## RE: [PrimeNumbers] Gruesome Runs - New Record 18 and 25

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• There are an inifinte number of Gruesome 2 Runs, take 2^p, and 2^p-1 prime. Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry
Message 1 of 12 , Mar 2, 2002
There are an inifinte number of Gruesome 2 Runs, take 2^p, and 2^p-1 prime.

Jon Perry
perry@...
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http://www.users.globalnet.co.uk/~perry/maths
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-----Original Message-----
From: David Cleaver [mailto:wraithx@...]
Sent: 02 March 2002 08:50
Subject: [PrimeNumbers] Gruesome Runs - New Record 18 and 25

OK, in keeping with my testing the numbers around powers of two, I just
tried around 128 and 256. At 128 I found a run of 18 which is:

122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139
61, 41, 31, 5, 7,127, 2, 43, 13,131, 11, 19, 67, 3, 17,137, 23,139

And at 256 I found a run of 25 which is:
the consecutive composites from 248 to 272 (inclusive) and the single
covering set which is as follows:
31,83,5,251,7,23,127,17,2,257,43,37,13,29,131,263,11,53,19,89,67,269,3,271,1
7

I guess one thing we can conjecture at this point is whether or not
there is a gruesome run of every integer length >= 1?

1) A run of 1 is any prime number.
2) A run of 2 (the only?) is 8,9. The answer to this is up to whether
or not there are any more a^x - b^y = 1 for a and b prime. (Actually,
now that I think about it, with inclusion of primes in the sequence,
Mersenne's fit nicely into this category.)
3) A run of 3 could be 7,8,9 or 8,9,10.

Anyway, I would like to hear what the list thinks of the possibility of
there being a gruesome run of all possible lengths?

David Cleaver wrote:
>
> Mine being:
>
> 31,32,33,34,35,36,37,38,39,40,41
>
> 31, 2,11,17, 7, 3,37,19,13, 5,41
>
> One thing I've noticed is that its best to start a run of these at a
> power of two [or maybe just before if you're near a Mersenne ;) ] The
> reason being is that the first element, the 2^k, eliminates the chance
> that any other succeding number could use 2 as its prime. And with such
> info, let me look at 64: and yup, I just got a gruesome run of 13,
> which is:
>
> 64,65,66,67,68,69,70,71,72,73,74,75,76
>
> 2,13,11,67,17,23, 7,71, 3,73,37, 5,19
>
> It took me about 5 minutes with pen and paper to find these two, I'm
> sure a program could find many more much more quickly. Don't know if
> I'll write it, I'm going to go rent some movies tonight. Anyway, have
> fun on your gruesome searches.
>
> -David C.
>
> Jon Perry wrote:
> >
> > Being:
> >
> > 16,17,18,19,20,21,22,23
> >
> > 2 ,17, 3,19, 5, 7,11,23
> >
> > -----Original Message-----
> >
> > Owing to the high probabilty that 8,9,10 is the longest gruesome run, I
have
> > modified the definition to allow primes.
> >
> > So, my new record is:
> >
> > 9,10,11,12,13,14
> >
> > length 6
> >
> > having the single pattern:
> >
> > 3,5,11,2,13,7

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• ... Ah, the infinitude of Mersenne primes, finally proved. Phil ===== -- .sig selecter broken, please ignore.
Message 2 of 12 , Mar 2, 2002
--- Jon Perry <perry@...> wrote:
> There are an inifinte number of Gruesome 2 Runs, take 2^p, and
> 2^p-1 prime.

Ah, the infinitude of Mersenne primes, finally proved.

Phil

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• I was chuffed. Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry http://www.users.globalnet.co.uk/~perry/maths BrainBench MVP for HTML
Message 3 of 12 , Mar 2, 2002
I was chuffed.

Jon Perry
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http://www.users.globalnet.co.uk/~perry/maths
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-----Original Message-----
From: Phil Carmody [mailto:thefatphil@...]
Sent: 02 March 2002 10:55
Subject: RE: [PrimeNumbers] Gruesome Runs - New Record 18 and 25

--- Jon Perry <perry@...> wrote:
> There are an inifinte number of Gruesome 2 Runs, take 2^p, and
> 2^p-1 prime.

Ah, the infinitude of Mersenne primes, finally proved.

Phil

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• 1: 2 2 2: 2,3 2,3 3: 3,4,5 3,2,5 4: 4,5,6,7 2,5,3,7 5: 7,8,9,10,11 7,2,3, 5,11 6: 9,10,11,12,13,14 3,5,11,2,13,7 7: 16,17,18,19,20,21,22 2 ,17, 3,19, 5, 7,11
Message 4 of 12 , Mar 2, 2002
1:

2
2

2:
2,3
2,3

3:
3,4,5
3,2,5

4:

4,5,6,7
2,5,3,7

5:

7,8,9,10,11
7,2,3, 5,11

6:

9,10,11,12,13,14
3,5,11,2,13,7

7:

16,17,18,19,20,21,22
2 ,17, 3,19, 5, 7,11

8:

16,17,18,19,20,21,22,23
2 ,17, 3,19, 5, 7,11,23

9:

26,27,28,29,30,31,32,33,34
13, 3, 7,29, 5,31, 2,11,17

10:

31,32,33,34,35,36,37,38,39,40
31, 2,11,17, 7, 3,37,19,13, 5

11:

31,32,33,34,35,36,37,38,39,40,41
31, 2,11,17, 7, 3,37,19,13, 5,41

12:

64,65,66,67,68,69,70,71,72,73,74,75
2,13,11,67,17,23, 7,71, 3,73,37, 5

13:

64,65,66,67,68,69,70,71,72,73,74,75,76
2,13,11,67,17,23, 7,71, 3,73,37, 5,19

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
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• 1: 2 2 2: 2,3 2,3 3: 3,4,5 3,2,5 4: 4,5,6,7 2,5,3,7 5: 7,8,9,10,11 7,2,3, 5,11 6: 9,10,11,12,13,14 3, 5,11, 2,13, 7 7: 11,12,13,14,15,16,17 11, 3,13, 7, 5,
Message 5 of 12 , Mar 2, 2002
1:
2
2

2:
2,3
2,3

3:
3,4,5
3,2,5

4:
4,5,6,7
2,5,3,7

5:
7,8,9,10,11
7,2,3, 5,11

6:
9,10,11,12,13,14
3, 5,11, 2,13, 7

7:
11,12,13,14,15,16,17
11, 3,13, 7, 5, 2,17

8:
16,17,18,19,20,21,22,23
2 ,17, 3,19, 5, 7,11,23

9:
26,27,28,29,30,31,32,33,34
13, 3, 7,29, 5,31, 2,11,17

---

The change from my orignal list is with 7, and I haven't validated beyond 9.

Jon Perry
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• In addition to David Cleaver s conjecture that there exists a grusome run of any length, I would like to add the conjecture that every integer is part of a
Message 6 of 12 , Mar 2, 2002
In addition to David Cleaver's conjecture that there exists a grusome run of
any length, I would like to add the conjecture that every integer is part of
a gruesome run.

This conjecture belies a new definition, which I have termed a 'dire
straight'. A dire straight is the smallest gruesome run that contains an
integer.

This therefore implies the longest gruesome run that contains an integer is
a 'horrible band'.

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry
http://www.users.globalnet.co.uk/~perry/maths
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• And a couple more: 1)There exists a grusome run of every length 2)Every integer partakes in a gruesome run 3)No integer has a dire straight length equal to its
Message 7 of 12 , Mar 2, 2002
And a couple more:

1)There exists a grusome run of every length

2)Every integer partakes in a gruesome run

3)No integer has a dire straight length equal to its horrible band length.

4)An integer partakes in gruesome runs of all lengths between its dire
straight length and its horrible band length.

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
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-----Original Message-----
From: Jon Perry [mailto:perry@...]
Sent: 02 March 2002 17:31

In addition to David Cleaver's conjecture that there exists a grusome run of
any length, I would like to add the conjecture that every integer is part of
a gruesome run.

This conjecture belies a new definition, which I have termed a 'dire
straight'. A dire straight is the smallest gruesome run that contains an
integer.

This therefore implies the longest gruesome run that contains an integer is
a 'horrible band'.

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com

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• 5) Every conceivable combination of ad hoc definitions will be posted eventually.
Message 8 of 12 , Mar 2, 2002
5) Every conceivable combination of ad hoc definitions will
be posted eventually.
• ... 5b) Each of these combinations will be posted one at a time, on a whim, without any forethought into fully (or even partly) thinking through the possible
Message 9 of 12 , Mar 2, 2002
> 5) Every conceivable combination of ad hoc definitions will
> be posted eventually.

5b) Each of these combinations will be posted one at a time, on a
whim, without any forethought into fully (or even partly) thinking
through the possible "set".

5c) Each of these singly 1/100th thought out definitions
(conjectures) will generally be sent with dozens of additional
lines per posting filled in with insignificant items such as
overblown .sig files and or the bottom of a top posted prior email
(possibly not even relevant to the current "conjecture addition").
• But Jim, just think how Jon outranks you. You are merely a DVP (David valued programmer) whereas Jon is a BrainBench MVP (M valued professional) and
Message 10 of 12 , Mar 2, 2002
But Jim, just think how Jon outranks you.
You are merely a DVP (David valued programmer)
whereas Jon is a "BrainBench" MVP (M valued professional)
and presumably M vastly outranks me,
David
[*] http://groups.yahoo.com/group/openpfgw/message/786
• M is for Most . Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry http://www.users.globalnet.co.uk/~perry/maths BrainBench MVP for HTML
Message 11 of 12 , Mar 3, 2002
M is for 'Most'.

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com

-----Original Message-----
Sent: 03 March 2002 02:08
Subject: [PrimeNumbers] Re: More Gruesome Conjectures

But Jim, just think how Jon outranks you.
You are merely a DVP (David valued programmer)
whereas Jon is a "BrainBench" MVP (M valued professional)
and presumably M vastly outranks me,