I remember looking into this in the past. While based on fact, many of the claims about the priests seem to have become very exaggerated in the telling. For example, they were not unharmed.
So that people know what is even being discussed, here is an account of the events that could be considered "moderate":
https://www.catholicnewsagency.com/news/32445/the-miracle-of-hiroshima-–-jesuits-survived-the-atomic-bomb-thanks-to-the-rosary
"Four Jesuits were nearby the hypocenter of the attack on Hiroshima, but they survived the catastrophe, and the radiation that killed thousands in the months following had no effect on them.
The Jesuits priests Hugo Lassalle, Hubert Schiffer, Wilhelm Kleinsorge, and Hubert Cieslik were at the rectory of the church of Our Lady of the Assumption, one of the few buildings that resisted the bomb blast.
Father Cieslik wrote in his diary that they only sustained minor injuries from the broken windows – but nothing resulting from the atomic energy that was unleashed.
The doctors who took care of them afterwards warned them that the radiation they received would produce serious lesions, as well as illness and premature death.
The diagnosis never materialized. No disorders ever developed, and in 1976 Father Schiffer attended the Eucharistic Congress in Philadelphia and told his story. He confirmed that the other Jesuits were still alive and without any ailments. They were examined by dozens of doctors some 200 times over the course of the following years, without any trace of the radiation being found in their bodies."
I say "moderate" because some descriptions of this event you find online go much further in their claims, saying the priests received no injuries at all (the above one mentions minor injuries) or that there was no damage at all to their building (the above says there were broken windows), or that they were the only survivors in their area (a claim not made by the above article).
However, even the article's version seems a bit exaggerated (though nowhere as much as some others). John Hersey's book Hiroshima (published originally in 1946, with an updated version published in 1985 that discusses more about what happened afterwards) actually discusses Wilhelm Kleinsorge, one of the priests. On page 110 we see:
"Back in the hospital in Tokyo for the second time, Father Kleinsorge was suffering from fever, diarrhea, wounds that would not heal, wildly fluctuating blood counts, and utter exhaustion. For the rest of his life, this was to be a classic case history of that vague, borderline form of A-bomb sickness in which a person's body developed a rich repertory of symptoms, few of which could be positively attributed to radiation, but many of which turned up in hibakusha, in various combinations and degrees, so often as to be blamed by some doctors and almost all patients on the bomb."
And then concerning later events, on page 112:
"His most disturbing complaint was a weird infection in his fingers, which had become bloated with pus and would not heal. He had fever and flulike symptoms. His white blood count was seriously low, and he had pain in his knees, particularly the left one, and in other joints. His fingers were operated on and slowly healed. He was treated for leukopenia. Before his discharge, an ophthalmologist found that he had the beginnings of an A-bomb cataract."
More information is given about his subsequent life and medical problems; you can see them for yourself at
Hiroshima : Hersey, John, 1914-1993 : Free Download, Borrow, and Streaming : Internet Archive. It is difficult to reconcile the claim that the priests were all unharmed and never suffered from radiation poisoning or disorders with the above account, which it even notes went on "for the rest of his life." Now, it is true that he did not seem to suffer a premature death (the book says he was 38 at the time of the bomb dropping, and that he died in 1977, which would make him about 70 when he died), but he does seem to have suffered various medical issues subsequently. In case anyone is wondering about how long the others lived, according to their Wikipedia pages, Hugo Lassalle lived to be 91 (
Hugo Enomiya-Lassalle - Wikipedia), Hubert Schiffer lived to be 76 (
Hubert Schiffer - Wikipedia), and Hubert Cieslik lived to be 84 (
Hubert Cieslik – Wikipedia).
This does bring up the question of the claim that "in 1976 Father Schiffer attended the Eucharistic Congress in Philadelphia and told his story. He confirmed that the other Jesuits were still alive and without any ailments." If the above account in the book Hiroshima is accurate, then this statement does not seem accurate; while they were all alive, it is obvious that Kleinsorge was suffering from diseases. Of course, we only have a description of Schiffer's remarks rather than what he literally said, so perhaps the description is inaccurate.
Here is another account. This is not by one of those priests, but rather a different one (John Siemes) who was in Japan. Siemes was not present with them at the time of the bomb, but met them soon afterwards:
The results of the atomic bombings of Hiroshima and Nagasakias reported by the Manhattan Engineer District
avalon.law.yale.edu
Here is his description:
"At the far corner of the park, on the river bank itself, we at last come upon our colleagues. Father Schiffer is on the ground pale as a ghost. He has a deep incised wound behind the ear and has lost so much blood that we are concerned about his chances for survival. The Father Superior has suffered a deep wound of the lower leg. Father Cieslik and Father Kleinsorge have minor injuries but are completely exhausted.
While they are eating the food that we have brought along, they tell us of their experiences. They were in their rooms at the Parish House--it was a quarter after eight, exactly the time when we had heard the explosion in Nagatsuke--when came the intense light and immediately thereafter the sound of breaking windows, walls and furniture. They were showered with glass splinters and fragments of wreckage. Father Schiffer was buried beneath a portion of a wall and suffered a severe head injury. The Father Superior received most of the splinters in his back and lower extremity from which he bled copiously. Everything was thrown about in the rooms themselves, but the wooden framework of the house remained intact. The solidity of the structure which was the work of Brother Gropper again shone forth.
They had the same impression that we had in Nagatsuke: that the bomb had burst in their immediate vicinity. The Church, school, and all buildings in the immediate vicinity collapsed at once. Beneath the ruins of the school, the children cried for help. They were freed with great effort. Several others were also rescued from the ruins of nearby dwellings. Even the Father Superior and Father Schiffer despite their wounds, rendered aid to others and lost a great deal of blood in the process."
Again, this demonstrates they weren't unharmed, and we see there were other survivors in their area as well. It does note that while their house was damaged, it still was able to keep standing, though it attributes it to the work of "Brother Gropper" who helped build it. But the injuries actually seem to have been fairly severe, rather than minor--though, to be fair, perhaps the "minor injuries" simply meant one that wasn't completely debilitating, as it does note they were able to help others still.
So we do have Jesuits who survived the dropping of the atomic bomb, and they were in a house that managed to (unlike most of the other buildings nearby) survive, and they did all live reasonably long lives, even the one who was suffering from various illnesses throughout his life. This is indeed a notable story, and they were fortunate to survive and live so long. But it is not as miraculous as some make it out to be.