# 21

This number is a composite. The smallest number with 2 prime factors that do not divide 10. 221 - 21 is prime. [Brown] Blackjack primes are separated by exactly 21 consecutive composite numbers. Note that 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] 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]

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