A 36,007 bit "nearly random" prime
This is a prime that had historic value. Creating primes like this is easier now.
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:
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