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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 'Antonious': (Click here to show all) 257 is the largest known prime of the form N^N+1. Note that if N^N+1 (for N>1) is a prime then it must be of the form 2^2^(2^m+m)+1 (m>=0). So according to the Fermat number factoring status, the next prime of the form N^N+1 (if it exists) is may be 2^2^70+1 and will have more than 8*10^20 digits (!). [Antonious]
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