- --- jbrennen <jack@...> wrote:
> As an interesting little project, I've been looking for

So basically one sieves out -1...-L (mod p) for each p not a factor

> sequences of consecutive integers where N+1 is prime,

> N+2 is 2 times a prime, N+3 is 3 times a prime, etc.

>

> Another way to look at it is to find an integer N that

> maximizes the number of primes in the sequence

> N+1, N/2+1, N/3+1, N/4+1, ...

>

> I've been searching for the smallest such N for each

> successive length:

>

> Length N

> ------ -

> 1 1

> 2 2

> 3 12

> 4 12720

> 5 19440

> 6 5516280

> 7 5516280

> 8 7321991040

> 9 363500177040

> 10 2394196081200

> 11 3163427380990800

>

>

> I'm currently sieving through about 7 million candidates/second

> while looking for the smallest such sequence of length 12.

> I'm sure that sieve maestro Phil could beat that quite easily,

> with his Alpha sieve programming skills, but it sure beats

> doing trial division :-)

of any 1..L. And one sieves _in_ 0 mod p otherwise?

Sounds, erm, doable...

Phil

__________________________________________________

Do You Yahoo!?

Yahoo! Movies - coverage of the 74th Academy Awards�

http://movies.yahoo.com/ - --- jbrennen <jack@...> wrote:
> As an interesting little project, I've been looking for

Alright, just for you I ran on an x86 machine...

> sequences of consecutive integers where N+1 is prime,

> N+2 is 2 times a prime, N+3 is 3 times a prime, etc.

>

> Another way to look at it is to find an integer N that

> maximizes the number of primes in the sequence

> N+1, N/2+1, N/3+1, N/4+1, ...

>

> I've been searching for the smallest such N for each

> successive length:

>

> Length N

> ------ -

> 1 1

> 2 2

> 3 12

> 4 12720

> 5 19440

> 6 5516280

> 7 5516280

> 8 7321991040

> 9 363500177040

> 10 2394196081200

> 11 3163427380990800

>

>

>

> I'm currently sieving through about 7 million candidates/second

> while looking for the smallest such sequence of length 12.

> I'm sure that sieve maestro Phil could beat that quite easily,

> with his Alpha sieve programming skills, but it sure beats

> doing trial division :-)

<<<

phil@nonospaz:brennen$ time ../gensv.nono brennen12.gf -s10000 -w300

| ./brennent 12

Verifying brennen 12

#I ZIP: 6 primes, relation = 0 mod 30030 (expanded)

#I SPESH: 4 primes, reduction = 215441 -> 6545

#I SMALL@2: 4 dumb, 6 quick to 71

#I PAUL: 190 primes <=1291

#I WHEEL: 300 other primes <= 3643

#I FACTOR: 2.442830e-11

#I Flags: INFO MARKS

BRENNEN 12 22755817971366480

^C

real 24m51.336s

user 11m51.350s

sys 0m0.560s>>>

All with 1 Fermat, so a few quick more MRs (this is a small number, I

think that 10 MRs is enough!

<<<

bash-2.05a$ calc

C-style arbitrary precision calculator (version 2.11.5t4.5)

Calc is open software. For license details type: help copyright

[Type "exit" to exit, or "help" for help.]

> p=22755817971366480

1

> for(i=1; i<=12; ++i) {

>> print ptest((p+i)/i)

>> }

1

1

1

1

1

1

1

1

1

1

1>>>

However, it's not all peachy, the 20 minutes I spent coding the

tester has left some bugs, as it claimed another result that only had

11 real terms...

ARGH - out by one error (loops from 1..12 are passed when the counter

reaches 13!!!!)

I did overrun quite a way before I noticed the result - shall we call

it 8 minutes CPU time?

Hmmm -

10: 2394196081200

11: 3163427380990800

12: 22755817971366480

Looks like either the 11 result is too high (from a moral obligation

sense), or my 12 result is a pretender. To be honest, I didn't even

run a quick test on <12 to see if the code works, so I've not

verified that I find the same results as yours.

However, I'm using the command-line/pipe version of gensv which has

been stable for several months now, so it's only my test code that

can have bugs (I hope).

13 is of course going to be substantially harder.

Phil

__________________________________________________

Do You Yahoo!?

Yahoo! Movies - coverage of the 74th Academy Awards�

http://movies.yahoo.com/ - Have you thought about extending this idea:

1)N+k is prime, N+2k is 2*{a prime}, etc...

2)N+1 is prime, N+2 is k*{a prime}, N+3 is 2*k*{a prime}

3)N+j is prime, N+2j is k*{a prime}, N+3j is 2*k*{a prime}

Jon Perry

perry@...

http://www.users.globalnet.co.uk/~perry/maths

BrainBench MVP for HTML and JavaScript

http://www.brainbench.com

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

From: jbrennen [mailto:jack@...]

Sent: 27 March 2002 20:37

To: primenumbers@yahoogroups.com

Subject: [PrimeNumbers] Interesting prime sequence

As an interesting little project, I've been looking for

sequences of consecutive integers where N+1 is prime,

N+2 is 2 times a prime, N+3 is 3 times a prime, etc.

Another way to look at it is to find an integer N that

maximizes the number of primes in the sequence

N+1, N/2+1, N/3+1, N/4+1, ...

I've been searching for the smallest such N for each

successive length:

Length N

------ -

1 1

2 2

3 12

4 12720

5 19440

6 5516280

7 5516280

8 7321991040

9 363500177040

10 2394196081200

11 3163427380990800

I'm currently sieving through about 7 million candidates/second

while looking for the smallest such sequence of length 12.

I'm sure that sieve maestro Phil could beat that quite easily,

with his Alpha sieve programming skills, but it sure beats

doing trial division :-)

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

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

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/