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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

+ 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 pi = 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 = pi(pi(pi(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 = pi(2*21) + pi(1*21). [Arabi]

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

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

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