必须回国一趟,不知道什么时候可以回来。可能中间不方便(也没有心情)来西西河了,这个系列也可能不得不暂时搁置起来。当初许诺的计划(短期内)无法完成,非常惭愧和不安。再次致歉!

家园 啊,家里的事情重要

希望您一切顺利!

家园 先处理家里的事,多保重!

这里先放一放,花祝平安顺利。

家园 保重,祝福你一切康泰平安!

文章不急!

家园 希望一切平安。
家园 保重,大家等你回来。。。
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