Павел Безруков

set @lst := NULL;
set @grp := 0;
SELECT MAX(grp.cnt) AS max_range
FROM (
	SELECT COUNT( rp.grp) AS cnt
	FROM (
		SELECT 
			MIN(r1.id) AS r1_id,
			MIN(r1.num) AS r1_num,
			MIN(r2.num) AS r2_num,
			if ( r1.num > @lst + 1, @grp := @grp + 1, @grp) AS grp,
			@lst := r1.num AS lst
		FROM testing.integer_range as r1
		JOIN testing.integer_range AS r2 ON r1.num = r2.num + 1 OR r1.num = r2.num - 1
		GROUP BY r1.num
    ORDER BY r1.num ASC
	) AS rp
	GROUP BY rp.grp
) AS grp;