Unless OP finds some way to turn our understanding of prime numbers on its head, the best case in one year is turning the 100k into 50k by finding the first prime with 1,000,000 digits.

Is that prize still being offered?

I think it was claimed in 2000, "The $50,000 prize will go to Nayan Hajratwala of Plymouth, Michigan, a participant of the Great Internet Mersenne Prime Search (GIMPS), for the discovery of a two million digit prime number found using the collective power of tens of thousands of computers on the Entropia.com network."

https://www.eff.org/press/releases/big-prime-nets-big-prize

The article linked refers to the smallest of four prizes offered.

$50,000 to the first individual or group who discovers a prime number with at least 1,000,000 decimal digits (awarded Apr. 6, 2000)

$100,000 to the first individual or group who discovers a prime number with at least 10,000,000 decimal digits (awarded Oct. 22, 2009)

$150,000 to the first individual or group who discovers a prime number with at least 100,000,000 decimal digits

$250,000 to the first individual or group who discovers a prime number with at least 1,000,000,000 decimal digits

Unfortunately that prize has already been awarded :(.

Current largest prime: 2^57885161-1

So take random prime numbers larger than 57885161 (such as 57885167), and find a script that can calculate with numbers that high using EC2s server constraints, then see if 2^(large_prime_numb)-1 is prime. Is that the correct method of doing this?

https://www.eff.org/awards/coop/primeclaim-43112609

What are the stats on testing large prime numbers on EC2 instances?