The shortest gap between two Friday the 13ths

Question

Friday the 13th comes round at least once every year, and sometimes several times.

What is the smallest possible number of days between one Friday the 13th and the next? In which months does this minimum occur, and does it need a leap year or an ordinary year?

As a follow-up, what is the longest possible wait between two Friday the 13ths?

Accepted Answer

28 days, between 13 February and 13 March in a non-leap year. Why. The 13th of one month and the 13th of the next are separated by exactly the length of the first month. For both to be Fridays, that length must be a multiple of 7. The only month length that is a multiple of 7 is 28, which happens only for February in an ordinary year. So if 13 February is a Friday in a non-leap year, 13 March is a Friday too, and the gap is 28 days. This happened in 2015 and happens again in 2026: 13 February 2026 and 13 March 2026 are both Fridays. Why nothing shorter. Two 13ths are always in different month…

The shortest gap between two Friday the 13ths

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