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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) 2^2004 + 823 is prime. It is the smallest prime of form 2^2004 + k. (Sent to "Prime Curios!" as a Happy New Year prime in 2004). [Cino] 2004*2^20238 + 1 is a 6096digit prime. Note that 2004*4002  1 is prime also. [Firoozbakht] r(4,2004)1 or 2004 four times repeated minus one (2004200420042003) is prime. [De Geest] 2^{2004} reversed is prime. [Nash] 2004 is the smallest multidigit number m such that phi((m))^(1/2)  (phi(m))^(1/2) = 1. Note the next year with this property is 2088. [Firoozbakht]
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