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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The smallest prime whose rearrangement of digits gives the famous HardyRamanujan number (1729). [Gupta] The smallest prime p such that 2^p1 is also a prime that contains the beast number. [Loungrides] The smallest prime number whose digits can be rearranged to make both a square and a cube (7921 = 89^2, 2197 = 13^3). [Gaydos] The smallest prime that remains prime for D= 0, 2, 4, 6 and 8 in 1D2D7D9. [Gupta] The smallest prime (emirp also) p such that p and p^2 contain all digits from 1 to 9. [Gupta]
(There are 2 curios for this number that have not yet been approved by an editor.)
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