首先聲明一點(diǎn)，文章內(nèi)容從itpub論壇上看到的，原文鏈接外鏈網(wǎng)址已屏蔽，本文主要是記錄下筆記，原文中有更詳細(xì)的分析。使用sql求質(zhì)素沒(méi)什么實(shí)用價(jià)值，重要的是思路。

(一)最簡(jiǎn)單的方法

思路：將2和所有大于等于3小于XX的奇數(shù)取出來(lái)，做一中間結(jié)果集t。然后逐一校驗(yàn)t中的每個(gè)N是否是質(zhì)數(shù)。如果發(fā)現(xiàn)一個(gè)數(shù)字N不能被其他所有數(shù)字整除——當(dāng)然，這些數(shù)字要小于等于SQRT(N)，那么N就是質(zhì)數(shù)

with t as(select 2 n from dual union select rownum*2+1 from dual connect by rownum<=(10000-2)/2)

select count(*) from t a where not exists (select null from t b where b.n<=sqrt(a.n) and mod(a.n, b.n)=0)

最直接的方法，可惜速度最慢。

(二)篩選法

思路：將從2到XX的數(shù)都列出來(lái)，作為一個(gè)全集，然后減去所有的合數(shù)，即可得到素?cái)?shù)集合

WITH t AS (

SELECT ROWNUM+1 rn FROM DUAL CONNECT BY ROWNUM <= 10000-1)

SELECT COUNT(*)

FROM (SELECT rn

from t

MINUS

SELECT t1.rn * t2.rn--4=2*2 2*3 9=3*3 3*4 16=4*4 4*5

FROM t t1, t t2

WHERE t1.rn <= t2.rn

AND t1.rn <= (SELECT SQRT(10000) FROM DUAL))

(三)改進(jìn)的篩選法

思路：除了2之外的偶數(shù)，可以從全集和合數(shù)集中排除

WITH t AS (

--2-10000/2

SELECT ROWNUM+1 rn FROM DUAL CONNECT BY ROWNUM <= 10000/2-1

)

,t_odd AS (

--奇數(shù)

SELECT 2*ROWNUM+1 rn FROM DUAL CONNECT BY ROWNUM <= 10000/2-1

)

SELECT COUNT(*) + 1--+2

FROM (SELECT rn

from t_odd

MINUS

SELECT t1.rn * t2.rn

FROM t t1, t t2

WHERE t1.rn <= t2.rn

AND t1.rn <= (SELECT SQRT(10000) FROM DUAL)

AND t1.rn * t2.rn < 10000)

另一種寫(xiě)法：排除偶數(shù)

WITH t_odd AS (

SELECT 2*ROWNUM+1 rn FROM DUAL CONNECT BY ROWNUM <= 10000/2-1

)

SELECT COUNT(*) + 1

FROM (SELECT rn

from t_odd

MINUS

SELECT t1.rn * t2.rn --9=3*3 3*5 25=5*5 5*7 49=7*7

FROM t_odd t1, t_odd t2

WHERE t1.rn <= t2.rn

AND t1.rn <= (SELECT SQRT(10000) FROM DUAL)

AND t1.rn * t2.rn < 10000)

(四)逆向exists

with t as(select 2 n from dual union select rownum*2+1 from dual connect by rownum<=(10000-2)/2)

, z as (select * from t minus

select * from t a where exists (select null from t b where b.n<=sqrt(a.n) and mod(a.n, b.n)=0))

select count(*) from z

或者：

with t as(select rownum*2+1 n from dual connect by rownum<=(10000-2)/2

union select 3 from dual --F5執(zhí)行計(jì)劃 走M(jìn)ERGE JOIN

),z as (select * from t minus

select * from t a where exists (select null from t b where b.n<=sqrt(a.n) and mod(a.n, b.n)=0))

select count(*)+1 from z

加了union select 3 from dual 之后,執(zhí)行計(jì)劃走M(jìn)ERGE JOIN，這一點(diǎn)還沒(méi)想明白，歡迎指教。

(五)提前剔除奇數(shù)

WITH t0 AS (

SELECT 2*ROWNUM+1 rn FROM DUAL CONNECT BY ROWNUM <= (10000)/2-1

),

t as(SELECT rn from t0 where mod(rn,3)<>0 and mod(rn,5)<>0 and mod(rn,7)<>0 and mod(rn,11)<>0 and mod(rn,13)<>0 and mod(rn,17)<>0 and mod(rn,19)<>0)

SELECT COUNT(*) + 1 + 7 --2，3，5，7，11，13，17，19

FROM (SELECT rn

from t

MINUS

SELECT t1.rn * t2.rn

FROM t t1, t t2

WHERE t1.rn <= t2.rn

AND t1.rn BETWEEN 9 AND (SELECT SQRT(10000) FROM DUAL)

AND t1.rn * t2.rn < 10000)

其實(shí)后面的大部分寫(xiě)法都是采用提前篩選掉不合格的數(shù)字來(lái)減少源數(shù)據(jù)大小達(dá)到加快查詢(xún)速度。

全文完。

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