# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## Unique Properties of 37

• 37 is the smallest irregular prime (submitted by Andy Baker and John Kiehl)
• 37 is the smallest left and right truncatable prime having more than one digit
• 37 is the only prime with period length three: 1/37 = 0.027 027 027 ...
• 37 is the prime you get if a three digit number having the same digits is divided by its digit sum
• In the famous Sultan's Dowry problem, the commoner, who want to maximize his chances to marry the daughter with the highest dowry, should skip the first 37 daughters (our of the total 100) and marry the daughter whose dowry exceeds the ones he saw before
• Besides trivial 1, 37 is the smallest centered hexagonal number which is at the same time a star number (also known as a centered 12-gonal number)
• 37, that is XXXVII, is the last odd Roman numeral alphabetically
• A web page about 37: "37 Factoids" page
• Every positive integer is the sum of at most 37 fifth powers
• 37 is the smallest prime that doesn't divide the order of the Monster group
• Every positive integer is the sum of at most 37 fifth powers
• 37 is the smallest number that appears in its factorial twice
• 37 is the smallest emirp that doesn't have a twin