One less formal way of looking at it is this: there are an infinite number of multiples of 35. starting with 35, 70, 105. Add 6 to each of the odd multiples. 35+6=41 (prime); 105+6 = 111 (prime). With an infinite # of candidates, you’ve gotta get to an infinite number of solutions (for some value of infinity!)
As for that Dirichlet stuff, it’s way beyond any of the useful stuff I learned too.
Yes, but it obviously wouldn’t work for +5 or +7. I don’t think you can just assume that the number of primes wouldn’t converge to some finite number just because the number of candidates goes to infinity.
Dirichlet’s theorem proves that. I have since looked it up, and that’s correct. I didn’t realize at the time that I was asking it to elaborate the proof for Dirichlet’s theorem. Whether the elaboration is correct is something I will pass.
No, I wouldn’t assume non-convergence either … NOR would I assume that that AI didn’t just grab that ‘high-level’ ‘Elaboration’ from some site … without a citation.
(Very human … Lots of people use quotes to sound smart, hoping they’ll get away with it. LAWYERS! Ministers! Presidents, even! )
One less formal way of looking at it is this: there are an infinite number of multiples of 35. starting with 35, 70, 105. Add 6 to each of the odd multiples. 35+6=41 (prime); 105+6 = 111 (prime). With an infinite # of candidates, you’ve gotta get to an infinite number of solutions (for some value of infinity!)
As for that Dirichlet stuff, it’s way beyond any of the useful stuff I learned too.
Yes, but it obviously wouldn’t work for +5 or +7. I don’t think you can just assume that the number of primes wouldn’t converge to some finite number just because the number of candidates goes to infinity.
Dirichlet’s theorem proves that. I have since looked it up, and that’s correct. I didn’t realize at the time that I was asking it to elaborate the proof for Dirichlet’s theorem. Whether the elaboration is correct is something I will pass.
No, I wouldn’t assume non-convergence either … NOR would I assume that that AI didn’t just grab that ‘high-level’ ‘Elaboration’ from some site … without a citation.
(Very human … Lots of people use quotes to sound smart, hoping they’ll get away with it. LAWYERS! Ministers! Presidents, even! )
The OP article doesn’t say it explicitly, but those mathematicians are getting paid.
The chatbots at duckduckgo don’t have search.