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DEAR DR HAYLEY,
In an article entitled 'The unconscious significance of numbers', Sir Harold Jeffreys (1936) discussed the emphasis laid on certain numbers such as 2, 3, 7, and 12 in legend and superstition, and he commented on possible sexual significance of the number 5 and also on the interest shown for centuries in the prime numbers. I first became aware of this article several years ago when I reviewed one of the volumes of Jeffreys' collected works, and I re-read it recently after hearing Dr Beate Schmolke-Hasselmann (1982) of Göttingen University remark on evidence in medieval literature that the number 31—which is not mentioned by Jeffreys—appears to have had some obscure sexual significance around the time of the Crusades, a matter that clearly deserves investigation.
Thirty-one is the maximum number of days in a month, the approximate period of the menstrual cycle. Other more or less obvious and possibly trivial remarks that one might make about the number 31 are (a) that it is the 12th prime number (just as 13 is the 7th prime number) and (b) that the factors of 31 + 1 = 32 = 25 = 2 x 2 x 2 x 2 x 2 add up to 31, in accordance with the general result that the sum of the factors of 2n is equal to 2n - 1 if n is any positive integer. But more interesting are the findings of a very brief investigation of the occurrence of the number 31 in idiomatic expressions in various languages. The opportunity to make this study was provided one evening last June outside a café in Varenna, Italy, during a course on 'Turbulence and predictability in geophysical fluid dynamics' at the International School of Physics 'Enrico Fermi'. The native languages represented by those participants in the course who were present (and to whom together with Dr Karen Pratt of Jesus College, Oxford, I am grateful for helpful discussions) were Arabic, Dutch, English, French, Hebrew, Hindi and other major Indian languages, Hungarian, Italian, Parsee, Polish, Roumanian, Spanish and Turkish