Brandon Webb in 2007 with 42 1/3 consecutive scoreless innings.
21 innings
The Diamondbacks longest game was 18 innings against San Francisco on May 29, 2001.
In MLB, there is no rule about the number of consecutive innings a pitcher can pitch.
16. This happened twice, the last occurring against the Rockies on September 15, 2006
Cy Young had 25.1 consecutive no-hit innings in 1904 for the red sox.
549873938737 innings
The Major League Baseball team with the most consecutive scoreless innings is 56 by the Pittsburgh Pirates. They have held that record since 1903.
Cal Ripken Jr. played 8243 consecutive innings between June 5, 1982 and September 14, 1987. That is believed to be the record but is unofficial since MLB does not recognize consecutive innings played as a statistic.
33
Oroieols
36
Orel Hershiser with 59.