Titanic Sophie Germain Prime

Theorem
The integer defined as:


 * $39 \, 051 \times 2^{6001} - 1$

is a titanic prime which is also a Sophie Germain prime:

Proof
At $1812$ digits, it is clear by definition that this prime is titanic.

To show that it is in fact a Sophie Germain prime, we also need to check that:
 * $2 \paren {39 \, 051 \times 2^{6001} - 1} + 1 = 39 \, 051 \times 2^{6002} - 1$

is also prime.