20210414, 03:33  #12 
P90 years forever!
Aug 2002
Yeehaw, FL
3^{5}×31 Posts 
Yes, useless.
I'm not even sure it will be useful to the let's get number of unfactored exponents below 20M crowd. The biggest advantage I see to studying P+1 is that stage 2 should be faster and Montgomery showed a way to convert a P1 stage 2 into a P+1 stage 2. Last fiddled with by Prime95 on 20210414 at 03:34 
20210414, 03:41  #13  
Jun 2003
2·3·7·11^{2} Posts 
Quote:
It is more costly than P1, it loses the free "2p", and there is only a 50% chance of picking the correct seed. Sure, the other 50% of time you have done a stealth P1, but since it is costlier than P1 you might end up choosing smaller bounds. Honestly, I don't know. It is worth crunching the numbers to see if it might be worthwhile. However, it *will* be useful for the "20M unfactored" project. Quote:
Quote:
So after a failed P+1 attempt, you still might want to run a P1, but this time, your expected probability of success is reduced 

20210414, 03:51  #14  
Jun 2003
13DA_{16} Posts 
Quote:
Basically, deeper P1 on already P1ed exponents have poor costtobenefit ratio. Having P+1 which searches a different factor space doesn't suffer from prior P1 runs. Anyway, I don't think there is any urgency in having this feature, if at all. Although, now that I think about it, P95 deals with the general form (k*b^n+c)/f, and so other projects might be able to use it. 

20210414, 14:22  #15  
Jun 2003
1001111011010_{2} Posts 
Quote:
If f=1 (mod 6) and f1 is smooth, then also 2/7 will find it If f=3 (mod 4) and f+1 is smooth, 6/5 will find it If f=1 (mod 4) and f1 is smooth, then also 6/5 will find it. In terms of mersenne factors, we have the following success matrix: Code:
f mod 24  P+1 smooth  P1 smooth  Neither smooth +++ 1  Neither  2/7, 6/5  Neither 7  6/5  2/7  Neither 17  2/7  6/5  Neither 23  2/7, 6/5  Neither  Neither 

20210414, 18:52  #16  
Aug 2002
Buenos Aires, Argentina
1366_{10} Posts 
Quote:


20210415, 02:15  #17  
Jun 2003
5082_{10} Posts 
Quote:
/IIUC 

20210415, 13:36  #18 
Aug 2002
Buenos Aires, Argentina
2526_{8} Posts 
In Prime95 running one curve with specified B1 and B2 is 10 times slower than running P1 with the same bounds.
So I think that for some cases with exponents less than about 10 million, P+1 could help. 
20210425, 01:26  #19 
Bemusing Prompter
"Danny"
Dec 2002
California
4533_{8} Posts 
Dumb question: does P+1 have an analogue of the Brent–Suyama extension?

20210425, 02:20  #20 
Jun 2003
2×3×7×11^{2} Posts 

20210425, 04:30  #21 
P90 years forever!
Aug 2002
Yeehaw, FL
3^{5}·31 Posts 

20210503, 20:00  #22 
Bemusing Prompter
"Danny"
Dec 2002
California
95B_{16} Posts 
Another question: I know it's possible to further generalize P1 and P+1 using cyclotomic polynomials. Would this be beneficial to GIMPS?
Last fiddled with by ixfd64 on 20210503 at 20:01 
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