## Soju and prime numbers

Earlier this evening, I went with my girlfriend to eat Samyeopsal, a barbecue pork dish. The traditional accompaniment for this pork dish is Soju, a type of sweet vodka from Korea. One normally drinks the liquor from a two ounce shot glass, so a 360 ml bottle will almost fill seven glasses. Traditionally, one fills the glass of one’s dining partner whenever their glass is empty. If two people drink one bottle, then one ends up drinking four glasses and the other drinks three. If three people drink one bottle, then one person drinks three glasses, but the other two just have two glasses. Because it is awkward for one person to drink alone, one often ends up buying a second bottle to keep the solitary drinker company. The only time that there would not be one shot left over is a table of one (how sad!) or a table of seven (who would certainly order more than one bottle, anyway). Choosing a size of bottle than is a prime multiple of the size of a standard glass is clearly a clever trick from a marketing point of view.

I’m reminded of the periodicity of cicada migrations that Daniel C Dennett writes about in “Darwin’s Dangerous Idea”. Apparently, colonies of different species of cicadas return to different sites at different periods. However, the periods are always a prime number of years, sometimes as long as seventeen years. The explanation that he offers is that if there is a predator that returns to that site regularly (say once ever two years) then the cicadas will avoid that predator more often if the period of their return is a prime number. If they returned with a periodicity that was a composite, non-prime number of years, then one of the factors of that number of years might be the frequency that the predator returned, which would ensure that they met up regularly.