Today’s an international prime day

Today’s a prime day. Whether you write the date in American (MMDDYY), European (DDMMYY), or ISO 8601 (YYYYMMDD) format, you get a prime. That is, 112913 and 291113 and 20131129 are all prime numbers.

We’ll call a date an American prime date if MMDDYY is prime, a European prime date if DDMMYY is prime, and an ISO prime date if YYYYMMDD is prime. (Single-digit days and months are padded with a zero.) If a date is prime by all three criteria, we’ll call it an international prime date. Today is an international prime date, and there won’t be another one until August 11, 2019.

If a date is an American prime date and a European prime date, we’ll call it a transatlantic prime date. After today, the next transatlantic prime dates are December 4 and 13 this year. There will be no transatlantic prime dates in 2014, 2015, and 2016 since these dates correspond to numbers that are divisible by either 2 or 5. The first transatlantic prime date of 2017 will be January 16.

9 thoughts on “Today’s an international prime day

  1. Isn’t the ISO format written CCYYMMDD these days?

    I was in a very boring class a few weeks back and when I saw it written that way it made me smile.

  2. It’s also a pretty neat coincidence that each pairing (MM, DD, YY) happens to be a prime as well which is not the case for the next international prime.

  3. @Ed: Why would it? According to ISO 8601, absolutely not (amongst other things, it would be ambiguous – 2012 is CCYY, or YYYY? IIRC, both the year 1912 and 2012 have actually happened).

    You are correct that some aaaaancient – as in “1980s” – standards used this format, but I haven’t seen it in anything modern (except for systems _interfacing_ with the dinosaurs, by necessity).

  4. Is there an infinite number of extended ISO prime dates? (where the year does not have modulus 10000 applied). Knowing that there are infinite pairs of primes within 600 of each other doesn’t seem like enough by itself.

  5. @Piskvor: I won’t call my clients client a dinosaur (in a public forum), but it’s the Army Core of Engineers… Levee database stuff.

  6. George Phillips: You should be able to prove there are infinitely many such primes using Dirichlet’s theorem on primes in arithmetic progressions.

  7. Thanks, John. Taking Wikipedia’s word for it (for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is a non-negative integer), I can pick d=10000 and a=903 and learn that my birthday will have infinitely many extended ISO prime dates. Yay!

  8. Neat! What about if we write dates with dashes, e.g. YYYY-MM-DD:
    2013-11-29 = 1973 which is pleasingly prime!

    DD-MM-YY follows suit with 29-11-13 = 5, but MM-DD-YY will have to wait until next century.

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