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  • zaljohar
    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

      20 FOR y = x TO s STEP 2

      30 k = 1

      40 w = 0

      50 FOR i = 1 TO k

      60 READ p

      70 n = y - p

      80 a = 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 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,









      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

      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
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