Centre #

N

Low Prime

High Prime

f sl

4

1

3

5

1

2

5

2

3

7

2

3

6

5

5

7

1,5

4

7

4

3

11

4,6

5

8

3

5

11

3,5

6

9

8

1

17

2,4,8

7

10

7

3

17

3,7,9

8

11

6

5

17

4,6,8

9

12

11

1

23

1,5,7,11

10

13

10

3

23

6,10

11

14

9

5

23

3,9

12

15

14

1

29

2,4,8,14

13

16

15

1

31

3,13,15

14

17

12

5

29

6,12,14

15

18

13

5

31

1,5,11,13

16

19

18

1

37

12,18

17

20

17

3

37

3,9,17

18

21

16

5

37

2,8,10,16,20

19

22

19

3

41

9,15,19,21

20

23

20

3

43

6,18,20

21

24

23

1

47

5,7,13,17,19,23

22

25

22

3

47

6,12,18,22

23

26

21

5

47

3,15,21

24

27

26

1

53

4,10,14,16,20,26

25

28

25

3

53

9,15,25

26

29

24

5

53

12,18,24

27

30

29

1

59

1,7,11,13,17,19,23,29

28

31

30

1

61

12,28,30

29

32

27

5

59

9,15,21,27,29

30

33

28

5

61

4,10,14,20,26,28,

31

34

33

1

67

3,27,33

32

35

32

3

67

6,12,18,24,32

33

36

31

5

67

5,7,17,23,25,31,35

34

37

36

1

73

6,24,30,34,36

35

38

35

3

73

9,15,21,33,35

36

39

34

5

73

2,8,20,22,28,32,34

37

40

39

1

79

3,21,27,33,39

38

41

38

3

79

12,18,30,38

39

42

37

5

79

31,37,39

40

43

40

3

83

30,36,40

41

44

45

-1

89

39,45

42

45

44

1

89

44

43

46

43

3

89

43

44

47

42

5

89

42

45

48

41

7

89

41

46

49

48

1

97

48

47

50

47

3

97

47

48

51

46

5

97

46

49

52

49

3

101

49

50

53

50

3

103

50

51

59

56

3

115

56

N, as I discovered as I go along adding to this, may be greater than I, for example, see I=44 and N must be 45, which makes the loosey-goosey prime pair -1 and 89. So must revise to say if want only 1 unique N (which is an integer), not just 1 or 3 or 5 plus a prime to make loosey-goosey prime pairs, but should be absolute values of -1 or 1 or 3 or 5 makes all even numbers. but N still holds for being unique to I.

Also, I may have erred in saying alternate around best fit line of slope 2, may be all above.

I'm a lawyer, not a mathematician.

See graph below:

Bill Krys

This communication is intended for the use of the recipient to which it is addressed, and may contain confidential, personal, and or privileged information. Please contact the sender immediately if you are not the intended recipient of this communication, and do not copy, distribute, or take action relying on it. Any communication received in error, or subsequent reply, should be deleted or destroyed.

--- On Fri, 10/17/08, Devaraj Kandadai <dkandadai@...> wrote:

From: Devaraj Kandadai <dkandadai@...>

Subject: Re: [PrimeNumbers] Loosey-Goosey Goldbach vs. Riemann

To: billkrys@...

Date: Friday, October 17, 2008, 1:19 PM

I feel that in all such communications it is better to give one or two numerical examples; one numerical = a thousand words.

Devaraj

On Thu, Oct 16, 2008 at 8:56 PM, Bill Krys <billkrys@...> wrote:

Is there any relation between a loosey-goosey (loosey-goosey because I'm saying that 1 is a prime number) Goldbach Conjecture in which each positive integer >4 (I) may be represented by the sum of the loosey goosey prime pair )(1 or 3 or 5) + (some prime number (P), such that the absolute difference (N) between I and (1 or 3 or 5) = the absolute difference (N) between I and P and each N is a unique integer, thus producing a best-fit line of slope = 2 when P is graphed against the rank of I (where the 1st I (4) has rank 1, the 2nd I (5) has rank 2, the 3rd I (6) has rank 3, and so on. The primes (P) then oscillate seemingly unpredictably but on average equally on either side of this line of slope 2.

So then does this slope of 2 have any relationship to the multiplicative inverse of the real part (1/2) of non-trivial zero solutions of the zeta function, in which they are hypothesized to occur equally on either side of the critical line?

Bill Krys

This communication is intended for the use of the recipient to which it is addressed, and may contain confidential, personal, and or privileged information. Please contact the sender immediately if you are not the intended recipient of this communication, and do not copy, distribute, or take action relying on it. Any communication received in error, or subsequent reply, should be deleted or destroyed.

[Non-text portions of this message have been removed]