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p = 1019 and 1021 are the largest known pair of twin primes where both p# + 1 and (p+2)# + 1 are primorial primes. The largest prime date in a common year falling exactly in between a prime number (71) of remaining days and a prime number (293) of elapsed days is October 21 or 10/21. Note that 71293 is prime. [Beedassy] The only prime formed from the concatenation of two semiprimes (10 and 21) whose prime factors consist of the four prime digits. [Silva] The only fourdigit emirp pair whose reversals each occur on a 12hour clock is 10:21 and its reversal. [Punches]
Note that in the matrix product: [ 1 0 ] [ 2 3 ] [ 2 3 ] = [ 2 1 ] [ 1 1 ] [ 5 7 ]1021 is prime, 2311 is prime, 2, 3, 5 and 7 are the first four primes (and incidentally, 2357 is prime). This is the only pair of 2by2 matrices with this property. [Hartley] The least prime > 11 whose digit sum equals the number of digits. [Hasler] The smallest prime whose sum of digits and digital length are squares. [Silva] The smallest concaveconvex prime. [Pol] The smallest emirp which begins and ends with the same digit. [Silva] The smallest emirp containing three consecutive digits. [Loungrides]
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