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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) 312 is the only number m less than 30000 such that prime(k*m) + k*m is prime for k = 1, 11, 1111, 111111, 11111111, and 111111111. [Firoozbakht] 312 = prime(3*1*2) * phi(3*1*2) * sigma(3*1*2). It is the only known number with this property (up to 10^8). [Firoozbakht] 312 is the average of a twin prime pair. Describe 312 to find another, i.e., 312 is 'one 3, one 1, one 2' or 131112. This is the smallest example. [Honaker]
(There are 2 curios for this number that have not yet been approved by an editor.)
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