# 2004

This number is a composite.

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 6096-digit 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 multi-digit number m such that phi(π(m))^(1/2) - π(phi(m))^(1/2) = 1. Note the next year with this property is 2088. [Firoozbakht]

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