### Countdown to 2021:

Here is a countdown you can use on New Year’s Eve to bring in 2021:

### It’s Almost Like 2021 Is Looking in a Mirror!

Squaring means multiplying a number by itself. Something unusual happens when you square 2021 and you also square its reverse, 1202. Complete the two multiplication problems below to see for yourself!

There are only 50 numbers less than 10000 with this same property. They are all listed in the table below:

For each pair of numbers in the table, the smaller number was listed first, but if you look carefully you will notice 2001, 2011, 2012, **2021**, and 2022 in this century and 2101, 2102, 2111, and 2121 in the next.

### Math Facts about the Number 2021:

2021 is the difference of two squares in two different ways:

45² – 2² = 2021 and

1011² – 1010² = 2021.

2021 is not the hypotenuse of any Pythagorean triples, but it is a leg in four:

180-2021-2029, calculated from 2(45)(2), 45² – 2², 45² + 2²,

2021-43428-43475, which is (**43**-924-925) times **47**,

2021-47472-47515, which is **43** times (**47**-1104-1105)

2021-2042220-2042221, from 1011² – 1010², 2(1011)(1010), 1011² + 1010².

### Factors of 2021:

The previous year had many negative factors, although it had just as many positive ones. I can predict that 2021 will have only four negative factors to go along with its four positive ones. I think we will see a lot of the negative factors at the beginning of the year, but hopefully, the positive ones will be more evident as the year goes on.

- 2021 is a composite number.
- Prime factorization: 2021 = 43 × 47.
- 2021 has no exponents greater than 1 in its prime factorization, so √2021 cannot be simplified.
- The exponents in the prime factorization are 1 and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 2021 has exactly 4 factors.
- The factors of 2021 are outlined with their factor pair partners in the graphic below.

Those factors can help you with quadratic equations like these:

### Mathematical Tweets about 2021:

Here are tweets about the number 2021 in the order that I’ve seen them. If I see more, I’ll add more.

2020 = 2^2 x 5 x 101

2021 = 43 x 47

Even the prime factorization is better! #gobearcatmath— Scottsbluff Math Club (@SBMathClub) December 26, 2020

While you’re on the topic of numbers that seem prime at first but aren’t, have you considered the upcoming year (2021)? [Spoiler: 2021 isn’t prime!] 🙂

— Math Nerd 1729 (@1729Nerd) December 26, 2020

2021 Mathematical Equation pic.twitter.com/X3OwEL0VWU

— Iva Sallay (@findthefactors) December 28, 2020

Everything you ever wanted to know about 2021, the first* date that is both the concatenation of consecutive integers (20, 21) and the product of two consecutive primes (43 x 47)

*and probably last, in human termshttps://t.co/kwMRMdkCZv

— Alex Bellos (@alexbellos) December 28, 2020

The next such number is

2307340946901148 2307340946901147

which is the product of the primes 4803478892324963 and 4803478892324969.https://t.co/K4BkOiVQ9i https://t.co/Kd3kOMxwDX— Ed Southall (@edsouthall) December 28, 2020

21 Mathematical Hightlights for 2021 https://t.co/F0tHQfo1i7

— INDER J. TANEJA (@IJTANEJA) December 28, 2020

As a result of its enormous success (😭thank you all so much!) the #dailymaths challenge will continue into 2021! The calendar from which the #dailymaths challenge problems will be taken in 2021 is the Mathematics 2021 calendar, available now! https://t.co/kp6TIZbC0R

— Great Women of Mathematics (@GWOMaths) December 28, 2020

2021 is the smallest number made from the concatenation of rising consecutive integers that can be expressed as the product of two consecutive primes (43 × 47).

The next is

794018604377235322848433897872605582794018604377235322848433897872605583#HappyNewYear pic.twitter.com/lt1e84pKnA

— Maths Ed (@MathsEdIdeas) December 28, 2020

Love that mathematical symbol! “Greater than “

“2021 will be greater than 2020”❤️👏🏾❤️👏🏾 From a math teacher! pic.twitter.com/pqHEcg5zkU— Sheryl Clayton (@sherylpc) December 28, 2020

The perfect 2021 puzzle to get over 2020. Take your time. #mathiratti #20202021 pic.twitter.com/VTHjzjkfSq

— Diego Rattaggi 🇨🇭 (@diegorattaggi) December 28, 2020

2021 > 2020

It’s just math.

— Michigan Athletics 〽️ (@UMichAthletics) December 22, 2020

No, ２０２１ no es un número primo, pero es producto de dos primos consecutivos: 43 y 47

👉 El primo anterior es el 2017 y el siguiente, el 2027

La suma de sus cuatro divisores es un palíndromo: 2112

Su binario: 11111100101

Y lo más importante: 🌟 Que sea bueno para todos 🌟 pic.twitter.com/chDU39vJkB

— RSME (@RealSocMatEsp) December 30, 2020

2021 is the smallest number that can be expressed as the product of two consecutive primes that produces a palindrome when multiplied by its reverse and that is a position in π, e and φ with the same digit.#HappyNewYear pic.twitter.com/ROIvyKLEEt

— Maths Ed (@MathsEdIdeas) December 30, 2020

2021 multiplicado por su reverso, 1202, nos da un palíndromo: pic.twitter.com/eJ3LRZvbwQ

— fun with functions (@funfunfunctions) December 31, 2020

2021 se puede obtener como suma simétrica de cuadrados de varios números primos:

7² + 11² + 41² + 11² + 7² = 2021

13² + 19² + 31² + 19² + 13² = 2021

— fun with functions (@funfunfunctions) December 31, 2020

My final #paperfolding of 2020. I’m hopeful and optimistic about the New Year! #HappyNewYear2021 ⭐🕯️☮️ pic.twitter.com/TxzEfkVgi9

— Mark Kaercher (@shskaercher) December 31, 2020

A geeky number fact that’s a reminder we can turn things around in 2021…

2021 reversed ↩️ is 1202

2021² reversed ↩️ 1202²#HappyNewYear ❤️ pic.twitter.com/2AEZdFbEaW

— Chris Smith (@aap03102) December 31, 2020

Traditionally, my last puzzle of the year 🥂 #mathiratti pic.twitter.com/TMnSo8Ml3x

— Diego Rattaggi 🇨🇭 (@diegorattaggi) December 31, 2020

#NewProfilePic pic.twitter.com/pHSmiU7Q9M

— msk (@maths247366) December 31, 2020

An easy excercise but a really nice one to evaluate on this New year’s Eve. 😄

Happy New year to everyone. 🙂

Enjoy solving this problem. @SrinivasR1729 @RamaInExile @KrrishDhiman4 @AYUSHDM1 @Expert_Says @Manas92949812 @Bannu16750368 @BossGercek @svv1729 pic.twitter.com/q42nEFqRRN— Arka Mehatari (@ArkaMehatari) December 31, 2020

Happy New Year 43×47! 🎆 🎇 🎉 🎊 🥂 pic.twitter.com/kNlWBKFZHF

— Mathigon (@MathigonOrg) December 31, 2020

2020 has been an eventful year. It has taught a great lesson to everyone and the entire world. I know everyone has suffered, we all have learned so much and persevered through some challenging times. However, was still able to lead our daily life and activities this year. pic.twitter.com/RdCYhNAtq4

— Srinivasa Raghava ζ(1/2 + i σₙ )=0 (@SrinivasR1729) December 31, 2020

2021 és el numerador del resultat de la diferència de fraccions 1/4 – 1/45²

— Ferran Montardit 🎗 (@FerranMontardit) December 31, 2020

Next year will be a year of wisdom,

so I wish everyone

to focus and surrender to wisdom… pic.twitter.com/JOdttcGfnv— 𝕋𝕒𝕠 ℂ𝕙𝕚 (@be_the_source_) December 31, 2020

1573 Ring Out Wild Bells https://t.co/mMCOKfNXgO

— Iva Sallay (@findthefactors) January 1, 2021

2021 is the concatenation of two consecutive integers 20|21

2021 is also the product of two consecutive primes 43|47

The next such number is

2307340946901148 2307340946901147

which is the product of the primes

4803478892324963 and 4803478892324969.#HappyNewYear2021

— Ed Southall (@edsouthall) December 31, 2020

2021年は素数じゃなかった… pic.twitter.com/I0Dk0ycds2

— たくれ (@tackrei_) January 1, 2021

Celebrate. 2021 can be formed by multiplying two consecutive primes. What will life be like the next time this is true? (Thanks @DSMac27) pic.twitter.com/KkvEWBCFqH

— Cliff Pickover (@pickover) January 1, 2021

Happy New Year @LaSalleEd , @EmathsUK , @StudyMaths !!! I guess you already know 2021 is the product of consecutive primes !! pic.twitter.com/hmZg2VJksO

— Robert J Smith (@RJS2212) January 1, 2021

A couple others…

10*(9*8+7+6*5*4)+32-1 = 2021

(10*9+8!/(7*6)-5*4!/3)*2+1 = 2021

(10-9*8+7-6+5+4^(3!))/2+1 = 2021

Even my PhD advisor, Bard Ermentrout, got in on it (and I didn’t have this one!):

10*9*8+(7+6)*5*4*(3+2)+1 = 2021

— Derek Orr (@Derektionary) December 31, 2020

— しゅん (@s_yn_u) January 1, 2021

【今年の入試で出そう】

2021

=2025-4

=45²-2²

=(45+2)(45-2)

=47×43— 数学を愛する会 (@mathlava) January 1, 2021

数学の問題です

この無限級数の和はな〜んだ？ pic.twitter.com/o3RLlOCZhG— ａｐｕ (@apu_yokai) January 1, 2021

— Diego Rattaggi 🇨🇭 (@diegorattaggi) January 1, 2021

— ポテト一郎🥔 (@potetoichiro) January 1, 2021

2021 is a squirrel number!

X(2021²)=X(2021)². https://t.co/yKpJtuKCVs— Vincent Pantal🍩ni (@panlepan) January 1, 2021

A Powerful Countdown to 2021#HappyNewYear2021 pic.twitter.com/sHCNWBfNFa

— Tamás Görbe (@TamasGorbe) December 31, 2020

2021 formado a partir de los nueve primeros números naturales https://t.co/QOOWLdTkxI a través de @matescercanas

— emilio lindosa lucas (@411emilio) January 1, 2021

— Bannu (@Bannu16750368) January 1, 2021

2021 can be written as sum of consecutive integers in 6 ways pic.twitter.com/2vMX2YHsy5

— . (@Expert_Says) January 1, 2021