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.

Part 2: Learning about prime numbers.

4. 5 is a twin prime of _____

5. 11 is a twin prime of _____

6. 17 is a twin prime of _____

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

8. _____ 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.

External Hyperlink(s)

• Wikipedia.org:: 61 (number)

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 [8])
   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