[QUOTE=science_man_88]\ is floor and in a way but I'm trying to get more specific.[/QUOTE]

It can also mean, "nearest multiple of n ≤ x." Are you stating that the nearest multiple of a prime dividing a composite Mersenne number is always divisible by 8? The remainder is zero. The nearest multiple of a prime dividing a composite Mersenne is the number itself. An odd number cannot be divisible by 8.

[QUOTE=3.14159;223460]It can also mean, "nearest multiple of n ≤ x." Are you stating that the nearest multiple of a prime dividing a composite Mersenne number is always divisible by 8? The remainder is zero. The nearest multiple of a prime dividing a composite Mersenne is the number itself. An odd number cannot be divisible by 8.[/QUOTE]


no look 2^11-1 divides by 8(1)*11+1
2^23-1 divides by 8(970)*23+1
2^29-1 divides by 8(1)*29-1 and 8(9)*29+1


this doesn't work for some but that's with 3 factors and I think it falls under if one of the first 2 factors don't fit such a division neither will the third.

[QUOTE=3.14159;223453]Wait.. I seem to forget what the \ function is. Is it the floor function? By the way, are you still working on the trial factor code?[/QUOTE]

/ is division. 14/8 is the rational number 7/4.

\ is integer division. 14\8 is the integer 1.

a\b is essentially the same as floor(a/b). (I can't remmeber if they're the same if a and b are of opposite signs; you could test this.)

Also: I'm performing some experiments using the Rho factorization method, via YAFU. Isn't there a separate implementation that uses Rho's only? (One source gives pseudocode, but I cannot open Java files anyway, so the pseudocode is useless.)

Factoring 745 * 2^120 + 1, a composite whose smallest divisor is a p17: 36002852207533361, was a failure for even 1.77M * 3 iterations. It seems that it is not practical for anything more than 30 digits, a limitation that is shared by trial division.

[QUOTE=3.14159;223500]Factoring 745 * 2^120 + 1, a composite whose smallest divisor is a p17: 36002852207533361, was a failure for even 1.77M * 3 iterations. It seems that it is not practical for anything more than 30 digits, a limitation that is shared by trial division.[/QUOTE]

Yes, 25 digits is about as far as I'd push it. Shanks' SQUFOF is better above 10-15 digits, I think.

[QUOTE=CRGreathouse]Yes, 25 digits is about as far as I'd push it. Shanks' SQUFOF is better above 10-15 digits, I think.
[/QUOTE]

The limitations of various algorithms: (Most or all of them may be incorrect)
Trial division: ≈ 20-30 digits
Rho's: ≈ 30-35 digits
SQUFOF: ≈ 40-50 digits
ECM: ≈ 60-75 digits ? (Note: Record factor is 73 digits)
QS: ≈ 100-115 digits ? (Note: Largest number factored was a c135, which was split as a product of a p66 and a p69.)
GNFS: 115+ digits?

Also: Prime searches underway: k * 12096[sup]16384[/sup] + 1

Also: The search range is in between 66893 and 66896 digits. Also, that'll set three personal records:
1. Largest PRP ever found, snaps the personal record by a factor of about 1.67
2. Largest Proth-GFN ever found.
3. Largest Generalized Proth ever found.

Also: Anyone happen to be in the PrimeGrid project?

I'm testing 689501 candidates, and so far only 51933 remain. About 1 in 13.

Also: What hasn't been done for a long time:
Submissions:
13245 * 2[sup]18680[/sup] + 1 (5628 digits)
3721 * 2[sup]8640[/sup] + 1 (2605 digits)
22507 * 2[sup]65218[/sup] + 1 (19637 digits)
110875 * 2[sup]53680[/sup] + 1 (16165 digits)

[QUOTE=3.14159;223553]
Also: Anyone happen to be in the PrimeGrid project?
[/QUOTE]

Well, Lennart is a big portion of PrimeGrid. rogue is the developer of PRPnet, also he creates the newer releases of PFGW. Jean Penné LLR developer. opyrt mod at PSP. The list goes on.

[QUOTE=Mathew Steine]Well, Lennart is a big portion of PrimeGrid. rogue is the developer of PRPnet, also he creates the newer releases of PFGW. Jean Penné LLR developer. opyrt mod at PSP. The list goes on.
[/QUOTE]

LLR, PFGW, and NewPGen are the programs that I happen to have for large prime searches, seeing as they are (probably) the only *usable* programs out there.

My params on prime testing:
4-27 digits (Primes under 1500, I can easily recite): Proving via applets. These apps can be found [URL="http://www.naturalnumbers.org/"]here[/URL].
28-900 digits: APRT-CL test, can be found [URL="http://www.alpertron.com.ar/ECM.HTM"]here[/URL].
901-10000 digits: PARI's isprime function.
10k + digits: PFGW's PRP test. (Pseudoprimes, anyone?)
Okay: I'm guessing the pseudoprimes for PFGW's tests are [URL="http://www.research.att.com/~njas/sequences/A020229"]here[/URL]. (They would be if it weren't for the trial factoring that takes place.)
[code]79666464458507787791865*2^2+1 is 3-PRP! (0.0000s+0.0001s)[/code]

Guess confirmed.

[quote=3.14159;223565]LLR, PFGW, and NewPGen are the programs that I happen to have for large prime searches, seeing as they are (probably) the only *usable* programs out there.[/quote]
With the exception of NewPGen, yes, those are the premier programs out there now for this kind of testing. For sieving, you'd probably be better off using srsieve (or any of its various specialized renditions) since it's faster than NewPGen. (I believe srsieve has already been suggested earlier in this thread, so I won't bother to post a link.)

[QUOTE=mdettweiler]With the exception of NewPGen, yes, those are the premier programs out there now for this kind of testing. For sieving, you'd probably be better off using srsieve (or any of its various specialized renditions) since it's faster than NewPGen. (I believe srsieve has already been suggested earlier in this thread, so I won't bother to post a link.)
[/QUOTE]

You have to set up a file just for the sieving. I think srsieve's programmer warns that NewPGen maybe/is faster than it on the readme.txt file for the program. (I think this was solely for srsieve.)
I'll take a closer look at the readme.
Wait: I got an example file in the same folder as the applet, and it refuses to open the file to be sieved.