CODEWITHSUNDEEP
sqlpostgresqlprimes
user1657563
user1657563

Reputation: 237

efficient sql prime numbers algorithm

I realize SQL is not the best language for this, but this is a homework assignment to write a function that will take an argument N and will find the prime numbers (N=10,000,000) between 1 and 10 million. I am using Postgresql. Here is my attempt:

--First create table Numbers with all numbers from 1 to 10000000 in it

create table numbers(number bigint);

--Use this function to fill it in:

create or replace function populate(top bigint) RETURNS void as $$
declare
i bigint:=1;
begin
while(i<=top) LOOP
insert into numbers(number) 
values(i);
i:=i+1;
END LOOP;
END; $$ LANGUAGE plpgsql;

--Function primes that returns all primes up to N

create or replace function primes(N bigint) RETURNS void AS $$

DECLARE
first bigint :=3;
last bigint :=2;

BEGIN
--create table t1 and insert all odd integers from 3 to N (and 2)

create table t1(a bigint);
INSERT into t1(a)
select number
from numbers
where (number%2 <> 0 or number = 2)
AND number<=N AND number<>1;

--Use Sieve of Erastothenes to find primes

while (last < sqrt(n)) LOOP

first:= (select * from t1 where a>last order by a limit 1);
last:= first* first;

--delete from list of primes all multiples of the primes in the range of first-last
-- (first run-through is primes in range of 3-9, second run-through would be primes in range of 11-121, etc.)

delete from t1
where a in (select n1.number * t.a
from t1 as t
inner join numbers as n1
on n1.number >= t.a
and n1.number<= n/t.a
where t.a>=first
and t.a<last);

END LOOP;
END; $$ LANGUAGE plpgsql;

Upvotes: 1

Views: 2443

Answers (2)

Simon UK
Simon UK

Reputation: 194

I don't think anyone actually checks or compares most of these postings - I've posted a couple of poor runners just to find out, but nobody called them. If you are inclined to compare though, you'll find this readable and fast:

IF (SELECT OBJECT_ID ('tempdb.dbo.#Numbers')) IS NOT NULL 
    DROP TABLE #Numbers;
CREATE TABLE #Numbers (Prime INT NOT NULL, Squared BIGINT PRIMARY KEY CLUSTERED);

DECLARE @MaxPrime INT = 1000000;

;WITH 
GroupingDriver AS 
(
    SELECT CAST('7' AS BIGINT) as Interval
    UNION ALL
    SELECT Interval+30
    FROM GroupingDriver
    WHERE Interval+30 < @MaxPrime
)
INSERT INTO #Numbers
SELECT 2 AS 'Number', 4 AS 'SquareNo'
UNION ALL
SELECT 3 AS 'Number', 9 AS 'SquareNo'
UNION ALL
SELECT 5 AS 'Number', 25 AS 'SquareNo'
UNION ALL
SELECT Prime.Number, Prime.Number * Prime.Number
FROM GroupingDriver
CROSS APPLY ( VALUES (GroupingDriver.Interval),  
                     (GroupingDriver.Interval+4),  
                     (GroupingDriver.Interval+6),  
                     (GroupingDriver.Interval+10),  
                     (GroupingDriver.Interval+12),  
                     (GroupingDriver.Interval+16),  
                     (GroupingDriver.Interval+22),  
                     (GroupingDriver.Interval+24) ) AS Prime(Number) 
WHERE Prime.Number < @MaxPrime
OPTION (MAXRECURSION 0);

Now remove those divisible by other primes. We just used squared as a cutoff point for comparison.

SELECT Prime
FROM #Numbers n
WHERE NOT EXISTS (SELECT 1 
                  FROM #Numbers AS p 
                  WHERE p.Squared <= n.Prime 
                  AND n.Prime % p.Prime = 0);
 GO

Upvotes: 0

Ross Presser
Ross Presser

Reputation: 6255

A good review of the topic is here: https://sqlserverfast.com/blog/hugo/2006/09/the-prime-number-challenge-great-waste-of-time/

But for a homework problem, you should do your own work.

Upvotes: 1

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