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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 21^st 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 multi-digit number m such that both numbers m*m! - prime(m) & 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]