The original post is probably prime. A prime factor can be up to the square root of a number. For this 1800 digit number, the square root is 900 digits. How can anyone know for sure that the number Elon posted is in fact prime?
For this post "potentially prime" means contains no prime factors smaller than 1 million. That is the limit of my patience. (About 6 minutes with my quickly cobbled together C++ program, compiled with -O3.)
If the 7 is shifted one character to the right, the prime factors are 29, 83, ...
If the 7 is shifted one character to the left, the prime factors are 1399, ...
If the 7 is shifted one character up, the prime factors are 231529, ...
If the 7 is shifted one character down, the prime factors are 12277, 47981 ...
If the 7 is changed to 1, the prime factors are 7, 11, 13, 2591, 24373 ...
If the 7 is changed to 2 it is potentially prime.
If the 7 is changed to 3, the prime factors are 3, 19, ...
If the 7 is changed to 4, the prime factors are 653, ...
If the 7 is changed to 5 it is potentially prime.
If the 7 is changed to 6, the prime factors are 3, ...
If the 7 is changed to 8, the prime factors are 7, 21701 ...
If the 7 is changed to 9, the prime factors are 3, 439 ...
TL;DR It's likely that the 7 needs to be where it is and it needs to be a 7.
Thanks.
To be sure, we need to check all primes up to ~10^900. The number of factors to check is given by the prime counting function π(n), a lower bound of which can be estimated by calculating n/ln(n), where ln(x) is the natural log.
Doing this, you see the number of primes that need to be checked is on the order of 10^895. This is literally impossible in the age of the universe even with several supercomputers doing trillions of multiplies per second. So we are left with 2 options:
Elon lied and he has no idea if that number is prime or not. He just found a number that couldn't be easily detected.
Elon has access to an extremely advanced quantum computer that can run Shor's algorithm on a number that large.