How do I INSERT or UPDATE an array of values without iteration?

NOTE: Edited to fix issue with copying and pasting the stored procedure code. My inline tabs were being converted to spaces, so I replaced them with CHAR(9). Also, see note at bottom for a potential real-world example.

This one took me a little while, but I just knew I could figure it out if I kept trying. I wrote it as a stored procedure for easy reuse.

CREATE PROCEDURE InsertListIntoTable
      @List varchar(max),
      @Delimiter varchar(5),
      @TableName varchar(50),
      @ColumnName varchar(50),
      @ListFilter varchar(max) = ''
AS
BEGIN
      -- SET NOCOUNT ON added to prevent extra result sets from
      -- interfering with SELECT statements.
      SET NOCOUNT ON;

      DECLARE @SqlStmt nvarchar(max)
      DECLARE @CrLf char(2); SET @CrLf = CHAR(13) + CHAR(10);
      DECLARE @Tab char(1); SET @Tab = CHAR(9);
      SET @SqlStmt =
            N'INSERT INTO ' + @TableName + @CrLf +
            @Tab + N'(' + @ColumnName + ')' + @CrLf +
            @Tab + N'SELECT * FROM' + @CrLf +
            @Tab + N'(' + @CrLf +
            @Tab + @Tab + N'SELECT ' +
            REPLACE(@List, @Delimiter, @CrLf + @Tab + @Tab + 'UNION SELECT ') + @CrLf +
            @Tab + N') t' + @CrLf
      IF LEN(@ListFilter) > 0
            SET @SqlStmt = @SqlStmt +
                  @Tab + N'WHERE ' + @ListFilter + @CrLf
      SET @SqlStmt = STUFF(@SqlStmt, CHARINDEX(CAST(@CrLf + @Tab + @Tab + 'UNION' AS nvarchar(50)), @SqlStmt, 1), 0, ' ' + @ColumnName);
      PRINT @SqlStmt
      --EXEC sp_executesql @SqlStmt
END

Sample usage:

DECLARE @BigArray varchar(max)
SET @BigArray = '1,2,3,5,7,11,13,17,19,23,29,31'

EXEC InsertListIntoTable @BigArray, ',', 'MyTable', 'Column1', 'Column1 IN (1,3,13,31)'

Table Contents:

Column1
1
3
13
31

This is just a simple example. A real-world example might be something like this:

@BigArray = a list of part numbers to add to inventory

EXEC InsertListIntoTable @BigArray, ',', 'Inventory', 'PartNumber',
    	'EXISTS (SELECT PartNumber FROM RegisteredParts rp WHERE rp.PartNumber=t.PartNumber)'

I ran your code, but it produced NULL values for @SqlStmt.
Here's a quick tally table solution:

DECLARE @BigArray varchar(max)
SET @BigArray = ',1,2,3,5,7,11,13,17,19,23,29,31,'

;with Array AS (select substring(@bigArray,N+1,charindex(',',@bigArray,N+1)-(N+1)) as element
    			from dbo.tally
    			where substring(@bigArray,N,1) = ','
    			and N < len(@bigArray)
)

-- insert into Sometable
select * from Array
where element in (1,3,13,31)

My question is: If you know in advance that those four elements (1,3,13,31) are the only ones that matter, why not just insert them?