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AP26  AP27 Search :
List for all APs
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Hello. I see here http://www.primegrid.com/stats_ap26.php
there is so many quantity for arithmetic progressions with length 2022
and I did found 9 progressions with length 0..19 (AP20).
But there is published only list for AP23AP26 (the biggest discoveries).
Is there any FULL LIST for all this progressions?
With length lower then 20 or Primegrid not logging this discoveries?
Maybe OEIS?
I see in progressions can be saved many prime numbers,
and this is short note for the wide range of primes.
This can be used for prime number generators for example,
but is there any FULL LIST with all progressions?
Also is there any great formula for generating prime numbers?
Thanks.  


I just crunched my first AP20 and I was also wondering about this. (Data/info for lower APs)  

Michael GoetzVolunteer moderator Project administrator Project scientist
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Joined: 21 Jan 10 Posts: 12911 ID: 53948 Credit: 194,837,816 RAC: 205,774

Please remember that the only purpose of this project is to find the world's first AP27.
We don't show or even record smaller sequences because they're very common.
____________
Please do not PM me with support questions. Ask on the forums instead. Thank you!
My lucky number is 75898^{524288}+1  


Please remember that the only purpose of this project is to find the world's first AP27.
We don't show or even record smaller sequences because they're very common.
I did write a simple JS script where arithmetic progressions of primes is go to array
and then this script do selecting the some progression and do generation random prime number.
I can publish the source here,
and now I do copy and paste all progressions from the link, like
http://www.primegrid.com/ap.php?userid=N , where N is number of userID.
I can see there a many progressions, but I think you can do it faster,
if administration will using SELECT SQL query in DATABASE.
Because there is 1 million users.
And if you know any faster algorithm for generating true prime numbers, you can tell me.
Best Regards.
____________
 

JimBVolunteer moderator Project administrator Project developer Send message
Joined: 4 Aug 11 Posts: 882 ID: 107307 Credit: 851,282,650 RAC: 154,327

You appear to have grabbed data for the first 50,000 userids at up to 23 queries per second. You've now spoiled it for everyone. The ap.php page no longer honors the userid parameter.  


You appear to have grabbed data for the first 50,000 userids at up to 23 queries per second. You've now spoiled it for everyone. The ap.php page no longer honors the userid parameter.
I did open 50 windows periodically every time by using "cyclefor" and window.open in JS.
And I did this successfully  from 31/03/2018 to 07/04/2018.
I have the list with 100000 progressions (mainly AP20  AP21).
And now I see only my progressions on my page, but after log in.
But today I don't see any progressions for any another users.
As I can see you calculated approximately my (queries/per second).
and as I understanding PrimeGrid admins decided to close access to AP's for any users.
Not very good idea.
If there is problem on your site  you can restart the Webserver on your host.
But I don't think there is any problem on the site.
I think this is any limit from admins,
because yesterday all progressions was been available for each user.
And will be better to do publish all AP's here http://www.primegrid.com/stats_ap26.php
to not get this in such a tedious way.
Best regards.  


The ap.php page no longer honors the userid parameter.
If this is the administration's decision to unbind the userid parameter from the page ap.php,
you can turn it back, and then I can use the timeout.
Earlier the timeout was not used in my script:
<script>
y = 200; //round
x = 40000+50*y; //start
for (i = x; i < x+50; i++) {
document.write('user '+i+' <a href="http://www.primegrid.com/ap.php?userid='+i+'">User '+i+'</a><br>');
window.open('http://www.primegrid.com/ap.php?userid='+i, '_blank');
}
</script>
and 50 windows were opened immediately, within two seconds.
Also, to do limit the load on the server and control this  you can set timeout yourself, on the server side,
With answers, like "Try again after x... seconds."  

ReggieVolunteer moderator Volunteer tester Send message
Joined: 10 May 14 Posts: 31 ID: 311759 Credit: 79,615,550 RAC: 0

I'm still not quite sure WHY you're trying to get everyone's APs. The significant APs (23+) can all be found here. These aren't really all that helpful for generating primes. A better technique would be to use the Sieve of Eratosthenes or something else. Is there any other reason you want the small APs?  


I'm still not quite sure WHY you're trying to get everyone's APs. The significant APs (23+) can all be found here. These aren't really all that helpful for generating primes. A better technique would be to use the Sieve of Eratosthenes or something else. Is there any other reason you want the small APs?
Originally, my idea of using AP's to generate prime numbers,
was been based on the fact, that the progression record is fairly short.
It is not necessary to store 20 prime numbers by a row,
in the form of a list  and it's enough to write only one record with an arithmetic progression to the array.
At the moment, I have an array containing more than 100,000 unique progressions, and this is about two million prime numbers, because most of all  they are AP20.
Thus, the generator containing 100,000 AP20 contains two million prime numbers, and size of this is less than 5 MegaBytes.
Different algorithms require checking the numbers for their primality and generate this numbers from the beginning, algorithmically  but in a certain limited range. The Sieve of Eratosthenes, also do generating prime numbers from beginning, moreover, it requires the recording of the entire array for ALL numbers.
The prime numbers contained in the arithmetic progressions have a very wide range (from zero) and have big common difference in the progression,
and this primes not easy to calculate algorithmically from the zero.
Nevertheless, all numbers are simple, they do not need to be checked for simplicity.
If you know how to get not "maybe primes", but really random prime number
in the big range, you can tell me, and my idea will lose its meaning.
For example, I saw the algorithms for calculate for digit N from Pi number,
and according to the Leibniz series  Pi is depending from prime numbers.
And maybe there is possible to get REALLY PRIMES in big range
1*10^40 to 2*10^50 without checking their primality.
I do not need ALL progressions if they are so difficult to get,
but the more of them, the better. This is the content for the generator and this expands the range for generation.
I can publish the source code here if you want.  

ReggieVolunteer moderator Volunteer tester Send message
Joined: 10 May 14 Posts: 31 ID: 311759 Credit: 79,615,550 RAC: 0

Ok, so is there any reason you're using AP20s? You could use the AP23s at the link I posted. There aren't as many of them, but it should work unless you really need two million primes. This would substantially reduce the server load as you only need to load one page.  


Ok, so is there any reason you're using AP20s? You could use the AP23s at the link I posted. There aren't as many of them, but it should work unless you really need two million primes. This would substantially reduce the server load as you only need to load one page.
There is no any reason to using exactly these AP20s, just this is the most common type of AP's in the list.
Also, I have already included all these progressions in the generator. And as you can see, I did post this link  in Original Post.
Now, on this page, there is 2440 unique arithmetic progressions
("1923 * AP23" + "447 * AP24" + "62 * AP25" + "8 * AP26").
1923 + 447 + 62 + 8 = 2440 AP's
and let's calculating primes there:
1923 * 23 = 44229 primes +
447 * 24 = 10728 primes +
62 * 25 = 1550 primes +
8 * 26 = 208 prime numbers.
Total 56715 prime numbers. And not very good range.
Also, I have on my hard disk  an archive, with 1,302,400,000 prime numbers, they are written in a row, from 2 to 30057700549.
This archive takes 1,401,613,717 bytes in a compressed state (7z, LZMA compressing),
and if I'll unzip this archive, it will expand on 16,418,727,846 bytes ~ 16.4 GB.
16418727846 bytes / 1302400000 primes = 12.60 bytes for each prime number  average space.
12.60 * 2000000 ~ 25213034 bytes ~ 25 megabytes.
At me, with progressions  it has appeared 5 megabytes space.
So I have in 5 times less space and high range, without any compression.
I do not want to do any load on the server any more, even if you open access to these APs. I can use a timeout to open the pages, but it's very long deal and tedious.
I think, would be better if the all progressions were public and quickly organized updates
on the site, or in the public sequences  like OEIS.  

compositeVolunteer tester Send message
Joined: 16 Feb 10 Posts: 706 ID: 55391 Credit: 559,363,658 RAC: 259,486

Originally, my idea of using AP's to generate prime numbers,
was been based on the fact, that the progression record is fairly short.
It is not necessary to store 20 prime numbers by a row,
in the form of a list  and it's enough to write only one record with an arithmetic progression to the array.
At the moment, I have an array containing more than 100,000 unique progressions, and this is about two million prime numbers, because most of all  they are AP20.
Thus, the generator containing 100,000 AP20 contains two million prime numbers, and size of this is less than 5 MegaBytes.
I'm not sure what you are trying to do.
If you are trying to devise a method of testing unknown numbers for primality, APs are not going to give you this information. You need to run primality tests.
It might be that you are trying to create a highly compressed list of known prime numbers, and you are looking to use APs as a method of condensing the information. Since you have a list of the first 30 billion or so prime numbers, you are free to search for subsets of primes in any manner you like, not necessarily arithmetic progressions. Invent a progression, label each prime in your subset that occurs in the progression at different starting positions, and select the subset of progressions that covers the most prime numbers in the least number of progressions. You might even get a more compressed set when you let some of the progressions overlap, where some prime numbers are represented more than once in your set.
It may also be that you are trying to develop a method of selecting a random prime number from the list of all prime numbers. Good luck. An uncompressed list is the only way of selecting with certainty an arbitrary Nth prime number with uniform distribution from the list.  


If you are trying to devise a method of testing unknown numbers for primality, APs are not going to give you this information. You need to run primality tests.
I don't want to using any primality tests and algorithms,
and I want to get random REAL prime number.
I can test is this prime at anytime,
by checking Prime Factorization on the site wolframalpha.com.
It might be that you are trying to create a highly compressed list of known prime numbers, and you are looking to use APs as a method of condensing the information.
Yes.
Since you have a list of the first 30 billion or so prime numbers, you are free to search for subsets of primes in any manner you like, not necessarily arithmetic progressions.
How to do this without save all primes?
I do not see any pattern in the distribution of prime numbers, which can be expressed by some formula, which would allow unambiguously to generate the present prime number depending on any parameter.
Maybe this is Pifunction (but there is using a limit).
And for me, arithmetic progressions from prime numbers is the shortest record, able to encode a whole series of numbers.
Invent a progression, label each prime in your subset that occurs in the progression at different starting positions, and select the subset of progressions that covers the most prime numbers in the least number of progressions. You might even get a more compressed set when you let some of the progressions overlap, where some prime numbers are represented more than once in your set.
If I will do assign additional addresses for prime numbers and if I will do algorithm to selection prime by addresses,
then the space of information in the list will growing.
I need to save an addresses, then.
It may also be that you are trying to develop a method of selecting a random prime number from the list of all prime numbers. Good luck.
Yes. To do generation prime my script do using two parameters from PRNG (random index and random n).
Index is sets the progression in AP's array,
and after select this  script using n
and return prime number from AP.
For example, I have an array:
//indexes is [0, 1, 2, 3, 4]
var progressions_array =
["327782912156715629+56579336*23#*n for n=0..20", //index 0
"282945022318458547+30504792*23#*n for n=0..20", //1
"204086274798537959+30504791*23#*n for n=0..20", //2
"366707529067925443+56138164*23#*n for n=0..19", //3
"298224021515636179+56089556*23#*n for n=0..19" //4
];
//(3*AP21)+(2*AP20) = 103 prime numbers in five string.
1. generation random index. index = 2;
2. generation n. n = 14;
3. Calculate 23# (23# is Primorial from 23 = 2*3*5*7*11*13*17*19*23 = 223092870  multiplication all primes before 23)
4. Select progression by index 2:
204086274798537959+30504791*23#*n for n=0..20
204086274798537959+30504791*223092870*0=204086274798537959
204086274798537959+30504791*223092870*1=210891676171478129
204086274798537959+30504791*223092870*2=217697077544418299
204086274798537959+30504791*223092870*3=224502478917358469
204086274798537959+30504791*223092870*4=231307880290298639
204086274798537959+30504791*223092870*5=238113281663238809
204086274798537959+30504791*223092870*6=244918683036178979
204086274798537959+30504791*223092870*7=251724084409119149
204086274798537959+30504791*223092870*8=258529485782059319
204086274798537959+30504791*223092870*9=265334887154999489
204086274798537959+30504791*223092870*10=272140288527939659
204086274798537959+30504791*223092870*11=278945689900879829
204086274798537959+30504791*223092870*12=285751091273819999
204086274798537959+30504791*223092870*13=292556492646760169
204086274798537959+30504791*223092870*14=299361894019700339
204086274798537959+30504791*223092870*15=306167295392640509
204086274798537959+30504791*223092870*16=312972696765580679
204086274798537959+30504791*223092870*17=319778098138520849
204086274798537959+30504791*223092870*18=326583499511461019
204086274798537959+30504791*223092870*19=333388900884401189
204086274798537959+30504791*223092870*20=340194302257341359
4. Calculate prime number for n = 14:
204086274798537959+30504791*223092870*14=299361894019700339
5. Return prime 299361894019700339 with wolframalpha.com link to check this: https://www.wolframalpha.com/input/?i=299361894019700339
As you can see this is a real prime number
Prime factorization:
299361894019700339 is a prime number.
And this prime number is 2.99361894019700339×10^17
This is more then 30 billion, like a maximum prime number in the list of my archive.
An uncompressed list is the only way of selecting with certainty an arbitrary Nth prime number with uniform distribution from the list.
In the range of n in arithmetic progression from (0 to progression_length), is also obtained an uniform distribution.
To check the number for simplicity, I would have to try to divide the candidates into a prime number  on the all the other prime numbers that stand before it. And this would require storing all this list of primes.
But AP's I can write by only one string, in array.  

compositeVolunteer tester Send message
Joined: 16 Feb 10 Posts: 706 ID: 55391 Credit: 559,363,658 RAC: 259,486

I don't want to using any primality tests and algorithms,
and I want to get random REAL prime number.
I can test is this prime at anytime,
by checking Prime Factorization on the site wolframalpha.com.
You are getting a number from a list of prime numbers, so you don't need to do any primality tests at all, and you certainly don't need to consult any external resource for primality or factorization. Your number is prime because someone else has already tested piles of numbers and made a list that excludes those that are not prime. The APs that we produce are by definition lists of primes.
Since you have a list of the first 30 billion or so prime numbers, you are free to search for subsets of primes in any manner you like, not necessarily arithmetic progressions.
How to do this without save all primes?
APs are NOT lists of consecutive primes. In general there are many primes between adjacent entries of an AP. What makes an AP interesting is that there are only primes in them and they occur a fixed distance apart.
For example: 5, 11, 17, 23, 29 forms a very small AP, each member separated from the next by a distance of 6. Note that there are primes in the span between the beginning and end of the AP that are not in the list: 7, 13, 19. It is coincidental that these missing primes also form a small AP having a distance of 6, but you can say that the entire set of primes between 5 and 29 (inclusive) are covered by this pair of APs.  


APs are NOT lists of consecutive primes. In general there are many primes between adjacent entries of an AP.
True. Sometimes the acronym CPAP is used instead of AP when the additional requirement that there are no primes in between, is included.
PrimeGrid does not search for CPAPs.
/JeppeSN  


The APs that we produce are by definition lists of primes.
I don't see any AP's now in any another user statistics.
Moreover, I see admins did delete AP link from another users.
Now, I can see only list of primes there. Hm...
Why access to AP's was been closed? And how long it will be closed?
Can admins do publishing this again? Or this is any top secret info?
APs are NOT lists of consecutive primes. In general there are many primes between adjacent entries of an AP. What makes an AP interesting is that there are only primes in them and they occur a fixed distance apart.
Yeap, that is what I wanted to say.
The numbers from the AP are very similar by bit length
and it looks like a uniform distribution of prime with fixed common difference for each progression.
For example: 5, 11, 17, 23, 29 forms a very small AP, each member separated from the next by a distance of 6. Note that there are primes in the span between the beginning and end of the AP that are not in the list: 7, 13, 19. It is coincidental that these missing primes also form a small AP having a distance of 6, but you can say that the entire set of primes between 5 and 29 (inclusive) are covered by this pair of APs.
Nice progression, but very shortly.
In the standard note this AP can be writed, like:
5+1/37182145*23#*n for n=0..5 :)
Is there any pattern or formula to easy find progressions in the primes list, that is wrote in a row sequence?
True. Sometimes the acronym CPAP is used instead of AP when the additional requirement that there are no primes in between, is included.
Yeah, I know, but in CPAP, there is so large primes!
I don't have any sence to using this...
On this site, there is specified a number of their digits!
And there is so difficult to operate with them.
But... If I will do multiplication two primes from AP's
I can easy turn this primes go back!..
For example two primes from my previous AP:
285751091273819999 (for n = 12) × 333388900884401189 (for n = 19)
= 95266242246297053145225031687578811
So I can get a large "composite number".
9.5266242246297053145225031687578811 × 10^34
Hm... But... I'd look at THIS:
And I can see there a field, Prime factorization:
285751091273819999×333388900884401189
Hehhehhh....
So an easy way to factorize compound numbers with this length
makes it useless to use these primes for encryption, like in RSA or DiffieHellman algorithms.
Prior to that, I was betting that most cryptosystems are cryptoresistant
as long as the PRNG have a cryptographically strength.
And now I did loss any sense to using AP's from PrimeGrid to seed PRNG for encrypting.
Maybe there is any sense to using large Mersenne Primes or another big primes, but random entropy is lossing, if I will do selecting one by one from when number of primes in list is limited (50 Mersenne primes only, for example).
Since you have a list of the first 30 billion or so prime numbers, you are free to search for subsets of primes in any manner you like, not necessarily arithmetic progressions.
Hm... People, any one know, how can I compress prime numbers
in the list to don't record all digits of this primes?
Is there any formula?
I see here short notes for big primes, but there is specially primary formulas by type for do brute force calculating this primes in BOINC...
Maybe, I can using formulas, like 3×10^10+(1, 13, 53, 77, 89, etc...)
Also, I have one another idea for using my large archive of prime numbers.
For example:
1. If I have an array with the primes sequence [2, 3, 5, 7, 11, 13, 17]
2. Then I can check maximum numbers from 0 to 17^2 = 289 and lowest odd number 287 can be divided by one of this primes (7×41).
3. If number can not be divided by this primes without remainder  this is "maybe prime number" and I can add this to the array.
4. So if I have 1.4 billion prime numbers in a row sequence,
with maximum value of last prime (30,000,000,001)
then I can calculate all primes in the square of this range (30000000001)^2 ~ 9 × 10^20 then again square (8.1 × 10^41), then again, and again... :D  


I don't see any AP's now in any another user statistics.
Moreover, I see admins did delete AP link from another users.
Now, I can see only list of primes there. Hm...
Why access to AP's was been closed? And how long it will be closed?
Can admins do publishing this again? Or this is any top secret info?
Try to read the first post by JimB in this thread (Message 116926) again! They removed this nice feature because you had a script that misused it. You harvested these pages too aggressively.
When you make a script that "crawls" a lot of pages, be sure to have long pauses between each page request. Otherwise you will put too much load on the server.
/JeppeSN  


Try to read the first post by JimB in this thread (Message 116926) again! They removed this nice feature because you had a script that misused it. You harvested these pages too aggressively.
When you make a script that "crawls" a lot of pages, be sure to have long pauses between each page request. Otherwise you will put too much load on the server.
/JeppeSN
I'd already read this.
I really did not set a delay when opening many windows,
but it would be wiser to set a timeout on the server,
instead of disabling it FOR ALL USERS.
To do this, admins can using Captcha, ConnectTimeout options for GET queries, and server timeout for HttpRequest at last
(with response, like HTTP 408 Request Timeout,
or message "try to update page lager, after 5... 4... 3... 2... 1... seconds.")
And after this all, I would like to ask admins for unlock AP's for another users.
I don't have any interest for using AP's in PRNG,
and any scripts without timeouts.
I will not try to get AP's or another data  so inconvenient way,
if your server so such an unstable.
And now, I will go to download  1 trillion prime numbers, in a row sequence. :D
Best regards.  

compositeVolunteer tester Send message
Joined: 16 Feb 10 Posts: 706 ID: 55391 Credit: 559,363,658 RAC: 259,486

Nice progression, but very shortly.
In the standard note this AP can be writed, like:
5+1/37182145*23#*n for n=0..5 :)
Is there any pattern or formula to easy find progressions in the primes list, that is wrote in a row sequence?
You are making things much harder for yourself than necessary.
There is a much shorter formula for this AP.
5+6*n for n=0..4
But... If I will do multiplication two primes from AP's
I can easy turn this primes go back!..
For example two primes from my previous AP:
285751091273819999 (for n = 12) × 333388900884401189 (for n = 19)
= 95266242246297053145225031687578811
So I can get a large "composite number".
9.5266242246297053145225031687578811 × 10^34
Yes, some numbers are more easily factored than others and must be avoided for cryptography.
Acceptable RSA modulus strength these days is around 10^616.
And now, I will go to download  1 trillion prime numbers, in a row sequence. :D
It doesn't take long to try them all. Multiplying a pair of numbers from a set of one trillion numbers results in a keyspace of size 10^24. And if you can download it, then clearly someone else already has this list.
It's also problematic to use very large primes from a list of known very large primes. These number in the thousands. It's not the size of your key that matters, rather it's the size of your keyspace.
So come up with a couple of original large primes and keep them secret. Now we're talking.  


I again want to ask admins to open access for AP's not for me, but
for any ALL another users.
Yes, some numbers are more easily factored than others and must be avoided for cryptography.
But see the range and exponent of this!.. And the speed of factorization!..
Acceptable RSA modulus strength these days is around 10^616.
Their length lower like MegaPrimes, here...
But this is so big numbers...
10^x = 2^y; y = (x (log(2) + log(5)))/log(2) = 2046.31
There is a point on the number line and this have value 2046.31.
That means 2046.31 bits, and bit length of key ≈ 2048 bits.
I don't think the prime numbers must to be so long.
For example, I can see here
a prime numbers over 1 trillion, in the custom range.
There I can collect lists of 1000 primes, without any lags.
It doesn't take long to try them all.
And if you can download it, then clearly someone else already has this list.
I don't think that every number really divided for all prime numbers there, which are writed in the row sequence list.
Wolfram's response so quickly, but this tooks long time
to try divide this for all 35 billion primes from 0 to 1 trillion. π(1T) this is prime pifunction...
Multiplying a pair of numbers from a set of one trillion numbers results in a keyspace of size 10^24.
Compound numbers are factorized there so easy in this range, as you can see in my previous example.
I did used in wolfram two prime numbers from progression, with exponential note n×10^17 for each prime, and compound numbers up to N×10^34
This is more than one and two trillion!
It's not the size of your key that matters, rather it's the size of your keyspace.
Do you have any list with prime numbers  in the range 2^256  2^1024?
100?.. 500?.. 1000?..
So come up with a couple of original large primes and keep them secret. Now we're talking.
But the better slowly way, to collect big prime numbers,
I can see in this algorithm...
1. Generate big odd number.
2. Copy and paste to wolframalpha.
3. See factorization, and using largest prime.
For example, here (≈5.52×10^85)
I can see prime factorization:
7^2×13^2×9829×678364058742890703359868245487209221658124995744414718166011817821443126850887
and number 678364058742890703359868245487209221658124995744414718166011817821443126850887 seems,
like a prime number.
This can be not prime, but "maybe prime".
It's also problematic to use very large primes from a list of known very large primes.
These number in the thousands.
Yeap. And if any number is not prime, can be lags and errors.
Cheers.  


Why be so demanding? They explained previously that you put unexpected and unnecessary stress on the servers that we donated money for. Perhaps if you explained what you wanted the information for and liaised courteously with the project admins they might concede to your request. Coming here and demanding data files is downright rude.  


Why be so demanding? They explained previously that you put unexpected and unnecessary stress on the servers that we donated money for. Perhaps if you explained what you wanted the information for and liaised courteously with the project admins they might concede to your request. Coming here and demanding data files is downright rude.
Isn't always the case of one single individual messing things up for everyone else? Just look what happened 10 days ago with Collatz and Gridcoin (albeit at an even more serious level).
We had a really good thing going with our discoveries (primes and AP) being displayed with a single click. Now, the AP functionality is gone.
Than ks, A_H_O_H.  

Michael GoetzVolunteer moderator Project administrator Project scientist
Send message
Joined: 21 Jan 10 Posts: 12911 ID: 53948 Credit: 194,837,816 RAC: 205,774

This thread, and this discussion, is now closed.
There have been private communications which are not going to be made public.
____________
Please do not PM me with support questions. Ask on the forums instead. Thank you!
My lucky number is 75898^{524288}+1  

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