AP21

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• I just got 620353098196661 + 84*37#*n, n=0..20 This improves largest known AP21 10.99P - 13.087P, where P=10^15. Jarek
Message 1 of 16 , Feb 3, 2007
I just got

620353098196661 + 84*37#*n, n=0..20

This improves largest known AP21
10.99P -> 13.087P, where P=10^15.

Jarek
• I just got 789337428437009 + 320*37#*n, n=0..21 This improves largest known AP21: 13.087P - 50.656P AP22: 5.734P - 50.656P where P=10^15. Jarek
Message 2 of 16 , Feb 4, 2007
I just got

789337428437009 + 320*37#*n, n=0..21

This improves largest known
AP21: 13.087P -> 50.656P
AP22: 5.734P -> 50.656P
where P=10^15.

Jarek
• I just got 3135462279378283 + 316*37#*n, n=0..21 This improves my previous AP21 and AP22: 50.656P - 52.379P where P=10^15. Jarek
Message 3 of 16 , Feb 4, 2007
I just got

3135462279378283 + 316*37#*n, n=0..21

This improves my previous AP21 and AP22:
50.656P -> 52.379P
where P=10^15.

Jarek
• ... Congratulations. http://hjem.get2net.dk/jka/math/aprecords.htm is updated. This combined AP21/AP22 record ended a 4-day period (the first) where no AP was
Message 4 of 16 , Feb 4, 2007
Jaroslaw Wroblewski wrote:
> 789337428437009 + 320*37#*n, n=0..21

Congratulations.
http://hjem.get2net.dk/jka/math/aprecords.htm is updated.

This combined AP21/AP22 record ended a 4-day period (the first) where no
AP was the largest known for two lengths.

--
Jens Kruse Andersen
• I just got another AP21: 1245653020090313 + 384*37#*n, n=0..20 This improves my previous AP21: 52.379P - 58.236P where P=10^15. Jarek ~
Message 5 of 16 , Feb 4, 2007
I just got another AP21:

1245653020090313 + 384*37#*n, n=0..20

This improves my previous AP21:
52.379P -> 58.236P
where P=10^15.

Jarek
~
• I just got 25521343898340097 + 37*41#*n, n=0..20 This improves AP21 record: 58.236P - 250.666P and misses AP20 record of 260.307P Jarek
Message 6 of 16 , Feb 5, 2007
I just got

25521343898340097 + 37*41#*n, n=0..20

This improves AP21 record:
58.236P -> 250.666P
and misses AP20 record of 260.307P

Jarek
• I just got 2036800114407689 + 66*41#*n, n=0..19 This improves AP20 record: 260.307P - 383.566P For n=-2,-1 the formula gives negative primes. Jarek
Message 7 of 16 , Feb 6, 2007
I just got

2036800114407689 + 66*41#*n, n=0..19

This improves AP20 record:
260.307P -> 383.566P

For n=-2,-1 the formula gives negative primes.

Jarek
• I just got 19-digit AP20 2962411312104427 + 185*41#*n, n=0..19 Jarek
Message 8 of 16 , Feb 7, 2007
I just got 19-digit AP20

2962411312104427 + 185*41#*n, n=0..19

Jarek
• I just got the following sequence 1925228725347080393 + 47#*n, n=0..20 with 20-digit last term: 14223024377116908593. I was aiming at AP20 and was surprised to
Message 9 of 16 , Feb 7, 2007
I just got the following sequence

1925228725347080393 + 47#*n, n=0..20

with 20-digit last term: 14223024377116908593.

I was aiming at AP20 and was surprised to get an AP21.

Jarek
• ... I do find your messages exciting, Jarek. Please continiue updating us like this. [... fumbles for nonsensical, ungrammatical, Polish phrase ...] Gratulacj
Message 10 of 16 , Feb 7, 2007
--- In primeform@yahoogroups.com, Jaroslaw Wroblewski
<Jaroslaw.Wroblewski@...> wrote:

> I just got the following sequence
> 1925228725347080393 + 47#*n, n=0..20
> with 20-digit last term: 14223024377116908593.
> I was aiming at AP20 and was surprised to get an AP21.

I do find your messages exciting, Jarek.
Please continiue updating us like this.

[... fumbles for nonsensical, ungrammatical,
Polish phrase ...]

Gratulacj na waszej niedawnej dobrej pracy

David
• ... Congratulations on your 7th AP21 record in 2007 - and the 6th since Sunday! http://hjem.get2net.dk/jka/math/aprecords.htm#history21 A 20-digit AP21 with
Message 11 of 16 , Feb 8, 2007
Jaroslaw Wroblewski wrote:
> I just got the following sequence
> 1925228725347080393 + 47#*n, n=0..20
> with 20-digit last term: 14223024377116908593.
> I was aiming at AP20 and was surprised to get an AP21.

Congratulations on your 7th AP21 record in 2007
- and the 6th since Sunday!
http://hjem.get2net.dk/jka/math/aprecords.htm#history21
A 20-digit AP21 with primorial difference is impressive.
As you know, the difference is too large for
http://hjem.get2net.dk/jka/math/simultprime.htm

--
Jens Kruse Andersen
• ... Unfortunately this result hits 2^64 limit. I can continue higher, but my search is going to be much less efficient. I will try AP19 with the difference 53#
Message 12 of 16 , Feb 8, 2007

> I do find your messages exciting, Jarek.
> Please continiue updating us like this.

Unfortunately this result hits 2^64 limit. I can continue higher, but
my search is going to be much less efficient. I will try AP19 with
the difference 53# now.

> [... fumbles for nonsensical, ungrammatical,
> Polish phrase ...]

> Gratulacj na waszej niedawnej dobrej pracy

Dziekuje.

Jens Kruse Andersen wrote:

> Congratulations on your 7th AP21 record in 2007
> - and the 6th since Sunday!

Thanks. I had a lot of fun working on this. And ceratinly I had a lot of
luck with some of my findings. Quite often I was getting results much

Thank you for keeping and updating your page - without it hunting large
AP's wouldn't make much sense.

> A 20-digit AP21 with primorial difference is impressive.

I wasn't taking finding AP21 there into account, otherwise I would have
written the program differently. In fact I shouldn't even get an AP20
with the difference 47# so quickly.

> As you know, the difference is too large for
> http://hjem.get2net.dk/jka/math/simultprime.htm

Yes, I am well aware of that. My program is working with the assumption of
fixed difference and a primorial is the best choice. To increase the
search area I was adding a factor to it, but for 47# and higher, the
search area is larger than I can go through, so I have no reason to
select a non-primorial difference.

Jarek
• ... It seems, that in fact this is longer sequence of prime numbers, than you have already thought about. According to my results, numbers
Message 13 of 16 , Feb 8, 2007
--- In primeform@yahoogroups.com, Jaroslaw Wroblewski
<Jaroslaw.Wroblewski@...> wrote:
>
> I just got the following sequence
>
> 1925228725347080393 + 47#*n, n=0..20
>
> with 20-digit last term: 14223024377116908593.
>
> I was aiming at AP20 and was surprised to get an AP21.
>
> Jarek
>

It seems, that in fact this is "longer" sequence of prime numbers,
According to my results, numbers

1310338942758588983 = 1925228725347080393 - 47# is prime as well

and furthermore also

695449160170097573 = 1925228725347080393 - 2*47# is prime!

This is really the end of prime sequence going "down", because the
next one is

80559377581606163 = 78218141 * 1029932143

Thus Jaroslaw has found AP23 starting at 695449160170097573 +
47#*n,n=0..22

Is there any mistake involved in my thoughts?

Stanislav Drastich
• ... I am getting the following factorizations: 1310338942758588983 {{6323, 1}, {207233740749421, 1}} 695449160170097573 {{2357, 1}, {4567, 1}, {4597, 1},
Message 14 of 16 , Feb 8, 2007
> It seems, that in fact this is "longer" sequence of prime numbers,
> According to my results, numbers
>
> 1310338942758588983 = 1925228725347080393 - 47# is prime as well
>
> and furthermore also
>
> 695449160170097573 = 1925228725347080393 - 2*47# is prime!
>
> This is really the end of prime sequence going "down", because the
> next one is
>
> 80559377581606163 = 78218141 * 1029932143
>

I am getting the following factorizations:

1310338942758588983
{{6323, 1}, {207233740749421, 1}}

695449160170097573
{{2357, 1}, {4567, 1}, {4597, 1}, {14054011, 1}}

80559377581606163
{{59, 1}, {83, 1}, {210319, 1}, {78218141, 1}}

Jarek
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