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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The smallest composite number r such that n = 4r + 3 and m = 8r + 7 are primes. [Rivera] Oliver Sacks' describes in his book 'The MAN Who MISTOOK HIS WIFE for a HAT,' a pair of autistic twin brothers who were swapping 20figure primes. The smallest number n such that neither 6n1 nor 6n+1 are primes. [Necula] 20 ones plus 20 is prime. This is the largest such twodigit number. [Opao] There are 20 books in the Bible that have a prime number of chapters. [Opao] 20^20  11...1 (20 ones) and 20 + 11...1 (20 ones) are primes. [Firoozbakht] The 20th palindromic prime contains a digit sum of 20. [Post] The smallest composite number which, summed to all previous primes, yields a prime. [Silva] (20) = 2^3 + 0^3. It is the smallest number with this property. [Kumar] The 20th prime divides the sum of the first 20 primes. 20 is the smallest composite with this property. [Hasler] The only number n < 1000, such that subtracting from it each of the first seven powers of 3, then all absolute differences that are obtained, 203^0, 203^1, …, 203^6 are primes, i.e., 19, 17, 11, 7, 61, 223, 709. [Loungrides] The smallest number n whose sum of digits equals omega(n).
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