In a message dated 29/05/02 08:35:16 GMT Daylight Time, I wrote:

> every integer = 2 mod 4 can be expressed as the sum of 2 primes each = 3

mod 4

No-one has said it has already been conjectured, so I assume it hasn't.

Here's some relevant data to back it up.

Given a cutoff n, if you total up the number of ways each of the integers

less than n which are = 2 mod 4 can be expressed as the sum of 2 primes each

= 1 mod 4 (total1), and do the same for = 3 mod 4 (total3), you get the

following:-

n total1 total3 total3/total1

10 5 3 0.6

100 105 107 1.01904762

1000 4045 4344 1.07391842

10000 209824 217155 1.03493881

100000 12602761 12773813 1.01357258

1000000 834142745 837815535 1.00440307

So the stronger conjecture, that the ratio => 1 as n => infinity, seems

eminently reasonable.

Anyone for a proof? (only joking...)

Mike

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