I know that this depends on which techniques you're using, but roughly speaking, when modern cryptography makes use of so-called "large prime numbers", how large (in bits or digits) are these primes typically?
For example, recent versions of OpenSSH typically use either
- ECDSA with a curve size of 256, 384, or 521 bits, which requires a prime of the same size, give or take a couple bits, or
- RSA with a key size of 1024, 2048, or 4096 bits, which requires two (distinct) primes of half the key size (e.g., a 2048-bit RSA key requires two distinct 1024-bit primes).
The reason for the difference in size is that RSA can be broken significantly faster than by brute force, which means it requires larger keys to achieve the same level of security.