[cvdvpjmf] safe primes below doubly exponential powers of 10

below are the largest safe primes below 10^10^n :

10^1 : -3 -5
10^10 : -1217 -3101
10^100 : -166517
10^1000 : -3159413
10^10000 : -1813107437

if there are multiple offsets on a line, the last entry is the largest safe prime with generator 2.  we were a bit lucky that the largest safe primes below 10^100, 10^1000, and 10^10000 have generator 2, so we did not have to search further.

10^10000 is 33220 bits, 10^1000 is 3322 bits, etc.  safe prime moduli 2048 bits or larger are currently considered secure for Diffie-Hellman.

related:

round(10^10^x) where x is a decimal number.

2^round(2^x) where x is a decimal number.