Recent content by raycb

I'm attacking the problem in two different ways: One, by proving that a number is reached that is smaller than n; two, by proving that n must have a remainder of -1 for a still higher power of 2. The fact that 6k -1 > 4k -1 doesn't apply here. Once it is proven that k is even in 6k -1...

Well, I'm trying to say that n has the form of a number with a remainder of -1 for some power of 2. The number 12k - 1 can be written as 8k + 4k -1, and the number has to have a remainder of -1 mod 8, therefore 4k is a multiple of 8, and k is even. My argument is that these operations always...

The conjecture states that: Given a positive integer n, If n is even then divide by 2. If n is odd then multiply by 3 and add 1 Conjecture: by repeating these operations you will eventually reach 1. Proof: Let n be the smallest positive integer that is a counterexample...

I wonder if the Goldbach Conjecture could be extended, so that the even number halfway between two primes that differ by 4n + 2 can be written as the sum of two primes from pairs that differ by 4n + 2? This conjecture often fails for the first few numbers, but then seems to begin working. For...