- I had problems understanding the original problem formulation

so I will try a more formal description.

Given two natural numbers a < b, find b-a+1 distinct natural

numbers N_a to N_b such that I +/- N_I is prime for I = a to b.

In other words, for each integer I from a to b, find a prime

pair of form I +/- N such that different N is used each time.

By my hand calculations, if I starts at a=6 then it can at

most go to b=44. It can do that in four ways, with two possible

combinations at I=8,10,12, and two options at I=43.

(I,N_I): (6,1) (7,4) (8,3 or 5) (9,2) (10,7 or 3) (11,6)

(12,5 or 7) (13,10) (14,9) (15,8) (16,13) (17,14) (18,11)

(19,12) (20,17) (21,16) (22,15) (23,18) (24,19) (25,22)

(26,21) (27,20) (28,25) (29,24) (30,23) (31,28) (32,29)

(33,26) (34,27) (35,32) (36,31) (37,30) (38,35) (39,34)

(40,33) (41,38) (42,37) (43,36 or 40) (44,39).

45+/-N is prime for N = 2, 8, 14, 16, 22, 26, 28, 34, 38,

but they are all taken.

Bill Krys wrote:> ... these are the only prime gaps I can reliably predict

The maximal prime gaps at

> where and for hong long they occur.

http://hjem.get2net.dk/jka/math/primegaps/maximal.htm

can be used to get an upper limit for how large b can be

for a given value of a, based on Mark's argument.

The actual highest value of b may turn out to be lower than

the limit given in this way.

--

Jens Kruse Andersen - --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen"

<jens.k.a@...> wrote:>

Well Jens I want compensation from Bill for what I feel is about 2

> I had problems understanding the original problem formulation

> so I will try a more formal description.

> Given two natural numbers a < b, find b-a+1 distinct natural

> numbers N_a to N_b such that I +/- N_I is prime for I = a to b.

> In other words, for each integer I from a to b, find a prime

> pair of form I +/- N such that different N is used each time.

>

> By my hand calculations, if I starts at a=6 then it can at

> most go to b=44. It can do that in four ways, with two possible

> combinations at I=8,10,12, and two options at I=43.

> (I,N_I): (6,1) (7,4) (8,3 or 5) (9,2) (10,7 or 3) (11,6)

> (12,5 or 7) (13,10) (14,9) (15,8) (16,13) (17,14) (18,11)

> (19,12) (20,17) (21,16) (22,15) (23,18) (24,19) (25,22)

> (26,21) (27,20) (28,25) (29,24) (30,23) (31,28) (32,29)

> (33,26) (34,27) (35,32) (36,31) (37,30) (38,35) (39,34)

> (40,33) (41,38) (42,37) (43,36 or 40) (44,39).

>

> 45+/-N is prime for N = 2, 8, 14, 16, 22, 26, 28, 34, 38,

> but they are all taken.

>

> Bill Krys wrote:

> > ... these are the only prime gaps I can reliably predict

> > where and for hong long they occur.

>

> The maximal prime gaps at

> http://hjem.get2net.dk/jka/math/primegaps/maximal.htm

> can be used to get an upper limit for how large b can be

> for a given value of a, based on Mark's argument.

> The actual highest value of b may turn out to be lower than

> the limit given in this way.

>

> --

> Jens Kruse Andersen

>

months taken off my life trying to do this by hand in the last three

hours. I went as far as cutting out fifty six little pieces of paper

with the numbers from 0 to 55 written on them. Yes, I started at zero

just to shake things up. (The application to Goldbach's conjecture

would still apply, ie, 3 + 0 = 3; 3 - 0 = 3 ; 6 = 3 + 3)

Is this what life was like before computers?

But lo and behold it worketh!:

(6,1) (7,4) (8,5) (9,2) (10,3) (11,6) (12,7)

(13,10) (14,9) (15,8) (16,13) (17,14) (18,11) (19,12)

(20,17) (21,16) (22,15) (23,0) (24,19) (25,22) (26,21)

(27,20) (28,25) (29,18) (30,23) (31,28) (32,29) (33,26)

(34,27) (35,24) (36,31) (37,34) (38,35) (39,32) (40,33)

(41,48) (42,37) (43,40) (44,39) (45,38) (46,43) (47,36)

(48,41) (49,30) (50,47) (51,46) (52,45) (53,50) (54,49)

(55,52) (56,51) (57,44) (58,55) (59,54) (60,53) (61,42)

Mark - --- In primenumbers@yahoogroups.com, "Mark Underwood"

<mark.underwood@...> wrote:>

Lo and behold it doesn't. Jen noticed that (41,48) yields a negative

> But lo and behold it worketh!:

>

>

> (6,1) (7,4) (8,5) (9,2) (10,3) (11,6) (12,7)

> (13,10) (14,9) (15,8) (16,13) (17,14) (18,11) (19,12)

> (20,17) (21,16) (22,15) (23,0) (24,19) (25,22) (26,21)

> (27,20) (28,25) (29,18) (30,23) (31,28) (32,29) (33,26)

> (34,27) (35,24) (36,31) (37,34) (38,35) (39,32) (40,33)

> (41,48) (42,37) (43,40) (44,39) (45,38) (46,43) (47,36)

> (48,41) (49,30) (50,47) (51,46) (52,45) (53,50) (54,49)

> (55,52) (56,51) (57,44) (58,55) (59,54) (60,53) (61,42)

>

>

> Mark

>

'prime', so is bad. Now, I have to determine if this whole exercise

actually caused my mental decline, or whether it was a pre existing

condition.

Mark - Mark and Jens,

thanks for trying. I am going to withdraw from the group for a while to tend to work, but I'll come back if I find anything or need more help. I'll try to see if either a continuous sequence of "N"s works starting from a higher integer and if no luck there, then I'll see if your idea of sequential fragments works, hopefully based on some easily predictable prime gaps because I don't like the idea of a prime gap I can't predict understand.

P.S. Mark, sorry for causing your cognitive dissonance, but that's learnin', ain't it?

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 Sun, 11/9/08, Mark Underwood <mark.underwood@...> wrote:

From: Mark Underwood <mark.underwood@...>

Subject: [PrimeNumbers] Re: Tightened-Lightened Goldbach Conjecture

To: primenumbers@yahoogroups.com

Date: Sunday, November 9, 2008, 2:57 PM

--- In primenumbers@ yahoogroups. com, "Mark Underwood"

<mark.underwood@ ...> wrote:

>

> But lo and behold it worketh!:

>

>

> (6,1) (7,4) (8,5) (9,2) (10,3) (11,6) (12,7)

> (13,10) (14,9) (15,8) (16,13) (17,14) (18,11) (19,12)

> (20,17) (21,16) (22,15) (23,0) (24,19) (25,22) (26,21)

> (27,20) (28,25) (29,18) (30,23) (31,28) (32,29) (33,26)

> (34,27) (35,24) (36,31) (37,34) (38,35) (39,32) (40,33)

> (41,48) (42,37) (43,40) (44,39) (45,38) (46,43) (47,36)

> (48,41) (49,30) (50,47) (51,46) (52,45) (53,50) (54,49)

> (55,52) (56,51) (57,44) (58,55) (59,54) (60,53) (61,42)

>

>

> Mark

>

Lo and behold it doesn't. Jen noticed that (41,48) yields a negative

'prime', so is bad. Now, I have to determine if this whole exercise

actually caused my mental decline, or whether it was a pre existing

condition.

Mark

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