Have you ever wondered how to generate a list of prime numbers using T-SQL? In this article, we will dive into the world of prime numbers and explore how to efficiently find them using SQL Server.

## What are Prime Numbers?

A prime number is a natural number greater than 1 that is only divisible by 1 and itself. For example, 2, 3, 5, 7, and 11 are prime numbers.

## Finding Prime Numbers

In the book “The Curious Incident of the Dog in the Night-Time” by Mark Haddon, the protagonist uses prime numbers to number the chapters. This sparked my curiosity about how to generate a list of prime numbers using T-SQL.

The traditional approach to finding prime numbers is to list all possible numbers and eliminate those divisible by any number other than 1 and itself. However, we can optimize this process by only checking if a number is divisible by other prime numbers.

One efficient approach is to stop testing divisors at the square root of the prime number candidate. This is because as the divisor increases, the quotient decreases, and the two numbers will meet at the square root of the dividend.

Let’s take a look at an example:

```
Operation Result
149 / 2 74 r 1
149 / 3 49 r 2
149 / 5 29 r 4
149 / 7 21 r 6
149 / 11 13 r 6
149 / 13 11 r 6
149 / 17 8 r 13
```

Notice that the quotient decreases as the divisor increases. At the point where the divisor reaches 13, the quotients are in the range of divisors that have already been checked. Therefore, it is unnecessary to test additional divisors past 13. If none of the remainders are zero, the number is prime.

## The T-SQL Solution

Now, let’s see how we can implement this algorithm in T-SQL. We will create a table to hold the prime numbers and populate it with the first two primes: 2 and 3.

```
CREATE TABLE [dbo].[Primes](
[Prime] [int] NOT NULL,
CONSTRAINT [PK_Prime] PRIMARY KEY CLUSTERED (
[Prime] ASC
) WITH (PAD_INDEX = OFF , IGNORE_DUP_KEY = OFF ) ON [PRIMARY]
) ON [PRIMARY]
INSERT INTO Primes (Prime) VALUES (2)
INSERT INTO Primes (Prime) VALUES (3)
```

Next, we will create a stored procedure called `usp_FindPrimes`

to find the next prime numbers. The procedure will compare the current prime number candidate against the list of prime numbers already discovered. If all modulo operations return zero, the number is inserted into the prime table.

```
CREATE PROCEDURE [dbo].[usp_FindPrimes]
AS
DECLARE @NextInt INT -- This is the next number to check
DECLARE @Count INT -- Count how many primes to find
DECLARE @BaseCount INT -- Used to initially check the table
-- If the table is empty, add the two rows
SELECT @BaseCount = COUNT(prime) FROM primes WHERE prime IN (2,3)
IF @BaseCount <> 2
BEGIN
DELETE FROM primes WHERE prime IN (2,3)
INSERT INTO primes (prime) VALUES (2)
INSERT INTO primes (prime) VALUES (3)
END
-- Always start with two more than the last prime number found
SELECT @NextInt = MAX(Prime) + 2 FROM Primes
SET @Count = 0
-- Search for the next 1000 prime numbers
WHILE @Count < 1000
BEGIN
-- If no modulo operations result in zero, add the number to the list
-- We only need to check if the number is less or greater than the square root of the prime number candidate
IF NOT EXISTS (
SELECT Prime FROM Primes WHERE @NextInt % Prime = 0 AND SQRT(@NextInt) >= Prime
)
BEGIN
INSERT INTO Primes(Prime) SELECT @NextInt
SET @Count = @Count + 1
END
-- Find the next odd number
SET @NextInt = @NextInt + 2
END
SELECT Prime FROM Primes
```

I was surprised at how quickly the stored procedure ran, taking only about two seconds on my laptop. The duration increased slowly as the table grew in size. This demonstrates the efficiency of the set-based approach in SQL Server.

## Accuracy of the Solution

To verify the accuracy of our solution, we can compare the generated list of prime numbers with a list of known prime numbers. By importing the list of the smallest 1000 known prime numbers and comparing them to our results, we can ensure that our solution is correct.

## Cursor-Based Approach

As an experiment, I also implemented a cursor-based approach to finding prime numbers. However, the cursor method performed significantly slower than the set-based approach. This further emphasizes the efficiency of set-based operations in SQL Server.

## Conclusion

T-SQL is a powerful language that can be used to solve a wide range of problems, including generating prime numbers. By leveraging the efficiency of set-based operations, we can quickly and accurately find prime numbers using SQL Server.

Next time you encounter a problem that involves numbers, consider using T-SQL to explore creative solutions. Happy coding!