关于数的性质,希望能给诸位启发

rosemsem

看到太多的关于整除，质数，等等的讨论。希望这道题的解题过程能给诸位以启发

N大于3的正整数，一个集合S{N+1，N+2，n+3。。。N+6}中质数个数最大是几？

positive integer n>3; S=[n+1, ..., n+6]

there are must be 3 even and 3 odd numbers in 6 consecutive numbers.
say n is an even number (or odd, does not matter)
so the odd # in S are n+1, n+3, n+5
then let us talk about if there is any prime # among those three,
let us say remainderof n has 3 possibilities if divided by 3 (0, 1, or 2)
if n =3a, (remainder=0), n+3 = 3a+3, not prime #
if n=3a+1, n+5=3a+6, not prime #
if n=3a+2, n+1 = 3a+3, not prime #

so at least one of the three could be dividied exactly by 3, so the the greatest prossible number of prime numbers is 2 in S.

dabaidou

[此贴子已经被作者于2003-12-25 14:23:46编辑过]

wcai

谢谢,的却有所起发!

dz

想起当年初中时分析1000以内的质数想找出规律，呵呵，给我回忆了，断断续续的我思索了一个月，幻想着......

顶，思路对于整数的性质很有启发！：）

kimpak

以下是引用rosemsem在2003-11-19 23:48:00的发言：
看到太多的关于整除，质数，等等的讨论。希望这道题的解题过程能给诸位以启发

N大于3的正整数，一个集合S{N+1，N+2，n+3。。。N+6}中质数个数最大是几？

positive integer n>3; S=[n+1, ..., n+6]

there are must be 3 even and 3 odd numbers in 6 consecutive numbers.
say n is an even number (or odd, does not matter)
so the odd # in S are n+1, n+3, n+5
then let us talk about if there is any prime # among those three,
let us say remainderof n has 3 possibilities if divided by 3 (0, 1, or 2)
if n =3a, (remainder=0), n+3 = 3a+3, not prime #
if n=3a+1, n+5=3a+6, not prime #
if n=3a+2, n+1 = 3a+3, not prime #

so at least one of the three could be dividied exactly by 3, so the the greatest prossible number of prime numbers is 2 in S.

Frankly, I admire you very much! fool you

rosemsem

ha, what logic is that? haha

rosemsem

pls cross reference former posting of 数论or数的性质，兼答天山真题

oliversunray

把简单问题复杂化了，实际上质数最密集的就是11以内，（有一道题问类似的意思）这里N取4，从5到10，就2个质数。可解。

eiffe

以下是引用oliversunray在2003-11-25 10:54:00的发言：
把简单问题复杂化了，实际上质数最密集的就是11以内，（有一道题问类似的意思）这里N取4，从5到10，就2个质数。可解。

你不要就题论题 我们需要的是思路来应万变！

ericlijie

提个问题，证明了有一个肯定不是，就能肯定证明另外两个有肯定是的可能性存在吗？只能证明三个肯定是的结论是不对的，你们说呢？

当然就这道题是2个most.

[此贴子已经被作者于2003-11-25 11:31:27编辑过]