- There are an inifinte number of Gruesome 2 Runs, take 2^p, and 2^p-1 prime.

Jon Perry

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-----Original Message-----

From: David Cleaver [mailto:wraithx@...]

Sent: 02 March 2002 08:50

To: primenumbers@yahoogroups.com

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:>

have

> 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

> > modified the definition to allow primes.

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com

> >

> > So, my new record is:

> >

> > 9,10,11,12,13,14

> >

> > length 6

> >

> > having the single pattern:

> >

> > 3,5,11,2,13,7

The Prime Pages : http://www.primepages.org

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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-----

From: djbroadhurst [mailto:d.broadhurst@...]

Sent: 03 March 2002 02:08

To: primenumbers@yahoogroups.com

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,

your truly grateful [*] user,

David

[*] http://groups.yahoo.com/group/openpfgw/message/786

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