This number is a composite.

+ 21 is the smallest number with two prime factors that do not divide 10.

+ 221 - 21 is prime. [Brown]

+ "Blackjack primes" are separated by exactly 21 consecutive composite numbers. The pair {1129, 1151} is the smallest example.

+ The smallest prime of the form n21 + 21 begins with a decimal expansion of π = 3.141....

+ Phi(21) is the reversal of 21. [Honaker]

+ The 21st set of blackjack primes (primes with a gap of 21) is 11329 and 11351. [Fougeron]

+ The smallest triangular number whose sum of aliquot divisors is prime. [Gupta]

+ 21 is the only number m such that m = π(π(π(m)!2))). [Firoozbakht]

+ 21 is the only known multidigit number m such that both numbers m * m! - prime(m) and m * m! + prime(m) are primes. [Firoozbakht]

+ The number of known positive integers which cannot be written as p * q + r, where p, q, r are three distinct primes. [Capelle]

+ The smallest semiprime that is a product of distinct Mersenne primes.

+ 21 repeated twenty-one times, following 1, forms a smoothly undulating palindromic prime. [Silva]

+ 21 followed by its reversal, plus/minus one, are twin primes. The first integer with that property. [Silva]

+ 21 = π(2*21) + π(1*21). [Arabi]

+ The first Fibonacci semiprime is followed by two others (34 and 55). [Silva]

+ The smallest composite Fibonacci number whose sum of digits is a Fibonacci prime. [Gudipati]

+ The 21st odd prime is the sum of first semiprimes up to 21. [Silva]

+ The only brilliant number n that creates two 4-digit emirps by inserting it between its prime factors, i.e., 3217, 7213. [Loungrides]

+ 21 is the second Fibonacci number sandwiched between two cousin primes (19 and 23), and the largest known. [Rivera]

+ Is 21 the largest Fibonacci number that falls between cousin primes (19 and 23)? [Gaydos]

+ Finding the fourth term in sequence A323604 will require counting the primes less than or equal to a 21-digit number.

+ The only Fibonacci number that is the sum of three distinct Fibonacci primes, i.e., 21 = 3 + 5 + 13. [Honaker]

(There are 2 curios for this number that have not yet been approved by an editor.)

Printed from the PrimePages <t5k.org> © G. L. Honaker and Chris K. Caldwell