So I managed to download Yves Gallot's program, Proth. I also downloaded PrimeForm (allows more forms of prime to be found). I'm currently searching for primes that are 11998 and 27560 digits in length. My personal record is a 13050-digit prime (Generalized Fermat prime, 1534^4096 + 1). The 27560-digit prime is a Proth prime. The 11998-digit prime to be searched for is a misc. prime:
It's of the form: (p(a)#)^c * (p(b)#)^d * (n! * x! * k) + 1, where a = 821, b = 126, c = 4, d = 4, n = 7, x = 11. The 27560-digit prime search, I have been conducting for two days: My exponent range is in between 91360 and 93200, and the range of the coefficient k is in between 10^4 and 10^5, so I'm testing about 165,600,000 candidates. By the time the search is over, I should have 2609 primes, between 27560 and 28114 digits in length, snapping my personal record by a factor of two. Any tips?

I left the machine on overnight, and found a prime of 27507 digits, which now makes it my personal record, snapping the previous by a factor of two. Now, I need to finish the other search, for the misc. prime of the form (p(a)#)^c * (p(b)#)^d * (n! * x! * k) + 1.
The prime recently found: 59991 * 2^91360 + 1 (27507 digits)

Advice: Don't use Proth or the original PrimeForm (assuming you are referring to the precursor to OpenPFGW). Both are really, really old. PFGW and LLR are many times faster than Proth.

I give up.. This program of yours is too confusing to set up.. I set up a text file, it gives me an error message. I try a quick test, it instantly fails. This shall face the wrath of my delete button. *deletes* For newpgen, I tried to locate 90-digit primes, as a test. Does it trial-divide all the way to 10^45? O_O

Attempted to test something again. Failed + Deleted out of frustration. The old programs will do.

I give up.. This program of yours is too confusing to set up..

Okay: I'm going to set it up, and I'm going to try to test a sample number: I'll choose a proven prime: 2216 * 1296^263 + 1. (You did advise to use simpler expressions.). I'll attempt to use your advice during testing. By the way, the only version that seems to work is WinPFGW. If I enter a number, using the syntax -q<expression>, it always gives the message: "Evaluator failed".Here's the error message:

PFGW Version 3.3.4.20100405.Win_Stable [GWNUM 25.14]

<2216*1296^263+1> - Evaluator failed

Alright.. I'll try that: Ah. I get the idea. The expression needs to be typed right next to the -q. Thanks for the help, all. Now, to test a few numbers at a time? It says I need to make a file that has all the numbers to be tested within it. Update: Like PrimeForm, it has a bunch of settings including what tests to use, what expressions to be evaluated, etc. Also, is there a limit to the amount of changing variables that can be used in an expression once you manage to mess with the settings? Here's what I mean: In both Proth and PrimeForm, you can only select how much the variables n and k vary, or, assign them a range. Can you assign a range to more than two variables? Does a text file have to be made for this to occur? Also: Would it be recommended to use the N-1 or N+1 tests using the forms of prime I am seeking? (k * 2^n + 1, and (k * p(n)#^x + 1), for improved speed? Or should I stick with PRP?
Also.. "helper.txt"?
For the multiple number file: Or, "input.txt", I made it. When I enter it as a command, it gives an error message that reads: "Cannot open file input.txt"

Hmm.. You can't get it to test a range.. So I have to manually list all candidates myself. Using an advanced text editor, this will be relatively simple. I guess a few extra seconds to a minute of work beforehand isn't too much work. Concerning the prime tests to use: I'll set up an experiment to see whether N-1 or PRP works faster. The command I use? I simply use the filename itself. To get to work on setting up my ranges:
k * p(n)#^x + 1, where k is between.. 6250 and 31250; n is between 250 and 1250; x is between 1 and 625. The digit range: 4382 to 2738750.

284 GB?!? How would that ever sum to 284 GB? It's testing 15.625 billion candidates in total. 15.625 billion would sum to.. only about 10-20 GB, if I remember correctly. Although I do not have any text editor willing to store 20 GB of digits. (Update: Assuming 8 bits/digit, 15625000000 digits would sum to 125000000000 bits. 125000000000 bits = 15625000000 bytes, assuming 8 bits = 1 byte. 1024 bytes = 1 KB, so 15258789.0625 KB, and 1024 KB = 1 MB, That would be 14901.1611 MB, and 1024 MB = 1 GB, so that would be 14.55191 GB, assuming only one character per line. Multiply the figure by about 14 (The average amount of characters in my ranges, that would be 203.7268 GB.

Woah. I didn't notice your post. And, was I correct in assuming 1 digit occupies 8 bits?

A question about NewPGen... where is it that you can find the output file it generates after sieving is finished?
It gives the message: "Output file '<filename>.txt' generated, contains <n>k's"
I then proceed to search for the file, and.. find that it does not exist. It's basically saving the results onto a file that does not exist. This must be fixed.

It's in the directory where you put the executable.

Did you put a name in the field for the output file?

I did a NewPGen run a few days ago and that's where it was located.

General form of the output file was:

866831026:M:0:60924526:2
27 155071
30 155071
44 155071
54 155071
134 155071
144 155071
149 155071
165 155071
168 155071
183 155071
195 155071

Interesting discussion.

____________

Of course I did. I named it workA.txt.Update: Got the pesky text file. Thanks for the help, all. All I need to do is make in an input in LLR, correct? Update 2: Got LLR working on the candidates that were sieved up to 16 billion. By the way, for sieving: Does it perform either:
1. Ex: Sieve up to 11 --> Eliminate multiples of 2, 3, 5, 7, 11
2. Eliminate only multiples of 11.

Also: Prime found! 9731 * 1296^2600 + 1 (Approx. 8097 digits) + Generalized Proth prime.
Another: 12472 * 1296^2600 + 1 (Approx. 8098 digits)
Also: On the search for a new personal record, Range: 83641 or 83642 decimal digits, breaking the previous personal record by a factor of three. Sieving up to 256B. So far, only 7.3% of the candidates remain. Also, if I do find an 83641-digit prime, it's going to be a prime-numbered amount of digits in length. Tips?

Update: The odds of a number in the ranges I selected of being prime is only 19.33% (After sieving for up to about 2 to 4 * 10^10). Must update the ranges, unless sieving actually improves probability.

Update: I sieved up to 256B, and it turned out to be insufficient. Based on LLR taking nearly 5 minutes to test an 83641-digit number, it would take 4 months to finish testing. And, who has that kind of time? I certainly don't. Sieving raised to 1.6 * 10^13.

The Prime Pages' article for the applet NewPGen makes the following suggestion:

This program, NewPGen, performs this type of sieving. NewPGen should be used to throw out candidate k's until the rate at which it is removing them exceeds the rate at which Proth.exe can perform a power test. At that point Proth.exe should be used to complete the search, with PMax=0 (as trial factoring has already been performed by NewPGen).

Hmm..

Again, use PFGW. You are wasting your time with Proth. Take the output file from NewPGen and pass as the lone parameter to PFGW. It can read NewPGen formatted files.