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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Just showing those entries submitted by 'Capelle': (Click here to show all) 666 can be expressed in different ways as a sum of different primes using all ten digits, i.e., 666 = 2 + 5 + 83 + 109 + 467 = 2 + 5 + 83 + 167 + 409 = 2 + 5 + 89 + 103 + 467 = 2 + 5 + 89 + 107 + 463. Note that it is the smallest even number and the smallest palindrome with this property. [Capelle](6*6*6) = 47 is the only prime number p such that the sum of the digits of 666^{p} is equal to 666. If we define S(n) as the sum of the digits of n, we can write that S(666^{(6*6*6)}) = 666. [Capelle] 666 = (3*5)^{2} + (3*7)^{2}, written with all the singledigit primes. Note that 666, which is formed from the triangular number 6 repeated 3 (the only prime triangular number) times, is the smallest triangular number n = a^{2} + b^{2} such that a, b and a+b are triangular numbers. [Capelle] If we define S(n) as the sum of the digits of n, then we can write that S((prime(6+6+6))^{6}) = S(prime(6+6+6)) + S(prime(666)) + S(prime(6*6*6)), where all the terms are prime. Note that 666 = (6+6+6) * S((prime(6+6+6))^{6}). [Capelle]
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