It occurs to me that noting it has been over 10 years since I found my innovative tweak to old ways of counting prime numbers, which leads to a simpler, fast approach, and a partial differential equation, may not help with those who may wonder, but what do the experts say?
And in retrospect I've thought that I made one basic mistake early on, which is I found and successfully contacted the leading mathematical experts in this area.
So yes, the result is verified.
But one of those men simply said I should put it on arxiv, and I replied as a non-academic I didn't have access to it, but could put it up if he helped me. He never replied further.
The other told me he didn't find it to be of interest.
But did refer me to a colleague who wrote the first implementation in C. But then begged off saying he had other research to do.
Which left me arguing with nasty people on the web, and as a lark just to see what they'd do, I posted the C program from the mathematician, and they ripped on it relentlessly. Which gave me an odd grim satisfaction. They thought I'd written it, not one of the top mathematicians on the planet.
But the leading mathematicians knew what I didn't then understand: without support from established mathematicians I would be a lonely figure making big claims, in a world where people see that as indication that you must be wrong.
I've contacted other mathematicians through the years, and noted reactions where my favorite was the mathematician who insisted my prime counting function didn't exist! I noted I had sent it to him, so he could see that it did exist. He did not reply further.
So why would they react that way?
I finally realized over time that in one swoop I could be seen to have topped them all, some guy, without a math degree even, who just happened to notice something.
No way they'd simply hand me what they might see as, the crown. I'd have to fight for it.
I don't even want it. I'm NOT a mathematician, and I don't want to be one, ever.
Still, turns out that leads to MUCH more adventure.
It is kind of weird though.
Just because you have a major mathematical result, doesn't mean you get social approval for it, as one thing is about facts, but the other is about choice.
Oh yeah, so now I would not have gone to mathematicians considered the leading experts in the field! But then again, one wonders where could I have gone?
Come to think of it, thankfully, I started with the mathematicians considered tops in this area in the world! And should be glad I was able to get feedback from them. Whew!
Talk about luck! I'm glad they did talk to me. Could have tried them and not received a response and then always wondered if that is what was needed. But with one also, later on down the line with other mathematicians could compare.
Of course now, I know, and no, would not take any new research to the top person or persons in that research field! Have the benefit of experience now.
So where could I have gone? Where can I go now?
Guess maybe I should put that out there.
The answer of course is easy: there is nowhere to go. It's a social problem. Which gets fixed over time by attrition. As more and more people become aware of better research, and as the established people are replaced by new people, it becomes acceptable and accepted.
It's worked that way for thousands of years.