The number 37 is the 12th prime number. It is both the fourth hex number,
 |
and the third star number,
 |
The factorization 
accounts for the familiar products 
,
, and 
. The number also occurs in the limiting solution
of the secretary problem: rejecting about 
percent of the candidates
and then selecting the next record maximizes the asymptotic probability
of choosing the best candidate, and that maximum probability
is 
.
The prominence of 37 in requests for a supposedly random two-digit number is a psychological and cultural phenomenon, not a consequence of these arithmetic properties. Veritasium (2024) discusses surveys of such choices, while a collection of coincidental appearances is maintained by Magliery.
