What is the largest prime number P less than 2^2048 for which the complete factorization of P-1 is known? I submit P=2^2048 - 11837, and P-1 = 2 * 263 * 1951 * 1105312961 * 3546914543 * 5142002513 * 54456987858649 * 14495377076529079 * P553, with which we can calculate that the least primitive root (generator) is 2.
There are 7 prime numbers larger.
Some other deltas I encountered while searching: -81255, -21359, and the safe prime -1942289.
Some recent related posts: 1024 bits, Safe primes and Sophie Germain, Factoring near smaller powers of two
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