The word “emirp” was featured in three bonus questions during last week’s episode of “University Challenge”, broadcast on Monday 4 February 2019 here in the UK. It’s available for another 22 days here on the BBC iPlayer. At 22:24 Jeremy Paxman introduces the bonus questions as follows: “‘prime’ spelt backwards is ‘emirp’, a term denoting a prime number that forms a different prime number when its digits are reversed”.
As you will now know if you followed the iPlayer link above, the first emirp is 13 (which becomes 31 when reversed). The 21st prime number (73) is also an emirp; it becomes the 12th prime number (37) when it is reversed, which makes it, according to Sheldon in “The Big Bang Theory”, the best number. The third and final question about emirps asked for the first 3-digit example. It’s 107. You might take a guess at 103 but it can’t be: 301 is not prime (it’s 7 x 43).
The Oxford Dictionaries website does not currently have a listing for emirp, so it joins a short list of “Word of the Week” pieces on this Blog that deal with terms that have not yet made it into the most authoritative publication about the English language. Like this recent example, plangonolist, I expect it to be included at some point in the future. In the meantime, there’s this short Wikipedia page which lists the first 30-odd examples, including all 2-digit and 3-digit emirps.
The last time I reflected on prime numbers was in this piece on 1 January 2017, noting that 2017 is prime. Like every other year in this millennium, 2017 cannot be an emirp: they all end in the digit 2 when reversed, making them even, and therefore not prime. This got me wondering, when was the last time that the year was an emirp, and when will it happen again? This page, on prime-numbers.info, lists the first 1000 emirps and gave me the answers. 1979 was the last time it happened, and we’ll have to wait until 3011 for the next time. Only another 992 years to go.