Prime Numbers and Prime Ministers

I occasionally watch University Challenge. Unlike many people, I do not think it is simply based on recall of facts.  But was really fascinated and humbled by this little episode 5 weeks ago:-

 A team successfully answered the question "Name three 20th British Prime Ministers and the year in which they were either elected or re-elected - in which the year of election or re-election is a prime number". Now I am sufficiently numerate (just) and sufficiently knowledgeable about 20th century general elections (1902(Balfour), 1906(Campbell-Bannerman), 1910(Asquith)...1929 (Ramsay Mac), 1931 (Ramsay Mac),.... 1945(Atlee), 1950(Atlee),1951(Churchill), 1955 (Eden),1959(Macmillan),1964 (Wilson).... etc.) to answer that question given 30 minutes notice and access to a calculator or even to paper and pencil; but they got three right answers almost instantly. ( I knew the numbers ending in an even number or in 5 cannot be prime)

I showed this to a prof of maths in my place - who said:-

"Dear Iain,
Thanks for this curious question. I'm quite hot on my prime numbers but not so hot on prime ministers !
Of the dates you mention, only 1931 and 1951 are prime and after that the only candidates are 1973, 1979 ( Thatcher ? ) 1987, 1993, 1997 ( Blair ? ) and 1999."

To which I replied
"Adam
Indeed.
1931(Ramsay Mac) 1951(Churchill) 1979 (Thatcher) 1987 (Thatcher again) 1997 (Blair).

1973, 1993 and 1999 had no general elections.
A truly inter-disciplinary question."

Iain