Sophie Germain primes and safe primes I am trying to find a list or table of safe prime  numbers i.e. the ones that are based on the Sophie Germain primes i.e. $N = 2p + 1$ where $p$ is also prime.

All I found till now is this database.
However the problem with that database is that all Sophie Germain primes in this database have at least 1000 digits. So, is out there any database that has the Sophie Germain primes  including the one that are less then 1000 digits long?

I am looking for Sophie Germain primes that will allow me to calculate safe prime numbers that are 512, 768, 1024, 2048, 4096  bit long.
A Sophie Germain prime is a prime $p$ such that $2p+1$ is prime (that later prime is deemed a safe prime). For small examples, see A005384 in the OEIS.

A random integer $n$ has odds commensurate to $1/\log(n)^2$ to be a Sophie Germain prime. Therefore, there's in the order of $2^{495}$ Sophie Germain primes of 511 bits, way too much to enumerate them, much less store them in a database.

In order to find a Sophie Germain prime that will allow to calculate safe prime of $k=$512, 768, 1024, 2048, 4096 bits, one can simply repeatedly find a random prime $p$ of $k-1$ bits, until $2p+1$ is prime (or repeatedly find a random $k$-bit prime $p$, until $(p-1)/2$ is prime); the smallest of the two related primes exhibited is the Sophie Germain prime, the other is the safe prime.

A large speedup is possible by sieving with small primes, noticing that $p$ and $2p+1$ being large primes implies $p$ odd; $p\bmod3=2$; $p\bmod5\in\{1,3,4\}$; and more generally $p\bmod q\not\in\{0,(q-1)/2\}$ for any small odd prime $q$.

For cryptographic applications, one can use the Miller-Rabin primality test.