Divisibility by 3, 5, 7, 11 etc. (for many numbers) is something that is not new to us, we understand it. For the concatenated quarcs to be prime, the number cannot be divisible by any of those numbers, therein by 3. For this case, we should understand that we have two types of primes: primes mod 3 that give either 1 or 2. When concatenating, that must be borne in mind. That”s for a good start. Also, the last quarc factor cannot be divisible by 5, i.e. the last digit of the last quarc factor cannot be 5 etc. These rules. Without the generalization of divisibility rules, one cannot do much about that do find big primes by hand. Therefore, yet another type of approach suggested.
211,311 and 811 are primes. 211 = (2)(11)=(21)(1). In the first case both are primes. In the second one, there is 1 and a composite 21. For 311, we have 311=(3)(11)=(31)(1), i.e. in the first case both are primes and in the second case there is 1 and prime 31. In the third case, we have 811=(8)(11)=(81)(1), the same case. 1091,1559 and 2053 are all prime. 1091=(109)(1)=(10)(91) etc.
And now, we could use do the following:
– for different pattern-based number construction models check if a number is prime,
– (A) cluster the results
– (B) use matrix factorization with kernelling for disclosing the pattern,
– conjecture a linear problem based on the results,
– try out convex optimization to redefine the clusters and go back to point (B)
Below, just a peomatic infographic of my thoughts. Mostly, it is about choosing own goals and passing the needing in the streets.
As for the lessons from Euler, who was indeed mathematically gifted for his age, I will refer to things in a longer book. That’d be more than referring to all his papers. As for the letters in the infographic, it says GOEDEL as it was his thoughts about using contradictions to get rid of “wrong paths” within the thought process. Therefore, what we should decide about the structure life. Indeed, we could start from memento mori. But, it is right there, where we notice that we cannot really be dead, as we influenced the world and it is also part of us, not only the physical body. For those that focus on physical “being”, such being, as is, would require from us accepting its gradual loss.