Time to procrastinate and get into some prime diversion. An observation: Finding the first odd number n > 1 that cannot be written as n = p + 2^a (p prime and...
I offer a $50 prize to the first person who can submit a verifiable counterexample or proof by 11/1/8 for either conjecture 1) or 2) below: x,A(x),K,M,S,n,p :...
Hello all: Next Prime Equation: Let p a prime number, consider the following equation: 1+z*(p!!)-x*p-x-x*y = 0 Let (x,y,z) a solution in positive integers....
To factor the arbitrary positive integer z, I found integers h1, h2, h3,h4 such that h1 + h2 + h3 + h4 = z and h1 * h4 - h2 * h3 = 0. Then I expected that x =...
... Thanks for presenting this extraordinarily interesting challenge. [And you confirmed offline that indeed K1=K.] After spending most of the last 2 days on...
... [snip] Proof of Conjecture 1): If K is even, n = K/2. If K is odd, n = (K-1)/2. Let's work in terms of n. Given n, denote the even-valued K by Ke = 2*n, ...
... [snip] ... Nowhere is it specified that n is maximal. Of course, it's underspecified if you don't assume that, but all that means is that the problem's...
The following is a test run of my most recent factor algorithm. Is anyone interested in knowing the details of this algorithm? I generate a twelve digit...
Coprimes Puzzle  Let G(n)=GCD(1+Product[Prime[i],{i,1,n}] , Sum[Prime[i],{i,1,n}])  G(n)=1 for all n=1,2,3,….,10000  except G(61)= 307  Find the...
... Nice puzzle. The heuristics were non-obvious. Each time I think I push the number of solutions towards infinity, I come up with a reason why it should be...
... A simple optimisation follows from your post: If gcd(pr+1,ps)>1 then gcd(pr+1,ps) must be f[l,1] (the largest prime factor of ps). So gcd(pr+1,ps)>1 can be...
I've constructed a benchmark factor program based on Brent's algorithm so that in the future, when ever I think I have a workable different algorithm, I can...
2 3 4 5 7 10 11 13 16 17 19 22 23 25 28 29 ... 1 plus 123 Sequence 123 Sequence is 1 2 3 4 6 9 10 12 15 16 ... where it starts 1 2 3 then successive terms have...
miltbrown@...
Oct 13, 2008 10:33 am
19640
... '2' and '3' do not fit the pattern (before 4 should come 1, not 3), you may as well drop them. And why do you include every third term when you then just...
Hello members, I have found on October, 12th the first known (probable) set of 3 primes wi= th more than 10000 digits ! So the Gigantic Prime Triplet Wall is...
Hello members, I have found on October, 12th the first known (probable) set of 3 primes wi= th more than 10000 digits ! So the Gigantic Prime Triplet Wall is...
... Big congratulations! The record table at http://hjem.get2net.dk/jka/math/simultprime.htm is only for proven primes but your amazing prp triplet is also...
... By Dirichlet's theorem, for any value of b^n there are infinitely many k such that k*b^n+1 is prime, and infinitely many k such that k*b^n-1 is prime. -- ...
... all n. ... Thank you Jens and Chris. Dirichlet is still a surprising result to me even after all the time I have spent looking at k*b^n+/-1. It has caught...
... many k ... k*b^n-1 is ... Yet I still find this counterintuitive. Take a base b=p[m]#+1, where p[m]is the mth prime and is quite large, # is the factorial....
Is there any relation between a loosey-goosey (loosey-goosey because I'm saying that 1 is a prime number) Goldbach Conjecture in which each positive integer >4...
OK, the configuration of the table should work as i tried emailing it to myself and the table held it's formatting, so hopefully it should work here too....
Hi Bill, Well, is this not further evidence that lawyers have a penchant for making simple things overly complex? :) Nonetheless you are still in good company...
... Now I'm making it more complex than necessary, and I'm not even a lawyer. :) Bill's proposal simply amounted to this: For every even integer there is a...
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