### About the Number 61 (sixty-one)

The `number 61` is a whole number that is also odd and prime.

More about `number 61`...

```   61 is opposite -61
61 is six units of 10 plus one 1
61 equals 075 octal; 061 is 49 decimal
61 equals 0x3D hexadecimal; 0x61 is 97 decimal
61 equals 111101 binary; 61 is not a valid binary number
```

Learning about `US Hwy-61` prompted us to see what the Wikipedia had to say about the `number 61`.

`61` the 18th prime number.

Two prime numbers are twin primes if they differ by two. `61` is a twin prime of `59`.

Wikipedia said that `61` is the sum of five squared and six squared.

##### Exercises

Part 1: Check Wikipedia for accuracy.

1. No or Yes. `52 + 62 = 61`

2. No or Yes. `61` is the `18th` prime number. {Wikipedia.org:: 1st 1000 primes}

3. No or Yes. `59` and `61` are twin primes.

4. Part 2: Learning about prime numbers.

5. `5` is a twin prime of `_____`

6. `11` is a twin prime of `_____`

7. `17` is a twin prime of `_____`

8. `_____` is the `1st` prime number greater than `61`. {Wikipedia.org:: 1st 1000 primes}

9. `_____` is the `1st` prime number less than `61`. {Wikipedia.org:: 1st 1000 primes}

##### More About 61

The Wikipedia indicated that `61` was also a cuban prime number.

```   (x^3 - y^3)
-----------   where  x = y + 1, y > 0
(x - y)

Let y equal 4...

x = y + 1 = 4 + 1 = 5

substitute every occurrence of x with 5
substitute every occurrence of y with 4

(5^3 - 4^3)   (125 - 64)
----------- = ---------- = 61
(5 - 4)          1

5^3 (five cubed) is 125
4^3 (four cubed) is 64
```

`[exercise]` Calculate the cuban prime number using one as input (i.e. let 'y' equal 1).

The "cuban" in "cuban prime number" has nothing to do with Cuba.

##### Update::2009.03.17

This nBAB about the number `61` was updated with the following MathBabbler Number Analyst output as a result of creating a nBAB for the number 62. While working on the nBAB for 62, MathBabbler learned that Sigmund Freud had an obsession with the numbers `61` and 62 thinking they might be his death age. Freud was wrong and he ended up dying in 1939 at the age of 83.

```   MathBabbler Number Analyst (MBNA) output:
=========================================
61 is a natural, whole, integer
61 is odd
61 proper divisors are: 1,
61 is deficient (sum of divisors is 1)
61 is unhappy
61 is not a Harshad number
61 is prime
...Sexy prime with 67
...Twin prime with 59
...Pythagorean
61 is undulating
61 is prime
61 in octal is 075
61 in hexadecimal is 0x3d
61 in binary is 111101 (is odious)
61 nearest square numbers: -12...3 (49...64 )
sqrt(61) = 7.81025
ln(61) = 4.11087
log(61) = 1.78533
61 reciprocal is .01639344262295081967213114754098
61! is 5.0758e+83
61 is 19.4169 Pi years
61 is 3 score and 1 year
61 written as a Roman numeral is LXI
```

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 07 March 2006 