22

This number is a composite.

+ There is no prime in which the mean gap between the first n successive primes is exactly 22. [Dodson]

+ It is unknown if there is a relatively prime pair of amicable numbers. If there is such a pair, their product must be at least 22 distinct primes.

+ The smallest integer such that its sum of digits ± 1 and the product of its digits is prime, together with the fact that the sum of digits is the same as the product. [Russo]

+ 22 is the smallest number which can be expressed as the sum of two primes in three ways. [Murthy]

+ 1π(1) + 2π(2) + 3π(3) + 4π(4) + ... + 22π(22) is prime. [Poo Sung]

+ The smallest multi-digit square-free number such that all the digits are primes. [Russo]

+ The smallest multi-digit composite palindrome whose total number of prime factors (counting multiplicity) is square-free. [Russo]

+ The longest known arithmetic sequence of primes is currently 22, starting with the prime 11410337850553 and continuing with common difference 4609098694200 (found by Pritchard, Moran, and Thyssen in 1993).

+ 22 is the smallest multidigit composite palindrome such that the concatenation (211) as well as the sum (13) of its prime factors are prime. [De Geest]

+ It is possible for a Queen to attack all 22 prime numbered squares on 9x9 Knight's Tour solution (Jacques Tramu, 2004).

+ 22 is the smallest Hoax Number.

+ The smallest dihedral semiprime. Note that it contains the smallest dihedral prime. [Capelle]

+ The smallest sum of TWO primes with prime subscripts (PIPs) in TWO ways: 22 = 11 + 11 = 17 + 5. [Post]

+ There are 22 twin prime pairs between 22 cubed and the next consecutive cube.

+ The smallest multidigit palindromic semiprime. [Silva]

+ The divisors of the 22 can be added to 22 in various combinations to form a larger semiprime, e.g., 22+1+2=25=5*5, 22+11=33=3*11, 22+11+1=34=2*17, 22+11+1+2=35=5*7, 22+22+11=55=5*11 and 22+22+11+2+1=58=2*29. Is there another semiprime that can produce more than six ways? [Bergot]

(There are 7 curios for this number that have not yet been approved by an editor.)

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