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2021 is rather special: it is the concatenation of two *consecutive*
integers (20 and 21) and also the product of two *consecutive* primes (43 and 47).

The next such number is

A further example, with the two parts in increasing order like 2021, is given by the concatenation of 794018604377235322848433897872605582 and 794018604377235322848433897872605583.

• Let's take all the prime numbers below 100, i.e., 2, 3, 5, 7, 11, ..., 89, 97 and make domino pairs: (2,3), (3,5), (5,7), ..., (83,89), (89,97). The sum of the numbers in all the pairs is 2021.

• 2021 is also equal to 33 plus the sum of the first 33 primes.

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2021 = 2^{(3+23)} - 3^{3}

2021 has 4 divisors (see below), whose sum is σ = 2112. Its totient is φ = 1932.

The previous prime is 2017. The next prime is 2027. The reversal of 2021 is 1202.

It is a semiprime because it is the product of two primes, and also a Blum integer, because the two primes are equal to 3 mod 4, and also a brilliant number, because the two primes have the same length, and also an emirpimes, since its reverse is a distinct semiprime: 1202 = 2 ⋅601.

It is a cyclic number.

It is not a de Polignac number, because 2021 - 2^{2} = 2017 is a prime.

It is a Duffinian number.

It is a plaindrome in base 11.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 1996 and 2014.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (2027) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 20 + ... + 66.

It is an arithmetic number, because the mean of its divisors is an integer number (528).

2^{2021} is an apocalyptic number.

It is an amenable number.

2021 is a deficient number, since it is larger than the sum of its proper divisors (91).

2021 is an equidigital number, since it uses as much as digits as its factorization.

2021 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 90.

The product of its (nonzero) digits is 4, while the sum is 5.

The square root of 2021 is about 44.9555335860. The cubic root of 2021 is about 12.6431542894.

Adding to 2021 its reverse (1202), we get a palindrome (3223).

Multiplying 2021 by its reverse (1202), we get a palindrome (2429242).

The spelling of 2021 in words is "two thousand, twenty-one", and thus it is an iban number.

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