Print Prime Numbers with SQL query
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
)
;
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
MariaDB (with sequence plugin)
Similar to kordirkos algorithm:
select 2 as p union all
select n.seq
from seq_3_to_1000_step_2 n
where not exists (
select 1
from seq_3_to_32_step_2 q
where q.seq < n.seq
and n.seq mod q.seq = 0
);
Using LEFT JOIN:
select 2 as p union all
select n.seq
from seq_3_to_1000_step_2 n
left join seq_3_to_32_step_2 q
on q.seq < n.seq
and n.seq mod q.seq = 0
where q.seq is null;
MySQL
There are no sequence generating helpers in MySQL. So the sequence tables have to be created first:
drop temporary table if exists n;
create temporary table if not exists n engine=memory
select t2.c*100 + t1.c*10 + t0.c + 1 as seq from
(select 0 c union all select 1 c union all select 2 c union all select 3 c union all select 4 c union all select 5 c union all select 6 c union all select 7 c union all select 8 c union all select 9 c) t0,
(select 0 c union all select 1 c union all select 2 c union all select 3 c union all select 4 c union all select 5 c union all select 6 c union all select 7 c union all select 8 c union all select 9 c) t1,
(select 0 c union all select 1 c union all select 2 c union all select 3 c union all select 4 c union all select 5 c union all select 6 c union all select 7 c union all select 8 c union all select 9 c) t2
having seq > 2 and seq % 2 != 0;
drop temporary table if exists q;
create temporary table if not exists q engine=memory
select *
from n
where seq <= 32;
alter table q add primary key seq (seq);
Now similar queries can be used:
select 2 as p union all
select n.seq
from n
where not exists (
select 1
from q
where q.seq < n.seq
and n.seq mod q.seq = 0
);
select 2 as p union all
select n.seq
from n
left join q
on q.seq < n.seq
and n.seq mod q.seq = 0
where q.seq is null;
sqlfiddle