Carter has passed Garner! He now holds ALL the records for anyone who has ever been President or VP! Only Alf Landon's still stands and he was never President!
Yes, you are correct! Jimmy Carter has now passed John Nance Garner on the list of longest-living Presidents or Vice Presidents (here was that list at the beginning of September). And we are 10 days away from President Carter becoming the first President or Vice President to ever celebrate their 99th birthday. Not bad for a guy who has been in hospice care since February.
And, yes, Alf Landon is the longest-living major party nominee for President or Vice President. Landon was the 1936 Republican Presidential nominee and lost the general election to Franklin D. Roosevelt. Landon was 100 years, 33 days old when he died in 1987. Think about that for a second: Alf Landon was the Republican Presidential nominee when FDR ran for his second term as President, and Landon died when Ronald Reagan had a little over a year left in his Presidency!
BUT, it's worth nothing that while Alf Landon is undoubtedly the longest-living Presidential or Vice Presidential nominee by a major party, he is NOT the longest-living person to ever win Electoral votes as President or Vice President.
In 1948, many Southern Democrats opposed to support for civil rights in the party's platform at the Democratic National Convention bolted from the party and formed the States' Rights or "Dixiecrat" party to run against incumbent Democratic President Harry S. Truman and Republican nominee Thomas Dewey. The Dixiecrats nominated South Carolina Governor (and future longtime Senator) Strom Thurmond as their Presidential nominee. Despite not being a major party nominee, Thurmond and the Dixiecrats, relying on voters in former Confederate strongholds in the South, performed better in the general election than just about any third-party Presidential candidate of the 20th Century.
Thurmond and the Dixiecrats won 4 states and 39 Electoral votes in 1948. In 1936, Republican nominee Alf Landon won two states and just 8 Electoral votes. So Thurmond's racist, third-party challenge performed far better than the GOP nominee had done twelve years earlier.
So, unfortunately, while we're talking about longest-living President or Vice Presidential nominees, we have to throw Strom Thurmond in the conversation considering the fact that he won far more Electoral votes in 1948 than Alf Landon did in 1936. And Thurmond lived longer, as well. Thurmond was 100 years, 203 days old when he died in 2003 -- he lived 170 days longer than Alf Landon did.
Thurmond is also almost certainly the oldest person to ever be one of the top officials in the Presidential line of succession. As I mentioned, Thurmond eventually served in the U.S. Senate from South Carolina -- a seat that he held from 1954-2003 (except for a period of about 7 months in 1956) -- where he eventually became the first (and only, so far) person to serve in Congress after their 100th birthday. Due to his lengthy tenure in office, Thurmond was president pro tempore of the U.S. Senate for several years when his party was in control of the Senate.
As president pro tem, Thurmond was third in the Presidential line of succession, behind the Vice President and Speaker of the House. This meant that, Thurmond was third in the line of succession well after turning 98 years old. In June 2001, Vermont Senator Jim Jeffords announced that he would begin caucusing with the Democrats in the Senate, which gave the Democrats a narrow majority and control in the Senate, However, if Jeffords had not made that decision when he did, Strom Thurmond would have been president pro tempore on September 11, 2001. That means a nearly 99-year-old man would have been third in the Presidential succession at the time of the 9/11 attacks.