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## DEEP EVENS???

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• 1 REM This is a program showing that below every even number y the superficial prime pairs fulfils Goldbach s conjecture:as y increases the number of even
Message 1 of 1 , Jan 12, 2005
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1 REM This is a program showing that below every even number y the
superficial prime pairs fulfils Goldbach's conjecture:as y increases
the number of even numbers that do not have superficial prime pairs
fulfilling Goldbach's conjecture becomes lower and lower that they
virtualy disapear above number 63274, non is demonstrated up to 5*10
^ 5, if testing the program at heigher numbers (after increasing the
data list of course), revealed also non, this mean that Goldbach's
conjecture is practically solved.

3 z = 0

REM z is a counter of deep evens

5 INPUT x

8 INPUT s

REM s shouldn't be more than the square of the last number in the
data list of primes.

10 INPUT v

REM v is the level of sliding, if increased the even numbers without
superficial goldbach prime pairs will disapear, in this program all
disapeared after v equalling six.The most resistant even is number
992.

20 FOR y = x TO s STEP 2

30 k = 1

40 w = 0

50 FOR i = 1 TO k

70 n = y - p

80 a = p

90 NEXT i

100 RESTORE 260

110 FOR j = 1 TO 172

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 230

190 RESTORE 260

200 IF v * y < a ^ 2 THEN 230

210 k = k + 1

220 GOTO 50

230 RESTORE 260

235 IF w <> 0 THEN 250

z = z + 1

240 PRINT y; z

250 NEXT y

260 DATA 2,3,5,7,
11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,

101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,1
91,

193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,2
83,293,

307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,4
09,419,421,

431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,5
41,547,557,563,

569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,6
61,673,677,683,691,

701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,8
23,827,829,839,853,

857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,9
77,983,991,997,

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

REM please for those who are interested increase the data list of
primes and run the program up to a very high number like 10^12 or
above , and report any even number without goldbach superficial
prime pair, and try increasing v till these numbers disapears, if
non is reported with v equalling one, then Goldbach's conjecture is
definitely prooved on practical bases.

300 END

REM During programming to solve Goldbach's conjecture,I had the idea
that for every even number 2n>2 ,

(P_i)^2 <= 2n < (P_i+1)^2 , if 2n is subtracted by P_1 or P_2 or P_3
or.......or P_i+1 ,the subtraction definitely yeilds a prime
number??!!!

thus I formed the above program to test that,to my great
disappointment,the idea turned to be fallicious, and some even
numbers defied the rule, I called these evens " deep evens" because
they had prime pairs fulfilling Goldbach's conjecture at a deeper
level than P_i+1

(as it is shown by increasing the value of v in the program,which of
course causes 2n to be subtracted by prime numbers >
P_i+1) ,increasing v caused all deep evens to disapear at v=6 , for
all 2n up to 5*10^5.

more interesting!!! these deep evens disapear without the need to
increase v above one, for all 2n values above 63274 up to 5*10^5,
this mean that the rule I thought about is true for 2n>63274,
however this needs to be prooved by running 2n up to very high
values, and then if no deep evens appears then Goldbach's conjecture
is prooved practically.

My three questions are :1) is that method followed before.

2) if yes: is there any deep evens occuring at values of 2n >63274,
and is there a limit for their appearance.

3) if no: is that a new conjecture or it can be prooved by number
theory.
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