About the Number 420 (four hundred twenty)

420 is only a number, but 4/20 has become a dreaded date.

   420 is a rational, natural, whole number
   420 is a positive integer
   420 is an even number
   420 is a composite number with prime factors 2 2 3 5 7
   420 is a multiple of 210 and a factor of 840
   420 in binary (base-2) is 110100100
   420 in octal (base-8) and hexadecimal (base-16) is 644 and 0x1a4
   420 is approximately 20.494 squared
   420 squared is 176,400
   4:20pm in military time is 42:20

   [output from the MathBabbler Number Analyst inserted 4/20/2008]

   420 is abundant (sum of divisors is 924)
   420 is unhappy
   420 is a Harshad number
   420 is evil

On 20 April 2007 (4/20), an attempt to do 420! using Google's calculator resulted in the "I'm Feeeling Lucky" hyperlink to http://en.wikipedia.org/wiki/420_(cannabis_culture).

According to the Wikipedia, 420 is the sum of four consecutive primes (101 + 103 + 107 + 109).

420 is a Harshad number in the base-10 number system. [Harshad number: sum of the digits is a factor of the number. 420/(4+2+0) = 70]

4/20 BADs (Basic Arithmetic Dates).

   [most of these were completed on 4/20/2008]

   4/20/00... (4 - 0!)! = 20base-3
   4/20/01... (4 - 1)! = 20base-3
   4/20/02... 4^2 = 20base-8
   4/20/03... 20base-3 / sqrt(4) = 3
   4/20/04... 4! - 20 = 4   or  sqrt(20 - 4) = 4
   4/20/05... 20 / 4 = 5
   4/20/06... sqrt(20base-8)! = 6 * 4
   4/20/07... (7 - 4)! = 20base-3
   4/20/08... sqrt(4) * 8 = 20base-8 ... 4 * 8 = 20base-16
   4/20/09... sqrt(4) * sqrt(9) = 20base-3
   4/20/10... sqrt(4) * 10 = 20

Stephen Stills once wrote... "4 and 20 years ago I come into this life."

Nursery rhyme... "Sing a song of sixpence, a pocketful of rye, 4 and 20 blackbirds baked in a pie."

Adolph Hitler was born on 20 April 1889.

[update: 4/20/2008] Edna Parker of Shelbyville, Indiana, celebrated her 115th birthday on 4/20/2008.

Update::2009.04.20

The MBNA has changed a lot since this BAB was created.

   MathBabbler Number Analyst (MBNA) output:
   =========================================
   420 is a natural, whole, integer
   420 is even
   420 proper divisors are: 1,2,3,4,5,6,7,10,12,14,15,20,21,
                            28,30,35,42,60,70,84,105,140,210
   420 is abundant (sum of divisors is 924)
   420 is unhappy
   420 is a Harshad number
   420 is not prime
   420 has the prime factors: 2*2*3*5*7 (sum=19)
   420 is pronic (oblong)
   420 in octal is 0644
   420 in hexadecimal is 0x1a4
   420 in binary is 110100100 (is evil)
   420 nearest square numbers: -20...21 (400 [20]...441 [21])
   sqrt(420) = 20.4939
   ln(420) = 6.04025
   log(420) = 2.62325
   420 reciprocal is .00238095238095238095238095238095
   420! is 1.17983e+921
   420 is 133.69 Pi years
   420 is 21 scoreyears
   420 written as a Roman numeral is CDXX

BAB::BABEs on 20 April 2009.

Update::2009.06.26

Michael Jackson died (may he RIP) on 25 June 2009. The day after his death MathBabbler posted an item to his AzFoo at AzCentral.com about how Jackson's death did not crash the Internet. The Jackson related AzCentral.com post number 420 for AzFoo.

Update::2010.01.24

The following was my Facebook status update on 2010.01.24.

   Wondering how the Facebook developers came up with 
   number 420 for the maximum length of a status update.

The number 420 is a popular number in the cannabis culture. I've been told that chronic is a type of cannabis [I confirmed this using UrbanDictionary.com]. The number 420 isn't a chronic number, but it is a pronic numbers (i.e. it is the product of two consecutive integers 20*21).

Since the last time this BAB was updated, the MBNA (MathBabbler Number Analyst) was modified to check if a number is the sum of two or more consecutive primes and it turns out the number 420 is the sum four consecutive primes (101+103+107+109).

Update::2011.03.21

The 420th nBAB, which was about the number 7909, was posted on 21 March 2011.

Update::2015.04.20

MBNA output generated on 4/20/2015.

MathBabbler Number Analyst (MBNA) output:
=========================================
420 is a natural, whole, integer
420 is even
420 proper divisors are: 1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,
420 has 23 proper divisors
420 is abundant (sum of divisors is 924; ratio: 2.2)
420 is unhappy
420 is not a Squarefree Number: 4,
420 is Harshad (Niven) number
420 is composite (not prime)
420 has the prime factors: 2*2*3*5*7 (sum=19)
420 is pronic (oblong) (20*21)
420 is Arithmetic (A003601)
420 is the sum of 4 consecutive primes
420 = 101 + 103 + 107 + 109
420 is not in A038853
420 in octal is 0644
420 in hexadecimal is 0x1a4
420 in binary is 110100100 (is evil)
420 nearest square numbers: -20...21 (400...441 [21])
sqrt(420) = 20.4939
ln(420) = 6.04025
log(420) = 2.62325
420 reciprocal is .00238095238095238095238095238095
420! is 1.17983e+921
420 is 133.69 Pi years
420 is 21 scoreyears
420 written as a Roman numeral is CDXX
420 is 106^2 - 104^2 and 2 * (106 + 104)
420 is a multiple of 2 & it contains a 2 (A121022)
420 is a multiple of 4 & it contains a 4 (A121024)
420 is a multiple of 20 & it contains a 20 (A121040)
420 is a multiple of 42 & it contains a 42

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 20 April 2007
+ filled in the 4/20 BADs
+ added Edna Parker 115th birthday tidbit
+ added output from the MathBabbler Number Analyst
+ AzFoo 420th posting to AzCentral.com
+ 420th nBAB posted
+ added MBNA output on 4/20/2015

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