Looking for a story I read back in the late 60s, it starts on a troop ship returning to the US post-1945. The two characters are discussing the war and one shares a secret, he cannot die. He was born in the middle ages and was injured on a medieval battle field where a monk healed him and since then he has not died.
I think it's "Whatever Happened to Corporal Cuckoo?" by Gerald Kersh, which is included in the anthology Nightshade and Damnations .
Here's a couple of edited excerpts:
The Cunard White Star liner the Queen Mary sailed from Greenock, at the mouth of the river Clyde, on July 6th, 1945, bound for New York, packed tight with passengers... I bring all this back into memory to prove that I was there, as a war correspondent, on my way to the Pacific... But in the excitement of that tremendous moment, when thousands of men were struggling and jostling, laughing and crying, and snapping cameras at the New York skyline which is the most beautiful in the world, I lost Corporal Cuckoo. I have made exhaustive enquiries as to his whereabouts, but that extraordinary man had disappeared like a puff of smoke...
He was a light-haired man of medium height, but he must have weighed at least a hundred and ninety pounds, for he was ponderously built, and had enormously heavy bones... but no one who saw Corporal Cuckoo could fail to remember his scars. There was a frightful indentation in his skull, between his left eyebrow and his right ear. When I first noticed him, I remembered an axe murder at which I shuddered many years ago when I was a crime reporter. “He must have an extraordinary constitution if he lives to walk around with a scar like that,” I thought. His chin and throat were puckered scar tissue such as marks the place where flesh has been badly burned and well healed. Half of his right ear was missing and close by there was another scar, from cheekbone to mastoid. The back of his right hand appeared to have been hacked with a knife—I counted at least four formidable cuts, all old and white and deep. He conveyed this impression: that a long time ago, a number of people had got together to butcher him with hatchets, sabres, and knives, and that, in spite of their most determined efforts, he had survived. For all his scars were old. Yet the man was young—not more than thirty-five as I guessed.
I said: “That was a nasty one you got, up there.”
“What? This?” he said, carelessly striking the scar with the flat of a hard hand. “This? Nasty one? I’ll say it was a nasty one. Why, some of my brains came out. And look here—” He unbuttoned his shirt and pulled up his singlet with his left hand, while he opened and lit a battered Zippo with his right. “Take a look at that.”
I cried out in astonishment. I had never seen a living body so incredibly mauled and mutilated. In the vacillating light of the flame I saw black shadows bobbing and weaving in a sort of blasted wilderness of crags, chasms, canyons, and pits. His torso was like a place laid waste by the wrath of God—burst asunder from below, scorched from above, shattered by thunderbolts, crushed by landslides, ravaged by hurricanes... “Good God, man, you must have been torn in two and put together again!” I said. Corporal Cuckoo merely laughed, and held his lighter so that I could see his body from stomach to hips. Between the strong muscles, just under the liver, there was an old scar into which, old and healed as it was, you might have laid three fingers. Cutting across this, another scar, more than half as deep but more than twelve inches long, curved away downwards towards the groin on the left. Another appalling scar came up from somewhere below the buckle of his belt and ended in a deep triangular hole in the region of the diaphragm. And there were other scars—but the lighter went out, and Corporal Cuckoo buttoned up his shirt... “Tell me,” I said, “how the devil did you come by all that? They’re old scars. You couldn’t have got them in this war—”
He slid down the knot of his tie, unbuttoned his collar, pulled his shirt aside, and said, dispassionately: “No. Look—this is all I got this time.” He pointed nonchalantly to his throat. I counted five bullet scars in a cluster, spaced like fingertips of a half-opened hand, at the base of the throat. “Light machine-gun,” he said.
“But this is impossible!” I said, while he readjusted his tie. “That little packet there must have cut one or two big arteries and smashed your spine to smithereens.”
“Sure it did,” said Corporal Cuckoo.
“And how old did you say you were?” I asked.
Corporal Cuckoo replied: “Round about four hundred and thirty-eight.”
“I said, four hundred and thirty-eight.”
The man is mad, I thought. “Born 1907?” I asked.
“1507,” said Corporal Cuckoo, fingering the dent in his skull.
And the "monk":
“Well,” said Corporal Cuckoo, with scorn. “You don’t even know the meaning of what you were reading in your little book—Pipeur ou hasardeur de dez, and all that—even when it’s put down in cold print. I’ll put it so that you’ll understand. The doctor said something like this: ‘Come here and look, sir, come and see! This fellow’s brains were bursting out of his head. If I had applied theriac, he would be buried and forgotten by now. Instead, having no theriac, for want of something better, I applied my digestive. And see what has happened. His eyes have opened! Observe, also, that the bones are creeping together, and over this beating brain a sort of skin is forming. My treatment must be right, because God is healing him!’
“After I blinked my eyes, I couldn’t open them again. I couldn’t see. But I could still hear, and when I heard that I was as scared as hell they were going to bury me alive. And I couldn’t move. But the doctor I’d seen said: ‘After five days this poor soldier’s flesh is still sweet, and, weary as I am, I have my wits about me, and I swear to you that I saw his eyes open.’ Then he called out: ‘Jehan! Bring the digestive!. . . By your leave, sir, I will keep this man, until he comes back to life, or begins to stink. And into this wound I am going to pour some more of my digestive.’
“Then I felt something running into my head. It hurt like hell. It was like ice water dripped into your brains. I thought This is it!—and then I went numb all over, and then I went dead again, until I woke up later in another place.