20180725, 07:43  #23 
"Robert Gerbicz"
Oct 2005
Hungary
2×3×227 Posts 

20180725, 08:26  #24  
Sep 2003
2·1,289 Posts 
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#! /usr/bin/python3 import fileinput with fileinput.input() as f: for line in f: p, f = line.strip().split(",", maxsplit=2) p = int(p) f = int(f) if (f  1) % (2*p) != 0: print ("UNEXPECTED FORM: ", p, f) What can we say for the general case of k × b^{n} + c ? Which values for the constants k, b, c let us do P−1 testing more effectively in the source code of mprime/Prime95? 

20180725, 08:32  #25  
Jun 2003
1217_{16} Posts 
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20180725, 10:40  #26  
Sep 2006
The Netherlands
1242_{8} Posts 
Quote:
Let's first focus upon the reality. that's that in the GIMPS project most people wanted a chance to find a prime. So they wanted to TEST rather than TF and initially there wasn't a gpgpu version of TF. They simply didn't do a very deep TF initially for Mersenne. It was just so so. Additionally Wagstaff TF's much better than Mersenne. so you keep left with a far smaller percentage of numbers to test for PRP than to LL. TF simply is more effective in that sense for Wagstaff. So there is a number of things that make this plausible: a) there is a smaller percentage of numbers left with wagstaff after TF than with mersenne. b) nowadays the TF is far far far deeper than years ago with Mersenne c) Mersenne is at dozens of millions of bits, Wagstaff still is at 10+ million bits. d) we divide by 3 so it's not a +1 number of bits. It's a 1 number of bits. It's especially B. the mersenne project has been pretty lazy in that respect. Everyone wanted a chance to find a prime. So they started testing long before a good TF had been done. Last fiddled with by diep on 20180725 at 10:44 

20180725, 10:55  #27 
Sep 2006
The Netherlands
1010100010_{2} Posts 
Let me focus upon argument D as this is the thing most researchers seem to forget.
x = 2^p + 1; We first divide a number length len = prime p number of bits We divide it by 3. If we take p = 5 2^5 + 1 = 33 = 0b100001 bits = 6 bits we divide it by 3 ==> 33 / 3 = 11 = 0b1011 = 4 bits So we want a prime of 4 bits which is p1 bits. That's a lot of constraints we want to find a prime. Last fiddled with by diep on 20180725 at 10:57 
20180725, 11:07  #28  
Jun 2003
11×421 Posts 
What alternative? P1 is a complementary method to TF, not an alternative. And ECM is not cost competitive with P1. What other alternative is there?
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Not sure I understand. What do you mean by this? 

20180725, 11:08  #29 
"Robert Gerbicz"
Oct 2005
Hungary
2×3×227 Posts 
Not likely, because when you'd divide by 3 you'd already know 2^p+1, right?
Last fiddled with by R. Gerbicz on 20180725 at 11:12 
20180725, 11:14  #30 
Sep 2006
The Netherlands
2×337 Posts 
>> Originally Posted by diep View Post
>>a) there is a smaller percentage of numbers left with wagstaff after TF than with >>mersenne. > I don't know why this should be so... but I'll take your word for it. However this has > no relevance as to whether doing P1 after TF is worthwhile. Sir, if you do not understand this one, i propose that you first study this one in depth first before claiming it doesn't matter. 
20180725, 11:17  #31 
Sep 2006
The Netherlands
2·337 Posts 
Originally Posted by diep View Post
>> b) nowadays the TF is far far far deeper than years ago with Mersenne > Due to GPUTF. If Wagstaff's have also been similarly deeply TF'ed with GPUs, then the P1 breakeven point would shift It is a very silly assumption to assume you will not be using some massive gpu's to TF. The amount of system time to factor with a silly algorithm like P1 provable is nonsense except if you can do that on hardware that wouldn't be used for PRPtesting otherwise. GPU's are so much faster than the hardware most have to do PRPtesting, it's just not even funny to compare the 2. 
20180725, 11:18  #32 
Sep 2006
The Netherlands
2×337 Posts 
Originally Posted by diep View Post
>> Oh it does compared to the alternatives. > What alternative? P1 is a complementary method to TF, not an alternative. And ECM is not cost competitive with P1. What other alternative is there? You get what you pay for. 
20180725, 11:19  #33 
Sep 2006
The Netherlands
2·337 Posts 
>> d) we divide by 3 so it's not a +1 number of bits. It's a 1 number of bits.
> Not sure I understand. What do you mean by this? Wagstaff is a much harder beast than Mersenne. 
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