Goldbach's conjecture is true for 2n where n is a multiple of 6

So the third number from the above list, is n=3 and 2n=6, so there is 1 way that 2n=6 can be written as the sum of two primes? 3+3 yep makes sense.

Then further along, the fifth number n=5 and 2n=10 there are 2 ways to write 10 as the sum of two primes 3+7 and 5+5 ok!

Here is something you can do to get it to go negative or positive at your choosing:

use a mod function with the sequence + - so that you only add or subtract 1/6 of the numbers, ie mod6:

0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 4, 4, 2, 3, 4, 3, 4, 5, 4, 3, 5, 3, 4, 6, 3, 5, 6, 2, 5, 6, 5, 5, 7, 4, 5, 8, 5, 4, 9, 4, 5, 7, 3, 6, 8, 5, 6, 8, 6, 7, 10, 6, 6, 12, 4, 5, 10, 3, 7, 9, 6, 5, 8, 7, 8, 11, 6, 5, 12, 4, 8, 11, 5, 8, 10, 5, 6, 13, 9, 6, 11, 7, 7, 14, 6, 8, 13, 5, 8, 11, 7, 9, 13, 8

turns into: (by erasing groups of 4 from that sequence and keeping consecutive groups of two numbers)

I may have erased the wrong ones btw :D

1, 2, 3, 3, 4, 2, 5, 4, 6, 3, 6, 5, 8, 5, 7, 3, 8, 6, 12, 4, 9, 6, 11, 6, 11, 5, 13, 9, 14, 6, 11, 7

no sum up the odd and even elements and compare for the +-+-.. sum:

odd sequence:

1,3,4,5,6,6,8,7,8,12,9,11,11,13,14,11

even sequence:

2,3,2,4,3,5,5,3,6,4,6,6,5,9,6,7

sums of those:

odd sequence:

1+3+4+5+6+6+8+7+8+12+9+11+11+13+14+11=129

even sequence:

2+3+2+4+3+5+5+3+6+4+6+6+5+9+6+7=76

The odd sequence is every 6th element from the original sequence, and the even sequence is every 6th+1 element from the original sequence. Since multiples of 6 have more ways to be written as sums of primes it has a higher count 129 vs 76.

Assuming I did the mod right just by erasing 4 consecutive elements out of every 6 from the original sequence..

If you do a mod for larger multiples of 6 and primorial multiples then the count between the odd and even sequence will be even greater, also can compare the counts for ie mod30 and mod6 and the mod30 odd sequence count will be greater than the mod6 odd sequence count for the odd sequence etc.

cheers, Jamie

There's clearly something wrong with your blacklist checker.

-- Richard

Since you don't know the context or background, jumping the gun noted.

I live under various "ISP"s that are rather paranoid about hackers. One of the key ones, in fact, hosts hackers of various kinds -- not all of them white or gray.

To operate any web page clients are forced to inherit their access lists.

At one point they allowed their clients to override any defaults e.g. the very extensive list of "denys" they had set up and update daily. I have added (e.g. relevant to you perhaps) .ac.uk in the "allow" column, in my access list extension, but it seems these days they do not take any notice of that given what I'm given to believe is a very large volume of people and robots based in the .uk that post bogus invoices or court noticed or other claptrap to every notice board and web chatroom, many operated by said ISP.

The situation is further complicated by having several different other organisations involved in hosting my various interests, some of them low grade us military or govt. E.g. the machine that actually is at the end of the chain for the "graphs" was until recently in the green zone in Baghdad.

Finally, my pages are not meant for the general public but for the benefit of associates, my clients, and myself. They are obviously (if you get to see any) a hold over (the phrase "trapped in amber" comes to mind) from 20-30 years ago when only people of various enlightened persuassions had any interest in using the internet or that new-fangled web.

So I don't mind if the onion keeps out various people; probably the more it cuts off, the better. Sometimes one or other of the groups involved in the various layers like to institute quotas or cutoffs and I've had occassions when

-- to use a technical term -- "morons" insisted on exhausting said quotas by repeatedly looking at pages they really didn't need to see or would understand since they were notes to myself.

In the current timeframe, as far as I can see ~2 distinct people out of perhaps 20 have been denied access to zzz.gif. The other ~18 I guess are wondering what you're complaining about, esp given you have as you describe it a near-identical graph on your own web pages. (In case you're wondering why I didn't bother to look ;).

If your claimed military and government interests mean that you can't put up a web page that anyone can read, then it's really not worth your posting links on usenet.

-- Richard

As I said -- since it's only an issue to people working from domains that are known spammers (apparently incl "ed") your speaking on the behalf of others is probably amusing a dozen people that seemed to have no trouble.

But feel free not to access anything I have again and again and again.

--

--

Rationalization is the use of feeble but seemingly plausible arguments either to justify something that is difficult to accept or to make it seem `not so bad after all'. A person who has been rejected by a love interest convinces herself that he rejected her because he did not share in her ideal of happiness, and, what's more, that the rejection is a blessing in disguise in that it has freed her to find a more suitable partner. The first rationalization (that her love interest rejected her because they did not share in the same ideal of happiness) is a case of justifying something that is difficult to accept, sometimes called `sour grapes'. The second rationalization (that the rejection has freed her to find a more suitable partner) is a case of making it seem `not so bad after all', also called `sweet lemons'.