When Jimmy Carter entered hospice care at his Georgia home last year, his family and friends thought he had only days to live. More than 19 months later, he is set to celebrate his 100th birthday on Tuesday, the first president in American history to hit the centennial mark.

The last chapter of Mr. Carter’s already remarkable life story is turning out to be one of astonishing resilience. The peanut farmer turned global statesman has over the years beaten brain cancer, bounced back from a broken hip and outlived his political adversaries. And now he is setting a record for presidential durability that may be hard to break.

Though frail and generally confined to his modest ranch house in Plains, Ga., Mr. Carter has not only refused to surrender to the inevitability of time, he has perked up in recent months, according to family members. He has become a little more engaged again, telling his children and grandchildren that he has a new milestone he wants to reach — not his birthday, which he professes not to care that much about, but Election Day, so that he can vote for Vice President Kamala Harris.

“It’s a gift,” Josh Carter, one of his grandsons, said of the last few months. “It’s a gift that I didn’t know we were going to get.”

Mr. Carter had already surpassed all of his predecessors to become the longest-living president, but some of those who have experienced his stubborn irascibility over the decades said they were not surprised that he is approaching his second century.

“That’s Jimmy,” said Gerald Rafshoon, his White House communications director and longtime friend. “It’s almost like his whole life has been to go against the norm. Tell him he can’t do something, just tell him that, and you’re bound to see the determination.”

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