Recent content by marteinson

I have an intuition about a method of attempting to solve the Goldbach conjecture. Does any more knowledgeable person here think the following would help simplify the problem? Instead of attempting to prove that p + q = 2n showing that all even numbers can be expressed as the sum of two...

Thanks to both recent posters for their interesting input. I'll think about all these ideas too. Still, I think it useful to consider prime distribution in terms of factor distribution and the interference (prim nodes and prime antinodes that occur so near to the prim nodes) between the factor...

Okay I've done some of my homework as Shmoe suggested. Highly divisible numbers, also called highly composite numbers, were considered to have been discovered or developed by Ramanujan. Ramanujan, S.: Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962, p. 87.

Professor Coombes at MIT also uses the term "highly divisible number", so I didn't make it up and evidently MIT faculty and students don't find it hard to understand. That's why I said some contributors here were being obtuse, i.e. deliberately using the claim of incomprehensibility as a...

To make things clear, "poor in factors" means a number has few of them (not many). Highly divisible means a number can be divided in many distinct ways. The words "few" and "many" are relative. For example, 24 has many factors (2*12, 3*8, 4*6) while 25 has few (5*5) and is therefore poorer in...

Many things I said were perfectly clear, to anyone who wasn't aiming at distorting them for the purpose of posing as a gadfly. The literature still has all sorts of claims that there is no explanation for the distribution of the primes, and that we lack any reason why primes often occur in...

Thanks, Shmoe, that's what this kind of forum is for. But do you mean, by "this is enough to get my vote" "to move this to TD" that the moderators should feel free to move anything to a location that has no relevance to its discussion, because of an unstated and anonymous judgment they form...

I think -1 should be prime, or should not be prime, for the same reasons 1 itself is or is not considered prime. For the record, I don't even think 2 and 3 should be considered the primes in the same way 5, 7, 11, 13 and the rest. In a way, 1, 2 and 3 are too small to be divisible by anything...

It's refreshing to see the Waterbreath is looking at my point with an open mind... he is also visualizing the prime cycles as wave phenomena, as I suggested, and has understood that at their nodes, when they are in phase, this is where we find natural numbers with especially high numbers of...

All the "objections" and "disclaimers" you have published here amount to narrowing and altering my statement before refuting it. You defined prims as multiples of 210 only, then used this to suggest my observations are incorrect. By the way, both your large primes quoted very recently above...

Are you sure of this? I don't see how you can find even *one* prime, much less 5161, not being adjacent to a multiple of six (that would contradict Eratosthenes 6N+-1 observation). If your "prims" were divisible by both 2 and 3, among the others, wouldn't they have to be divisible by 2x3, and...

I am honoured and grateful that you have examined the issue, Hurkyl, but may I suggest you have defined prims in the model above in so restrictive a manner that the property does not seem strong? For me, while primeness is an absolute quantitative property, primness is a qualitative and relative...

There is such a basis: when N (a multiple of 6) and N+2 together have as factors the entire sequence of primes between 2 and the square root of n+2, N+1 is prime; when N and N-2 together share that list of primes as factors, in whatever distribution between the two of them, once again, N-1 is...

Well it seems some respondents are answering quickly without reading the article and without thinking through what I have been observing. One person says, above "there are countless prims which are not next to primes", which I never suggested wasn't the case. Maybe it's easier to think of it...

Yes, I'm saying that such primes above 3 are prime BECAUSE the numbers at 6N have so many factors (though it is also true that often 6N-2 and 6N+2 have the others that 6N lacks). My point, basically, is that the most divisible numbers (those having the largest proportion of the series 2, 3, 5...