## Re: [PrimeNumbers] Re: Isomorphic Numbers

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• ... 3330 further seconds without the prime requirement provided: 1091876084..1091876109 is len 26 ... Agreed. 5901351..5901367 is len 17 (16s) 6120922..6120939
Message 1 of 26 , Mar 5, 2003
--- "jbrennen <jack@...>" <jack@...> wrote:

3330 further seconds without the prime requirement provided:
1091876084..1091876109 is len 26

> --- In primenumbers@yahoogroups.com, "Jon Perry" <perry@g...> wrote:
> >
> > So I think we should adopt a policy of a least 1 prime from a range.
> >
>
> In that case:
>
> run length 8 -> (5255..5262)
> run length 9 -> (8009..8017)
> run length 10 -> (16268..16277)
> run length 11 -> (16268..16278)
> run length 12 -> (118151..118162)
> run length 13 -> (252035..252047)
> run length 14 -> (267485..267498)
> run length 15 -> (267485..267499)
> run length 16 -> (305923..305938)
>
> With no length 17 run less than 5*10^6.

Agreed.

5901351..5901367 is len 17 (16s)
6120922..6120939 is len 18 (<1s)
15736249..15736267 is len 19 (35s)
15736249..15736268 is len 20 (instant)
75952831..75952851 is len 21 (3m49s)
311606294..311606315 is len 22 (15m9s)

I'm just going to break the code^W^W^Wdo a few tweaks, and then I'll re-run
them all, and push it further. 250000/s just isn't fast enough... ;-)

Phil

=====
"Only an admission that he does possess weapons of mass destruction
would do, sources said: 'The rest is just gesture politics." -- Hoon

"Are you still bombing your wife?" -- Winjer

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• Are the two elements supposed to be distinct? Jon doesn t state that in his first post today. This wasn t a condition in the original discussion, indeed we
Message 2 of 26 , Mar 5, 2003
'Are the two elements supposed to be distinct? Jon doesn't state
that in his first post today.'

This wasn't a condition in the original discussion, indeed we have 4+4=8,
4*4+1=17, same for 2.

For stringency this could be added, although graphs with loops are frowned
at...

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths/
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• ... You seem back-to-front, Jon. 8 is composite, 17 is prime and {1,2,3,4,5} was provided as a solution. Therefore the condition that the pair s elements are
Message 3 of 26 , Mar 5, 2003
--- Jon Perry <perry@...> wrote:
> 'Are the two elements supposed to be distinct? Jon doesn't state
> that in his first post today.'
>
> This wasn't a condition in the original discussion, indeed we have 4+4=8,
> 4*4+1=17, same for 2.

You seem back-to-front, Jon.

8 is composite, 17 is prime and {1,2,3,4,5} was provided as a solution.
Therefore the condition that the pair's elements are distinct _was_ a
condition in the first one?
If it wasn't a condition, then {1,2,3,4,5} wouldn't have been a solution.

> For stringency this could be added, although graphs with loops are frowned
> at...

Nope, trees and forests with loops are frowned upon (and any other DAGs, of
course)

Phil

=====
"Only an admission that he does possess weapons of mass destruction
would do, sources said: 'The rest is just gesture politics." -- Hoon

"Are you still bombing your wife?" -- Winjer

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• ... 311606294..311606316 is len 23 (instant, doh!) 467282388..467282411 is len 24 (9m50s) 1142221381..1142221405 is len 25 (42m33s) It was only 4% faster
Message 4 of 26 , Mar 5, 2003
--- Phil Carmody <thefatphil@...> wrote:
> > run length 8 -> (5255..5262)
> > run length 9 -> (8009..8017)
> > run length 10 -> (16268..16277)
> > run length 11 -> (16268..16278)
> > run length 12 -> (118151..118162)
> > run length 13 -> (252035..252047)
> > run length 14 -> (267485..267498)
> > run length 15 -> (267485..267499)
> > run length 16 -> (305923..305938)
> 5901351..5901367 is len 17 (16s)
> 6120922..6120939 is len 18 (<1s)
> 15736249..15736267 is len 19 (35s)
> 15736249..15736268 is len 20 (instant)
> 75952831..75952851 is len 21 (3m49s)
> 311606294..311606315 is len 22 (15m9s)

311606294..311606316 is len 23 (instant, doh!)
467282388..467282411 is len 24 (9m50s)
1142221381..1142221405 is len 25 (42m33s)

It was only 4% faster looking for ones with primes in the range. So I think
that for me it would make sense to look for all such runs, regardless of the
existance of primes in the sum's range.

Phil

=====
"Only an admission that he does possess weapons of mass destruction
would do, sources said: 'The rest is just gesture politics." -- Hoon

"Are you still bombing your wife?" -- Winjer

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• These are for the isomorph a+b ab-1. (no guarenteed prime) run length 1 [1,...,1] run length 2 [2,...,3] run length 3 [5,...,7] run length 4 [56,...,59]
Message 5 of 26 , Mar 5, 2003
These are for the isomorph a+b <=> ab-1.

(no guarenteed prime)

run length 1 [1,...,1]
run length 2 [2,...,3]
run length 3 [5,...,7]
run length 4 [56,...,59]
run length 5 [121,...,125]
run length 6 [211,...,216]
run length 7 [819,...,825]
run length 8 [1470,...,1477]
run length 9 [2231,...,2239]
run length 10 [15886,...,15895]
run length 11 [44275,...,44285]
run length 12 [44275,...,44286]
run length 13 [44275,...,44287]

I left the code running for about an hour after I found rl13, so rl14 is
high.

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths/
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• ... First ones with primes appended, and appended. ... 787374..787387 is len 14 1262441..1262455 is len 15 3623705..3623720 is len 16 7993838..7993854 is len
Message 6 of 26 , Mar 5, 2003
--- Jon Perry <perry@...> wrote:
> These are for the isomorph a+b <=> ab-1.
>
> (no guarenteed prime)

First ones with primes appended, and appended.

> run length 1 [1,...,1]
> run length 2 [2,...,3]
> run length 3 [5,...,7]
> run length 4 [56,...,59]
> run length 5 [121,...,125] 131..135
> run length 6 [211,...,216]
> run length 7 [819,...,825] 915..921
> run length 8 [1470,...,1477] 1470..1477
> run length 9 [2231,...,2239] 2231..2239
> run length 10 [15886,...,15895] 42672..42681
> run length 11 [44275,...,44285] 89663..89673
> run length 12 [44275,...,44286] 89663..89674
> run length 13 [44275,...,44287] 505989..506001

787374..787387 is len 14
1262441..1262455 is len 15
3623705..3623720 is len 16
7993838..7993854 is len 17
7993838..7993855 is len 18
7993838..7993856 is len 19
7993838..7993857 is len 20
117532072..117532092 is len 21 (6m40s)

=====
"Only an admission that he does possess weapons of mass destruction
would do, sources said: 'The rest is just gesture politics." -- Hoon

"Are you still bombing your wife?" -- Winjer

__________________________________________________
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• ... 535716000..535716021 is len 22 (27m35s) 535716000..535716022 is len 23 I stopped it at ~1.4G after nearly an hour looking for a 24. Phil
Message 7 of 26 , Mar 5, 2003
--- In primenumbers@yahoogroups.com, Phil Carmody <thefatphil@y...> wrote:
> --- Jon Perry <perry@g...> wrote:
> > These are for the isomorph a+b <=> ab-1.
> >
> > (no guarenteed prime)
>
> First ones with primes appended, and appended.
>
> > run length 1 [1,...,1]
> > run length 2 [2,...,3]
> > run length 3 [5,...,7]
> > run length 4 [56,...,59]
> > run length 5 [121,...,125] 131..135
> > run length 6 [211,...,216]
> > run length 7 [819,...,825] 915..921
> > run length 8 [1470,...,1477] 1470..1477
> > run length 9 [2231,...,2239] 2231..2239
> > run length 10 [15886,...,15895] 42672..42681
> > run length 11 [44275,...,44285] 89663..89673
> > run length 12 [44275,...,44286] 89663..89674
> > run length 13 [44275,...,44287] 505989..506001
>
> 787374..787387 is len 14
> 1262441..1262455 is len 15
> 3623705..3623720 is len 16
> 7993838..7993854 is len 17
> 7993838..7993855 is len 18
> 7993838..7993856 is len 19
> 7993838..7993857 is len 20
> 117532072..117532092 is len 21 (6m40s)

535716000..535716021 is len 22 (27m35s)
535716000..535716022 is len 23

I stopped it at ~1.4G after nearly an hour looking for a 24.

Phil
• Looking at: Check out his idea here: http://mnemo.nu/math/problems/?action=problem_view&id=107 I can t see how polytope has proved that all ab+1 are
Message 8 of 26 , Mar 31, 2003
Looking at:

'Check out his idea here:

http://mnemo.nu/math/problems/?action=problem_view&id=107'

I can't see how polytope has proved that all ab+1 are composites.

Indeed using this code:

{
forstep (n=4,20,2,v=vector(n/2);
for (i=1,n/2,v[i]=n!/2+i);
for (i=1,n/2,for (j=i+1,n/2,
if (isprime(v[i]*v[j]+1),print(n":"i","j)))))
}

yields the following exceptions.

16:4,7
18:3,6
18:5,8
20:7,10
20:8,9

(note 16:4,7 implies that (16!/2+4) * (16!/2+7) + 1 =
109440784174463838480384029 is prime)

We did adopt a policy of at least one prime in the thread, as the
all-composite sets seemed to be too easy; although we did not manage a proof
of the existence of arbitary sets as attempted by polytope.

The sets mentions are not the first composite-only runs:

And