# Fun Facts About the Number 420

TR Smith is a product designer and former teacher who uses math in her work every day.

Like the 666, the number 420 is significant in Western culture. Although it is most commonly associated with cannabis culture, the number 420 also has many curious mathematical properties. Here are some fun facts about this number you may already know, and some you may not.

## The Number 420 in Cannabis Culture

The phrase "four-twenty" first became associated with marijuana use in the 1970s. There are many stories about how this number came to be associated with smoking a doobie. The most accepted tale is that a group of cannabis smokers in San Rafael, California used to meet at 4:20 pm every day to look for an abandoned cannabis crop they had heard rumor of. Although they never found the secret garden, the phrase "four-twenty" stuck around as their code word for weed and stoner culture, eventually gaining popularity with teens and young adults in California.

A disproven theory about how 420 came to be shorthand for cannabis is that it was the police code for marijuana smoking in progress. Another disproven theory is that there are 420 chemical compounds in marijuana.

Not only is the time 4:20 associated with cannabis, but also the date April 20th (4/20). April 20th is celebrated as an unofficial holiday in many cities with people gathering to smoke pot, or to protest for the legalization of pot (where it is not already legal). The state of Colorado was the first to legalize retail sale of marijuana for recreational use.

Colorado Highway Patrol had an ongoing problem with stealing "420" mile-marker signs along the highways. To deter sign theft, all of the "420" signs were replaced with "419.99" signs.

• 420 is between the twin primes 419 and 421. One of the great unsolved problems in mathematics is if there are infinitely many twin primes.
• It is the sum of consecutive primes 101, 103, 107, and 109.
• It is a Niven number or Harshad number since it is divisible by the sum of its digits. 420 ÷ (4+2+0) = 70.
• It is also divisible by the some of its squared digits. 420 ÷ (4^2 + 2^2 + 0^2) = 21.
• There are 42 ways to partition a group of 10 objects, and 10*42 = 420.
• It is a pronic number, meaning it is of the form n*(n+1); in this case, 420 = 20*21. The number 420 is also 2 times a pronic number, since 420 = 210*2, and 210 is pronic as the product of 14 and 15.
• It is the least common multiple of the numbers 1, 2, 3, 4, 5, 6, and 7.
• Its factors are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, and 420. The sum of all the factors is 1344.
• There are four numbers whose sum of factors equals 420. They are 236, 278, 377, and 419.
• If you divide the number 50 by {3, 4, 6, 7, 8, 9, 11, 12, 13, 14,...}, i.e., all the numbers less than 50 except for the factors of 50, you get the remainders {2, 2, 2, 1, 2, 5, 6, 2, 11, 8, ...}. The sum of all these remainders is 420.
• If you flip a coin 11 times in a row, there are exactly 420 flip sequences that don't contain two consecutive tails.
• 420^420 -- that's 420 multiplied by itself 420 times -- is a number with 1102 digits that ends in 420 zeros.
• The product of all the numbers up to 420 -- that's 420 factorial, written as "420!" -- is a number with 922 digits that ends in 103 zeros.
• There are 420 ways to split up a group of 8 different objects into one set of 4 and two sets of 2.

## The Number 420 in Culture and Science

• April 20th is the birthday of Adolf Hitler (dictator), Joan Miró (painter), George Takei (actor), and Jessica Lange (actress). It is also the day of the Columbine, Colorado school shooting.
• The 420th episode of Gunsmoke was "The Newcomers" and the 11th episode of the series to be broadcast in color.
• The 420th episode of Lassie was "Fly Away Home" and was the 3rd episode of the 13th season.
• The 420th episode of The Simpsons was "All About Lisa."
• It is the number of grams in 14.815064 ounces.
• It is the number of kilometers in 260.9759 miles.
• It is approximately the molar mass of Rhenium(III) Oxide -- Re2O3.
• It is the number of calories in four medium bananas.
• At 4:20, the hour hand and the minute hand of an analog clock are 10 degrees apart.
• Seven hours is 420 minutes.
• In binary, it is written as 110100100.
• In Roman numerals, it is written as CDXX.

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• mark 14 months ago

Great info .. thank you :)

• Alan 12 months ago from Tasmania

It is so good to see a mind like yours working away and enjoying every minute of it!

My school days taught me that my mathematics potential was very low indeed, but in older age I am not so scared of it.

• Author

TR Smith 12 months ago from Eastern Europe

Thanks JCL, maybe I can make it to Hub of the Day on April 20th.

• Alan 12 months ago from Tasmania

That would be very well deserved! In my opinion.