full analytic deductive proof should be one that explains the

following inductive proof. The inductive proof states that for every

2n>2 : (P_i)^2 <= 2n < (P_[i+1])^2 ,were P_ i is the ith prime

like P_3 = 5 , at least one of the 2n- P_1 or 2n-P_2 or 2n-P_3

or........or 2n-P_2i should be prime! Since every even number has

primes below it more than or equal to 2i , then ALL 2n fulfills this

inductive proof and Goldbach's conjecture is true for all 2n>2. This

was induced from the fact that ratio of all primes below any even

number 2n>2 : (P_i)^2 <= 2n < (P_[i+1])^2 to the number of

building primes of the composite numbers up to that 2n ( which is

of cours i )is larger or equal to 2, and it increases as 2n increase.

REM Now a deductive full proof should explain why ? I think

overlapes of the building primes like 15+ 30j and 21 + 42j and 35 +

70j and....etc , are important key numbers,since it is in the

vicinity of these numbers there is a room for 2n-P_f to be prime.

REM the inductive proof was tested by this program up to 10^6, it

was true for all evens <= 10^6 and >2. And I assume that it is true

for all evens>2.

3 z = 0

5 INPUT x

8 INPUT s

REM s shouldn't be more than the square of the last number in the

data list.

10 INPUT v

15 INPUT b

REM it is v and b that shows' the infinite nature of this program,

as they are decreased the number of prime numbers subtracted from y

would be less , and this program shows' that as y increase,

Goldbach's conjecture becomes true at less values of v and b.thus

supporting views writtin in the message titled raw ideas?. For the

purpose of validating the inductive statement outlined above both v

and b should equal 1.

20 FOR y = x TO s STEP 2

g = 0

30 k = 1

40 w = 0

50 FOR I = 1 TO k

60 READ P

70 n = y - P

90 NEXT I

100 RESTORE 260

110 FOR j = 1 TO 172

120 READ q

130 IF n = q THEN 180

140 IF (n / q) = INT(n / q) THEN 190

150 IF n <= q ^ 2 THEN 180

160 NEXT j

170 GOTO 190

180 w = w + 1

185 GOTO 235

190 RESTORE 260

200 IF v * y < P ^ 2 THEN 230

210 k = k + 1

220 GOTO 50

230 g = g + 1

231 IF g <> 1 THEN 233

232 o = INT(b * k)

233 IF g = o THEN 235

234 GOTO 210

235 RESTORE 260

237 IF w <> 0 THEN 250

z = z + 1

240 PRINT y; z;

250 NEXT y

260 DATA 3,5,7,

11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,10

3,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193

,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,

293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,4

01,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,50

3,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617

,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,

739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,8

57,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,97

7,983,991,997,1009,1013,1019,1021

263 IF z <> 0 THEN 270

265 PRINT "Goldbach's conjecture is true!!!"

270 IF s = 0 THEN 300

280 GOTO 3

300 END

REM I hope the above information would help.