A 50,005 bit "nearly random" prime
This is a prime that had historic value. Creating primes like this is easier now.
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 preceding 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):
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