A 50,005 bit "nearly random" prime

This 15,053 (decimal) digit prime (69943...35111) does not have a nice short description! Preda Mihailescu formed it by computing a sequence of primes pi where prime is a "random" number times twice the proceeding prime plus one (see [Mihailescu94] and our pages on proving primality). A primality certificate is available.

Here is the 50005 bit number in hexadecimal (12502 hex-digits):

                            16210BD81E34A137E00E656CAD05E102A8243F6250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