Primes Arithmetic Progression (PAP) and CPAP

[Kebbaj]

I would like to make a page of reporting prime numbers in
Aritmetic Progression > 1000 digits, here is an example:

0 : 2699# *(4163780-0*1996857)+2729 Prime
1 : 2699# *(4163780-1*1996857)+2729 Prime
2 : 2699# *(4163780-2*1996857)+2729 Prime
3 : 2699# *(4163780-3*1996857)+2729 Prime

4163780*2699#+2729 AP |term 4| difference 1996857*2699#

[paulunderwood]

Originally Posted by Kebbaj

I would like to make a page of reporting prime numbers in
Aritmetic Progression > 1000 digits, here is an example:

0 : 2699# *(4163780-0*1996857)+2729 Prime
1 : 2699# *(4163780-1*1996857)+2729 Prime
2 : 2699# *(4163780-2*1996857)+2729 Prime
3 : 2699# *(4163780-3*1996857)+2729 Prime

4163780*2699#+2729 AP |term 4| difference 1996857*2699#

Ken Davis and I have found 5 AP9s over 1000 digits. When searching for them we did not log AP4s. I found:

AP5 1,020,833,527
AP6 7,270,362
AP7 63,368
AP8 336
AP9 5
(Not disjoint.)

Here is the top5000 top5 APs over the years:

[Kebbaj]

Originally Posted by paulunderwood

Ken Davis and I have found 5 AP9s over 1000 digits. When searching for them we did not log AP4s. I found:

AP5 1,020,833,527
AP6 7,270,362
AP7 63,368
AP8 336
AP9 5
(Not disjoint.)

Here is the top5000 top5 APs over the years:

Thank you Mr indrewood, your answer is complete and closes the question.
Your work is fabulous with Ken Davis. In particular, you have shelled the 2371 #.
I have a small question if you can inform me: I saw that you are working with newpgen for the sieve.
Newpgen can do k * b # + 1 because this form does not need primo for certification.

but I would like to make the sieve of k * b # + n. Like my exemple 4163780 * 2699 # + 2729.
Are you familiar with a program that can sive it?
Thank you.

[paulunderwood]

Originally Posted by Kebbaj

Thank you Mr indrewood, your answer is complete and closes the question.
Your work is fabulous with Ken Davis. In particular, you have shelled the 2371 #.
I have a small question if you can inform me: I saw that you are working with newpgen for the sieve.
Newpgen can do k * b # + 1 because this form does not need primo for certification.

but I would like to make the sieve of k * b # + n. Like my exemple 4163780 * 2699 # + 2729.
Are you familiar with a program that can sive it?
Thank you.

Maybe someone else knows of one. Mark a.k.a, rogue?

[Kebbaj]

I took only the primorial form k*p#+1 on top5000AP.txt tanks paul,

the attached files.

one litle error:
Code p46 in the year 2000 :
d=36364*5000# d=187314*5000# d=457410*5000#
5000# should be 4999#.

[paulunderwood]

Originally Posted by Kebbaj

5000# should be 4999#.

Effectively, they are the same.

[Puzzle-Peter]

Originally Posted by Kebbaj

but I would like to make the sieve of k * b # + n. Like my exemple 4163780 * 2699 # + 2729.
Are you familiar with a program that can sive it?
Thank you.

The gmp version of polysieve should be rather easy to adapt. It is not originally written for this kind of task, but with the correct input it will be doing this. The major modification will be calculating the primorial as it is not doing primorials at the moment. But that shouldn't be too hard.

[Kebbaj]

Originally Posted by Puzzle-Peter

The gmp version of polysieve should be rather easy to adapt. It is not originally written for this kind of task, but with the correct input it will be doing this. The major modification will be calculating the primorial as it is not doing primorials at the moment. But that shouldn't be too hard.

Thank you.
I downloaded polysieve. But I look for documentation. I dont find it.

[Puzzle-Peter]

I'm afraid there is no documentation apart from what you find in the code.


Just to make sure:
What is the running variable in your example?

[Kebbaj]

Congrats to Serge Batalov for a record :
Chaîne Cunningham 2ème type (8p - 7)

2072453060816*7699#+1 (3316 digits).
Serge you are the best!!

Reda kebbaj.

[Puzzle-Peter]

I gave it a try and I found an AP-6 with 10593 decimal digits:


N=(2,738,129,976+n*56,497,325)*24499#+1 for n=0..5