21 (another Prime Pages' Curiosity)
 Curios: Curios Search:   Participate: 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 = 3.141.... Phi(21) = 12. [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 = (((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 = (2*21) + (1*21). [Arabi] (There are 4 curios for this number that have not yet been approved by an editor.) Prime Curios! © 1999-2013 (all rights reserved)