A 36,007 bit "nearly random" prime

This 10,839 digit prime 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). Below you will find one of his notes announcing this prime and the complete expansion in hexadecimal.
From: Preda Mihailescu
Date: Mon, 29 Dec 1997 21:10:12 +0100 (MET)
To: caldwell@utm.EdU
Subject: Re: Mersenne cofactors, personal note, etc.

While new records with cyclotomy are being boiled, I have another kind of large prime for you: a 36007 bits almost random, proved prime. Obviously, it does not look nice at all and you cannot describe by any other short cut than its value itself: I built it for this very purpose, to get away from the very specially shaped primes in the larger size domain. The prime was built and proved using AP, my algorithm for building cryptographic provable primes (CRYPTO94). I attach the file.

Here is the 36007 bit number in hexadecimal:
                            51614D4F13CE0B4085FF242E9D585C206B81736923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