### About the Number 31 (thirty-one)

MathBabbler was mathematizing the song "Mama Said" by the Shirelles (circa 1961) when he discovered that the Shirelles also did a song titled "`31` Flavors" (circa 1963). He was working on "Obama Said" after having just completed a BAB titled "`31`% and 105% are Popular Percentages These Days."

```   MathBabbler Number Analyst (MBNA) output:
=========================================
31 is a natural, whole, integer
31 is odd
31 proper divisors are: 1,
31 is deficient (sum of divisors is 1)
31 is happy
31 is not a Harshad number
31 is prime
...Sexy prime with 37
...Twin prime with 29
...OEIS:002145 (4n+3; n=7)
...Super
...Right-truncatable
31 is undulating
31 is prime
31 in octal is 037
31 in hexadecimal is 0x1f
31 in binary is 11111 (is odious)
31 nearest square numbers: -6...5 (25...36 )
sqrt(31) = 5.56776
ln(31) = 3.43399
log(31) = 1.49136
31 reciprocal is .03225806451612903225806451612903
31! is 8.22284e+33
31 is 9.86761 Pi years
31 is 1 score and 11 years
31 written as a Roman numeral is XXXI
```

`sqrt(31) ÷ ln(31) = 1.62137` which is the Golden Ratio (`1.61803399`) rounded the nearest hundredth.

`[Wikipedia]` "`31, 331, 3331, 33331, 333331, 3333331, 33333331` are all prime. For a time it was thought that every number of the form 3w 1 would be prime. However, the next nine numbers of the sequence are composite."

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 25 February 2009 