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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The smallest number with 2 prime factors that do not divide 10. 2^{21}  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 n^{21} + 21 begins with a decimal expansion of = 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 = (((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 twentyone 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] The only brilliant number n that creates two 4digit emirps by inserting it between its prime factors, i.e., 3217, 7213. [Loungrides]
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