Thanks for all the replies. Alastair ... -- http://www.AlastairFarrugia.net One must live the way one thinks, or end up thinking the way one has lived. Paul...
I am about to lose my website as I no longer subscribe to btclick. The website has information about primoproths home.btclick.com/rwsmith/pp/page1.htm and...
Robert, I've saved everything (I think...) at http://witch.is-a-geek.com/~christ/RWSmith/ Please check if it's the full info you need 'saved'. This may not be ...
The Riemann Hypothesis essentially says that the primes are as regularly distributed as possible. The mathematician Enrico Bombieri put it: “If the Riemann ...
... The original poster might have intended to say that there is no -constant- upper bound on the gap between two consecutive primes -- which is obviously...
... To further clarify for the original poster's benefit, of course there exist arbitrarily large (greater than any chosen integer) gaps following primes. This...
... Correct and Correct. However, Bertrand's postulate indicates that at prime P1 the gap must be less than P1. RH itself does not bound the gaps, they are...
The poster is actually implying proof that there is always a prime between squares, when the square is a prime, apparently. In this case, about half the gap...
... oops, meant ... general case of a prime within x^2-x, because the gap between p1^2+p1 and p2^2-p2 is minimally of order ~2p for p1,p2 twins, ~6p when ... ...
... Yikes, sorry for the errors, but better for me to catch them than you. ... should be ... along the lines of C*x^(1/2) for a gap near x^2 or C*x^(1/4) for a...
I wouldn't call sum(something) a formula, but a calculating instruction. For example pi(x) = sum(1)(2,3,5…x) looks great, but is only an instruction to count...
Hello again. It has taken me approximately a week to analyze and rigourosly formulate this fundamental truth: the default address for replies in Yahoo groups...
Some philosophy about gaps The fact that the prime numbers are apparently so irregularly distributed is not at the prime numbers, but because of the question. ...
... Dick, I am not a math specialist. So I was discouraged by earilier replies to my post, which implies what I have conjectured is similar to Bertrand's...
... I don't think you're correctly stating what RH means. RH is equivalent to the assertion that: abs(Li(x)-pi(x)) <= c*x^(1/2)*log(x) for some constant c. The...
... I think Dick thought you were proving that there's a prime between p^2 - p and p^2 + p. I think the rest of us thought you were proving that there's a...
... Thanks for the clarification. ... "Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language...
... So proving the RH would prove that primes are both random and non random, which is the key property of being a prime or what make it interesting. The RH...
... Not really. RH states that the *degree* of irregularity in the distribution of primes can be quantified, and that its exponent is exactly 1/2. It has...
... If it remains unknown whether primes can be predicted, then at least one side of the duality is unproven. If one day, someone finds a formula to predict...
... You really *can't* prove that primes cannot be predicted. The set of primes is deterministic, and the primality of X, or the next prime after X, or the...
Hello Shi Huang, what do you mean by "unpredictable"? Simple example: If you build S = abs(M + or – N), where M,N are coprimes and M*N includes the whole ...
Hi Phil ... I must have at some point looked at the Wolfram article on "least prime factor" but I somehow missed the connection. Wolfram says that lpf(n) is...
... p-smooth sets are infinite for all p. Therefore so are sets of numbers with the same gpf. ... Countable and countable. I'm not sure I see the difference. ...
Hi Phil ... numbers with the same gpf. gpf sets are infinite, and their union is the set of all integers greater than one, and their intersection is empty. ...
... Bhup and Werner, By prediction, I mean a formular or pattern that does not include information of existing primes. But this formular can generate any...
... There are several ways to do that. I found this out by looking up "prime formulas" on the Prime pages. http://primes.utm.edu/notes/faq/p_n.html Also if...
Hi: I read on Jens Kruse's "Primes in Arithmetic Progression Records" that in January 18 2007 Jaroslaw Wroblewski found the first known AP24: 468395662504823 +...
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