“My hat was off to someone who was willing to take the time out of his life to go get these precious specimens,” said Dr. Church, the Harvard geneticist, who has devoted a portion of his laboratory to research into the reversal of aging.

The kind of ultrarare mutations that supercentenarians might harbor, Dr. Church believed, were not likely to be detected with standard techniques, which scan only the places in the genome where DNA is already known to vary between individuals.

To look for as-yet-uncataloged variations would require sequencing all of the supercentenarians’ six billion genetic letters, a far more expensive procedure. When he and Mr. Clement first discussed the idea in 2010, the cost was about $50,000 per genome.

But the price was falling. And with the financial support of a handful of like-minded wealthy individuals who agreed to invest in the exploratory phase of the project, “it just seemed,” Mr. Clement said, “like something I could do.”

Even with the Harvard name as a calling card, several of the families he contacted over the next few years did not respond to his inquiries. A few, Mr. Clement knew, had already been approached by laboratories at Stanford and Boston University, which were collecting their own stashes of supercentenarian DNA.

“She already did her DNA donation,” Paul Cooper, the grandson of Besse Cooper, a 116-year-old former suffragist, told Mr. Clement, who had driven several hundred miles to her Monroe, Ga., nursing home in 2012.

Walter Breuning, of Great Falls, Mont., one of just a handful of men known to have lived to 114, replied in late 2010 that it was his preference not to risk winter meetings. He died early the next spring.