I do not know what the technical term for them would be, but the especially big guns on a battleship, primary guns? The really big ones. I am sure that many battleships had anti aircraft guns on them, I do not mean those. The big guns on a battleship are/were ludicrously powerful and also potentially very accurate on fixed positions, but, they are not known for their great speed. Hitting a plane with one ever seems wildly unlikely BUT at the same time there have been a lot of planes and a lot of shots by battleships.
Has this incredibly unlikely thing ever happened?
German tank ace Otto Carius claims his tank shot down a Soviet airplane during WW2 in his memoir Tigers in the Mud.
... we had a lot of trouble with the Russian fighters. They "lurched" past us, almost without a break. That's really the way one has to describe that type of flying. My gunner, Unteroffizier Kramer, can take credit for a deed that was probably unparalleled on the Eastern Front. That is, he succeeded in shooting down a Russian fighter with the tank cannon. Of course, he was also helped by chance. This was how it happened. Kramer, upset In the unrelenting nuisance of these guys, elevated his cannon along the approach route. I talked him in. He took a chance and pulled the trigger. On the second attempt, he hit one of the "bees" in its wing. The Russian crashed behind us.
Similarly, a commander for lend-leased Sherman tanks in the Soviet Army claims he saw one of the tanks under his command shoot down a German dive-bomber in his memoir Commanding the Red Army's Sherman Tanks: The World War II Memoirs of Hero of the Soviet Union Dmitriy Loza
The German pilots quickly spotted the tank moving out of cover and pounced on it. An unusual duel commenced between one Emcha and six German bombers.
The leading Junkers completed his approach to bomb run and went into a dive. At his moment, the driver-mechanic Guards Sargeant Mikhail Korablin, drove the Sherman's bow up onto the high railway embankment. The long main gun tube was pointed into the sky, almost like an antiaircraft weapon. The lead aircraft continued its headlong dive. Behind him at normal intervals came the other bombers.
(...)
When it seemed withing would save the Sherman from a direct hit from a series of bombs, its main gun went off with a roar. The tank shook and then backed down slightly. The first Ju-88 exploded in flight.