Nerd trivia: The inauguration of Joe Biden means the beginning of the fifth period of time with 6 living Presidents. Four of the five periods have come since 1993:
1993-4: Nixon, Ford, Carter, Reagan, Bush I, Clinton
2001-4: Ford, Carter, Reagan, Bush I, Clinton, Bush II

2017-18: Carter, Bush I, Clinton, Bush II, Obama, Trump
2021-: Carter, Clinton, Bush II, Obama, Trump, Biden

The earlier one was 1861-62: Van Buren, Tyler, Fillmore, Pierce, Buchanan, Lincoln.

There have never been seven Presidents alive at the same time

Another trivia 6 - there have been 6 Presidents who at one point in their lives were the only President alive:
Washington
Adams
Grant
T Roosevelt
Hoover
Nixon

Nixon is the only President who has been the only President alive and one of a set of 6 living Presidents

The rule of 6 also travels across the Atlantic - we are currently in the 11th period of history with 6 living British Prime Ministers. There have never been 6 PMs alive at the same time. Here are the groups of 6 in the last 100 years:

May-Oct 1923: Rosebury, Balfour, Asquith, Lloyd George, Law, Baldwin
1924-1928: Rosebury, Balfour, Asquith, Lloyd George, Baldwin, Macdonald
1964-65: Churchill, Eden, Attlee, Macmilland, Home, Wilson
1976-77: Eden, Macmillan, Home, Wilson, Heath, Callaghan

1979-86: Macmillan, Home, Wilson, Heath, Callaghan, Thatcher
1990-95: Home, Wilson, Heath, Callaghan, Thatcher, Major
2019-date: Major, Blair, Brown, Cameron, May, Johnson

Combining this with the Presidents list I conclude we are now only the second period of history when there have been 6 Presidents alive and 6 PMs alive. The earlier one was in 1993-94.

There have been 4 PMs who were the only PM alive at some point in their lives. Three of them date from the earliest days of the office: Walpole, Pelham and Newcastle. The fourth is Gladstone - between 1881 and 1885, when Lord Salisbury took the job, he was the only PM living.

Given the respective age distributions of the two groups, I think the chances of Britain getting to 7 PMs alive at once for the first time ever in coming years are better than the US's chances of having 7 living Presidents

The oldest of Britain's former PMs is John Major, still only 77 and thus younger than the currently serving US President Joe Biden (78)!

Carter is now 96, and Clinton, Bush II and Trump are all in their 70s

Not too late for a Sir John Major "centrist grandad" comeback?