## Numerical facts

• A trick for testing a number for divisibility by 37.
• 37 is a "hex number", also known as a centered hexagonal number. (Note).
• 37×3 is 111; 37×6 is 222; and so on. 37×18 is 666.
• 3×7×37 = three 7's (777).
• If you multiply 37 by palindromic "3-ish" numbers, e.g. 63636, you get amusing palindromic products.
• 1/37 is .027027027... and 1/27 is .037037037...
• 3333333333333^3 = 3.703703703703×10^37.
• Numbers of the form "abczyx" are divisible by 37. (Note).
• If "abc" is a multiple of 37, then so are "bca" and "cab". (Note).
• 3×(3+7)+7=37
• 37/3.7=3+7
• 37 minutes is about a Golden Section of an hour. (Note).
• Some 37-related numbers:  2^37 137438953472 37! 13763753091226345046315979581580902400000000 37^37 10555134955777783414078330085995832946127396083370199442517
• The first 37 decimal places of some numbers:  pi 3.14159 sqrt(2) 1.41421 e 2.71828 1/e 0.367879
• Some 37-related numbers in base 37, choosing as 'digits' the 37 ASCII characters beginning with 37 (truncated, where appropriate):  2^37 &59I:C'' 37! +/%'HG1GA52&:9>%)3));;D46+I% 37^37 &%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% pi ( *-D(4E<80+C)-(?FG9<,D>-6=AA&;=)E@I>, e ' ?:1)B-3*,:(E(I*=%.8,G-F@>/0B@@I82D<, sqrt(2) & 41'*F5H%G'BEC:C&8FD=<'?>-C'';73?*73(
• Landon Curt Noll had too much (Cray) time on his hands, so he sent me a vast collection of huge prime numbers that are related to the number 37 in various ways.

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Tom Magliery, tom@magliery.com