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The HardyRamanujan number is the smallest product of three distinct primes of the form 6n + 1. [Pol] The largest number which is divisible by its prime sum of digits (19) and reversal (91) happens to be Ramanujan's famous taxicab number (1729 = 12^{3} + 1^{3} = 10^{3} + 9^{3}). It is the smallest number expressible as the sum of two positive cubes in two different ways. The smallest number that is a pseudoprime simultaneously to bases 2, 3 and 5. [Pomerance , Selfridge and Wagstaff] If you reverse the middle digits of this pseudoprime you get 1279 and 2^{1279}  1 is a Mersenne prime. [Luhn] Schiemann's first pair of isospectral lattices L^{+}(1,7,13,19) and L^{}(1,7,13,19) are of determinant 1*7*13*19 = 1729. [Poo Sung] The HardyRamanujan number is equal to the average of the only known prime squares of the form n! + 1, i.e., 25, 121, and 5041. [Gudipati]
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