I thought of this taking place in real life in my mind so I did it
ehh it works as multiplying all previous, add 1, factor that number, and finding the biggest prime factor bigger than the previous number. The first 3 work different, as the first prime that is not achieved from adding up and previous primes plus one. But if all the available factors found are composite, break down the last number of the multiplication in about half, then treat both parts as a part of the multiplication and multiply, and do the steps adding one, to finding the prime factor. As of now, there are only 7 Dwindledary primes found as of now, because factoring the resulting 22 digit number’s factoring is only accessible with very good computers