... Doesn't it depend on the universe of discourse? You are absolutely correct about "mathematically certainty" (e.g., proof). But if this is "certainty" in...
Ok, now you have me thinking outside of “lurk mode” about the largest known primes and the following question: For lack of better terminology at this...
On Tue, Feb 5, 2013 at 10:42 PM, James J Youlton Jr ... s/o else already defined this as http://oeis.org/A006862 see the references there for more (terminology...
... Absolutely agreed. Because we don't have the mathematical smarts to either prove the finiteness or infiniteness of the set of Mersenne primes, either would...
The problem with 19 turned out to be minimal. There is a unique (up to permutations) way to do with 19 for the first 56 primes what was done for 7 with the...
Dear groupmembers, The conjecture, which did not make a whole lot of sense anyway and was already showing itself unsupported empirically before the following...
Dear James Why not apply your mind to some more basic aspects of prime number problems? For example, if you inspect the natural numbers line, be they odd or...
Quite an interesting problem in fact, full of features and properties. I have been studying Goldbach partitions for even numbers of the form 2p where p is...
Leonel I think what you are seeing is a simple property of all prime numbers, excepting 3. If we ignore the special prime 3, all odd primes take the form 6n+1...
Thanks a lot Alan! I really appreciate you explanation. And then when 3 is involved d = 6k +- 2. I have calculated thousands of those and haven't noticed that....
The set {11,13,17,19, 41,43,47, 71,73,79, 101,103,107,109} shows two sets of quadruplets 90 apart, and the intervening "+30" and "+60" decades have triplets...
Sorry, I had initially posted as a forward on my own recent post and then erased more than I had meant to on a bounce caused by using 'yahoo.com' rather than...
... There are only 2 admissible patterns, the above and its mirror {11,13,17,19, 41,47,49, 73,77,79, 101,103,107,109} A search found 10 occurrences in total...
Thank you Jens, also to Maximilian for his replies. It certainly confirms a long gap to the next occurrences. No doubt these should occur infinitely often...
hi C_twin=pi^2/12*prod(p>=5 odd primes) (1-2/(p*(p-1)))=0.66016.. You will need tens of thousands of terms to get several decimal places, but the appearance of...
I expected the twin prime constant to be irrational because I expected that any constant that requires EVERY prime in order to calculate it, would necessarily...
Surely the rationality of irrationality depends on the truth of otherwise of the twin prime conjecture. ... [Non-text portions of this message have been...
What is the product over all of the primes p of: (p^2+1)/(p^2-1) ? That's a constant that requires EVERY prime in order to calculate it. It turns out to be...
... Thank you David. I see how (zeta(2))^2/zeta(4) = (p^2+1)/(p^2-1), but how do we know what zeta(2) is, and how do we know what zeta(4) is? zeta(2) = sum(k...
Re: Is the twin prime constant irrational? Twin prime constant = (3/2)(1/2)(5/4)(3/4)(7/6)(5/6)(11/10)(9/10)...(p/(p-1))((p-2)/(p-1))... I expected that it...
How about this infinite product here? (99/10)*(111/110)*(1111/1110)*(11111/11110)*... The partial products are: 9.9 9.99 9.999 9.9999 and so on... The product...
Absolutely fascinating David, including your CV! Thank you for sharing this paper with us. Bob ... [Non-text portions of this message have been removed]...
Since you asked... If F(n) is the nth Fermat prime, then sum(n odd) 1/F(n) and sum(n even) 1/F(n) and product(n odd) (1-1/F(n)) and product(n even) (1-1/F(n)) ...
Here is a new prime 18-tuplet record (and a new 18 Simultaneous Primes record): 2650778861583720495199114537 + d, d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42,...
Wojciech Izykowski has discovered AP19 with the smallest possible start of 19: 19 + 13234551541698967679 * 17# * n, n=0,...,18 (27 digits) At the moment it is...
