Modern Cryptography is based on prime numbers. When the research started out on cryptography, they were looking for what is called a reversible function. While most mathematical functions are reversible, they are also very easy to crack through.
If you wish to know more about how we arrived at this point, I advice a more detailed piece I had written on cryptography.
If I said 21 is the product of 2 prime numbers you can figure out the prime numbers fairly easily. But what if the number I gave you was a 64 digit number?
When you talk about 64 bit encryption that is precisely the case! We are using an encryption key that is the product of two 32 digit prime numbers. As we have been discovering more primes, we have been cataloging them for such use.
So the news that we found primes that are 23 Million digits long got me excited! Imagine 46 million bit encryption!
Today, we use 512 or 1024 bit generally and 2048 bit is thought to be impenetrable today even with AWS. Computation will improve and we will use larger prime numbers in the future. I do not suppose it would go anywhere close to even a million digit number in my lifetime.
But given that this is an exponential series, you never know. In 10 steps we might just be there!