20160305, 19:07  #1 
"NOT A TROLL"
Mar 2016
California
197 Posts 
How to create file to test primes automatically
I want to easily find primes of the form k*b^n+c. However, manually testing the variables takes a long time. I am using Pfgw. Can someone please help create a file so I can always find the nearest k, n, or c values. For example, I want to find a prime of the form 43*71^n +300, (for large primes) and I do not want to manually test exponents, so is there a format file that tests primes of the form k*b^n+c, so all I can do is just plug in the variables. Thanks for helping.

20160305, 21:20  #2  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
89·107 Posts 
Quote:
Take (mod 7) of 43*71^n+300. To do that you can take mod 7 of each coefficient: 1*1^n+6, which is 7 = 0 (mod 7). Anyway, this is just a poor example. The bigger problem is that if you find large enough (say, > 50,000 digits) prime candidates (probable primes), you will not be able to prove that they are prime. If you still want to search for these large PRPs, use srsieve to sieve. You can submit large PRPs to PRP top. 

20160305, 21:22  #3 
Sep 2002
Database er0rr
2^{3}×5^{2}×19 Posts 
You need this sort of thing in your input file:
Code:
ABC 43*71^$a+300 1 2 3 4 5 6 ... Code:
ABC2 43*71^$a+300 a: from 1 to 1000000 You might find that someone has written a sieve for this form. A word of warning: To prove a number prime you need at least 12.5% of the factorisation of N^21, where N is the number being proven. See this page. Otherwise, general purpose proving algorithms, such as ECPP, work up to about 30k digits if you are very patient, whereas numbers that can be proven by BLS N+/1 can be proved in minutes to hours. Look in pfgwdoc.txt and abcfileformats.txt for more info. Last fiddled with by paulunderwood on 20160305 at 21:24 
20160306, 01:45  #4 
"NOT A TROLL"
Mar 2016
California
197 Posts 
New Prime Form
Thanks for your advice!
And that form 43*71^n+300 is a bad example since it is divisible by 7, so I replaced the form with 24*181^n+229, anyways I created a file called input.txt and here were the following lines: ABC2 24*181^$a+229 a: from 1 to 3000 ... I then used the Pfgw (Win64Pfgw.exe) compatible command line and typed in: input.txt and gave me; PFGW Version 3.7.10.32BIT.20150809.Win_Dev [GWNUM 28.6] Error opening file input.txt Do you know what went wrong? Please let me know. 
20160306, 07:06  #5 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
22463_{8} Posts 
43*71^n+c has many c values that generate allcomposite sequences; they have a socalled covering set. But a few c values are working fine, e.g. c=4.
For kicks and giggles I sieved the c=4 series and ran it for a while. There are a few small primes (43*71^0+4, 43*71^4+4, 43*71^144+4, 43*71^784+4) and then a larger unprovable PRP: 43*71^38292+4 (submitted to PRPtop) _________________________ Re: "Error opening file input.txt" Check where you put the input.txt file. Is it in the same folder as the pfgw executable? If not  provide the full path, or move it in the same folder. Then put "f l input.txt" in the text window of Win64Pfgw.exe. Works fine here, and quickly finds a few tiny primes 24*181^14+229 24*181^51+229 
20160307, 04:29  #6 
"NOT A TROLL"
Mar 2016
California
197 Posts 
Prptop
I am Trying to submit my own PRP, and I came up with the form: 60*79^n+19, known primes are for n = 0, 1, 3, 42, 91, 165, 585, 763, 2472, 3535, 3870, 5088. Do you know how to find the next term in less than 1 hour, if so what is it? (I tested exponents <10000) using pfgw.
Last fiddled with by PawnProver44 on 20160307 at 04:30 
20160307, 20:37  #7 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
89×107 Posts 
It is not very large. You can find it yourself, if you try hard enough.
It is already in the PRPtop. 
20160307, 21:20  #8 
"NOT A TROLL"
Mar 2016
California
305_{8} Posts 
you submitted it, right?

20160307, 21:43  #9  
Sep 2002
Database er0rr
7330_{8} Posts 
Quote:


20160307, 21:52  #10 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
89·107 Posts 

20160307, 22:03  #11 
"NOT A TROLL"
Mar 2016
California
C5_{16} Posts 

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