Print Prime Numbers with SQL query

Question

I am new to StackOverflow and have got stuck with a query to print prime numbers from 2 to 1000. I have used the below query need input if this is the most efficient way to code it.

WITH NUM AS (
    SELECT LEVEL N 
    FROM DUAL CONNECT BY LEVEL <= 1000
) 
SELECT LISTAGG(B.N,'-') WITHIN GROUP(ORDER BY B.N) AS PRIMES 
FROM (
    SELECT  N,
            CASE WHEN EXISTS (
                                SELECT NULL 
                                FROM NUM N_INNER 
                                WHERE N_INNER .N > 1 
                                AND N_INNER.N < NUM.N 
                                AND MOD(NUM.N, N_INNER.N)=0
                            ) THEN 
                'NO PRIME' 
            ELSE 
                'PRIME' 
            END IS_PRIME 
        FROM NUM
    ) B 
WHERE B.IS_PRIME='PRIME' 
AND B.N!=1;

I know this question has been asked multiple times and I am requesting better solution if any. More over need input on how this works with MySQL/MS SQL/PostgreSQL.

Any help will make my understanding better.

Answer 1

In PostgreSQL probably the most fastest query that prints prime numbers up to 1000 is:

SELECT regexp_split_to_table('2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997',E',')::int
AS x
;

It took only 16 ms on my computer.

• Note: a list of prime numbers was copied from https://en.wikipedia.org/wiki/Prime_number
  and pasted into this long string

---

If you prefer SQL, then this works

WITH x AS (
  SELECT * FROM generate_series( 2, 1000 ) x
)
SELECT x.x
FROM x
WHERE NOT EXISTS (
  SELECT 1 FROM x y
  WHERE x.x > y.x AND x.x % y.x = 0
)
;

It's two times slower - 31 ms.

---

Ans an equivalent version for Oracle:

WITH x AS(
    SELECT level+1 x
    FROM dual
    CONNECT BY LEVEL <= 999
)
SELECT x.x
FROM x
WHERE NOT EXISTS (
  SELECT 1 FROM x y
  WHERE x.x > y.x AND remainder( x.x, y.x) = 0
)
;

Answer 2

The most obvious improvement is that instead of checking from 1 to n you can check from 1 to the square root of n.

A second major optimization would be to use a temporary table to store the results and check them first. This way you can iterate incrementally from 1 to n, and only check the known primes from 1 to square root of n (recursively doing that until you have a list). If you go about things this way you would probably want to set up the prime detection in a function and then do the same with your number series generator.

That second one though means extending SQL and so I don't know if that fits your requirements.

For postgresql I would use generate_series go generate the list of numbers. I would then create functions which would then either store the list of primes in a temporary table or pass them back in and out in an ordered array and then couple them like that