When Russell M. Nelson was born in Salt Lake City, Utah had been a state for less than 30 years. Calvin Coolidge was the president of the United States. And total membership in the Church of Jesus Christ of Latter-day Saints, which is now 17 million around the world, was less than 600,000.

Mr. Nelson, the oldest president in the church’s history, turns 100 on Monday. He has been alive for more than half of the life span of the church itself.

In a presidential election cycle that has prompted soul-searching about aging and leadership, Mr. Nelson’s milestone suggests that, at least in his church, a triple-digit birthday does not merit much hand-wringing. He remains a popular figure among church members, who view their president not just as an executive but as a “prophet, seer and revelator.”

The remarkably advanced age of the church’s highest leader occasionally produces grumbling from the faithful, especially as it grapples with social issues relating to marriage, sexuality and gender that tend to be viewed more liberally by younger members. And leaders at extremely advanced ages may effectively pass most of their duties onto others less subject to public accountability.

“A power vacuum at the top, caused by the incapacitation of the Church president, can put the entire church at risk of damage that might otherwise be prevented by a competent president,” the authors of a paper titled “Gerontocracy and the Future of Mormonism” argued in Dialogue, an independent Latter-day Saints journal, in 2016.

A spokesman for the church, Doug Anderson, said Mr. Nelson was not available for an interview. But Mr. Nelson’s known concessions to his age include his giving up skiing at age 93 and curtailing international travel. After a fall on the day after his 99th birthday last year, he skipped attending the church’s twice-yearly General Conference, though he contributed a taped message.