20160112, 07:49  #111  
∂^{2}ω=0
Sep 2002
República de California
3·5^{3}·31 Posts 
Quote:
On the other hand, going back 10 previous Mprimes we get 13466917*1.4^10 = 389,536,843 which is much larger than the latest one. OTOOH, such distributions are wellknown to be 'clumpy', so much depends on the chosen starting point: going back 20 Mprimes we get 110503*1.4^20 = 92,455,932, which is again quite close (given the largeness of the logarithmic interval) to the latest one. You sure about that last one? Based on my estimates p ~= 85M should require FFT of ~4500K. Last fiddled with by ewmayer on 20160112 at 07:55 

20160112, 07:54  #112 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
41×229 Posts 
1.4 is a rather dubious number. Is that a new conjecture? ;)
There is a large difference between 1.4^10 and 1.47576^10; that's roughly 28.93 and 49, so (quote:) going back 10 previous Mprimes we get 13466917*1.47576^10 = Not much better going back 20 previous Mprimes: 110503*1.47576^20 = Last fiddled with by Batalov on 20160112 at 08:02 
20160112, 07:58  #113  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
Quote:
Edit: I two different jump tables after the AVX comment. The top one is directly below the AVX comment, and I'm not sure what the second jump table is. Code:
PRCSTRT 76210000, 4096000, 0.028093 PRCENTRY2 yfft_r4dwpn_4000K_12800_2, 8005632 PRCENTRY2 yfft_r4dwpn_4000K_6400_2, 6982912, I7_64 DD 0 PRCSTRT 76790000, 4128768, 0.027915 PRCENTRY2 yfft_r4dwpn_4032K_9216_2, 6665728 PRCENTRY2 yfft_r4dwpn_4032K_4608_2, 5633280 PRCENTRY2 yfft_r4dwpn_4032K_2304_4, 6786304 DD 0 PRCSTRT 77990000, 4194304, 0.026160 PRCENTRY2 yfft_r4dwpn_4M_14_4, 9644800 PRCENTRY2 yfft_r4dwpn_4M_14_2, 9644800 PRCENTRY2 yfft_r4dwpn_4M_14_1, 9644800 PRCENTRY2 yfft_r4dwpn_4M_13_4, 8500736 PRCENTRY2 yfft_r4dwpn_4M_13_2, 8500736, I7 + FMA3_64 PRCENTRY2 yfft_r4dwpn_4M_13_1, 8500736 PRCENTRY2 yfft_r4dwpn_4M_12_4, 5320704 PRCENTRY2 yfft_r4dwpn_4M_12_2, 5320704 PRCENTRY2 yfft_r4dwpn_4M_12_1, 5320704 PRCENTRY2 yfft_r4dwpn_4M_11_4, 6458368 DD 0 PRCSTRT 85200000, 4587520, 0.031930 PRCENTRY2 yfft_r4dwpn_4480K_10240_2, 7414272 PRCENTRY2 yfft_r4dwpn_4480K_5120_2, 6263040, I7 DD 0 PRCSTRT 87400000, 4718592, 0.030538 PRCENTRY2 yfft_r4dwpn_4608K_12288_2, 8322304 PRCENTRY2 yfft_r4dwpn_4608K_12288_1, 8322304 PRCENTRY2 yfft_r4dwpn_4608K_9216_2, 9464320, I7_64 PRCENTRY2 yfft_r4dwpn_4608K_9216_1, 9464320 PRCENTRY2 yfft_r4dwpn_4608K_6144_2, 7122944, I7_32 + FMA3_64 PRCENTRY2 yfft_r4dwpn_4608K_4608_4, 5932032 PRCENTRY2 yfft_r4dwpn_4608K_3072_4, 8450560 PRCENTRY2 yfft_r4dwpn_4608K_2304_4, 7235072 ... PRCSTRT 76050000, 4096000, 0.029047 PRCENTRY2 yfft_r4dwpn_4000K_ac_6400_2, 4583424, I7_64 DD 0 PRCSTRT 77950000, 4194304, 0.027172 PRCENTRY2 yfft_r4dwpn_4M_ac_14_4, 9577984 PRCENTRY2 yfft_r4dwpn_4M_ac_14_2, 9577984 PRCENTRY2 yfft_r4dwpn_4M_ac_14_1, 9577984 PRCENTRY2 yfft_r4dwpn_4M_ac_13_4, 5068288 PRCENTRY2 yfft_r4dwpn_4M_ac_13_2, 5068288, I7 + FMA3_64 PRCENTRY2 yfft_r4dwpn_4M_ac_13_1, 5068288 PRCENTRY2 yfft_r4dwpn_4M_ac_12_4, 3998720 PRCENTRY2 yfft_r4dwpn_4M_ac_12_2, 3998720 PRCENTRY2 yfft_r4dwpn_4M_ac_12_1, 3998720 DD 0 Last fiddled with by Dubslow on 20160112 at 08:07 

20160112, 08:18  #114 
∂^{2}ω=0
Sep 2002
República de California
3×5^{3}×31 Posts 
That's the approximate averageratio as I recall it from waybackwhen ... of course new data help us continue to refine it.
Perhaps someone with a handydandy stats bestfit suite can input the known Mprime exponents and compute the bestfit params for a Poisson distribution, and  if possible  'goodness of fit' to the given distribution. 
20160112, 08:23  #115  
Jun 2003
4913_{10} Posts 
Quote:
If 77990000 is the maximum for 4096, then 77990000 * 4480/4096 = 85301562.5 would be the maximum for 4480 (with some reduction due to fewer bits/limb). 

20160112, 08:31  #116 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
1C35_{16} Posts 
Last fiddled with by Dubslow on 20160112 at 08:33 
20160112, 10:55  #117 
"David"
Jul 2015
Ohio
1000000101_{2} Posts 
The Xeon run with a larger FFT and a separate CUDA run also came up positive. I think we have a winner here.
The clLucas run and mLucas runs are both on track to back those up right now. 
20160112, 10:59  #118 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
22255_{8} Posts 
some statistics for the weary eyes
If we take the first 40 Mprimes and do a linear regression of log_{2} log_{2} M_{n} ~ n, then the 95% confidence interval for the slope's estimate is (0.557, 0.587) and both Wagstaff's and Eberhart's conjectured slopes are within this CI.
Recall that Wagstaff's , while Eberhart's = log_{2} 3/2 = 0.5849625... If we take the first 48 known Mprimes, then the 95% confidence interval for the slope's estimate is (0.5366, 0.5659) and Wagstaff's is in 95% CI, but Eberhart's is not (in other words, Eberhart's, of "KY", conjecture can be rejected at 95% confidence level). If we take the first 49 known Mprimes, then the confidence interval slides slightly lower still, but Wagstaff's is still in the 95% CI, and Eberhart's can be rejected with slighly higher confidence level. (Note that if there exist "missed" Mprimes, the slope will be lower still.) The elementary implementation in R (following B.Caffo's class notation, if someone wants to check): Code:
x < 1:48 y < c(1,1.584962501,2.321928095,2.807354922,3.700439718,4.087462841,4.247927513,4.95419631,5.930737338,6.475733431,6.741466986,6.988684687,9.025139562,9.245552706,10.32080055,11.10525378,11.15545073,11.65150022,12.05426514,12.11080953,13.24213206,13.27917527,13.4528847,14.28316072,14.4054739,14.50239674,15.44142045,16.39611974,16.75372601,17.01071385,17.72127946,19.52962691,19.71302565,20.2624562,20.4152105,21.50505023,21.52677478,22.73326384,23.68291627,24.32361192,24.51872848,24.63006217,24.85768459,24.95760092,25.14711776,25.3458327,25.36160654,25.78669022) fit < lm(y ~ x) sumCoef < summary(fit)$coefficients sumCoef[2,1] + c(1, 1) * qt(.975, df = fit$df) * sumCoef[2, 2] [1] 0.5365694 0.5658668 > summary(fit) Call: lm(formula = y ~ x) Residuals: Min 1Q Median 3Q Max 1.71476 0.45148 0.07631 0.55816 1.24279 Coefficients: Estimate Std. Error t value Pr(>t) (Intercept) 1.042977 0.204827 5.092 6.45e06 *** x 0.551218 0.007277 75.743 < 2e16 ***  Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.6985 on 46 degrees of freedom Multiple Rsquared: 0.992, Adjusted Rsquared: 0.9919 Fstatistic: 5737 on 1 and 46 DF, pvalue: < 2.2e16 
20160112, 11:47  #119  
Jun 2003
17^{3} Posts 
Quote:


20160112, 12:35  #120 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
5,857 Posts 
Code:
> fit < lm(y  0.5849625*x ~ x) > summary(fit) Call:lm(formula = y  0.5849625 * x ~ x) Residuals: Min 1Q Median 3Q Max 1.71476 0.45148 0.07631 0.55816 1.24279 Coefficients: Estimate Std. Error t value Pr(>t) (Intercept) 1.042977 0.204827 5.092 6.45e06 *** x 0.033744 0.007277 4.637 2.94e05 *** Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.6985 on 46 degrees of freedom Multiple Rsquared: 0.3185, Adjusted Rsquared: 0.3037 Fstatistic: 21.5 on 1 and 46 DF, pvalue: 2.94e05 
20160112, 13:06  #121  
"Åke Tilander"
Apr 2011
Sandviken, Sweden
1066_{8} Posts 
Quote:


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