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RogerVolunteer moderator Project administrator Volunteer developer Volunteer tester Project scientist
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Joined: 27 Nov 11 Posts: 1112 ID: 120786 Credit: 261,530,863 RAC: 0

For all the remaining TRP k's I calculated their Riesel weight and the probability of there being a prime from their leading edge (~6.05M) to 10M.
k ; w ; Chance to 10M
2293 ; 0.1181815794 ; 8.56%
9221 ; 0.2101005857 ; 15.23%
23669 ; 0.090206229 ; 6.53%
31859 ; 0.097628261 ; 7.07%
38473 ; 0.059947178 ; 4.34%
40597 ; 0.151866184 ; 11.00%
46663 ; 0.065656433 ; 4.76%
67117 ; 0.111330473 ; 8.07%
74699 ; 0.050812369 ; 3.68%
81041 ; 0.065656433 ; 4.76%
93839 ; 0.160430066 ; 11.63%
97139 ; 0.078216794 ; 5.67%
107347 ; 0.11418510 ; 8.27%
121889 ; 0.08506790 ; 6.16%
129007 ; 0.05994717 ; 4.34%
143047 ; 0.05138329 ; 3.72%
146561 ; 0.10961769 ; 7.94%
161669 ; 0.03368460 ; 2.44%
192971 ; 0.03653923 ; 2.64%
206039 ; 0.07992957 ; 5.79%
206231 ; 0.07364939 ; 5.33%
215443 ; 0.11589787 ; 8.40%
226153 ; 0.08449697 ; 6.12%
234343 ; 0.08963530 ; 6.49%
245561 ; 0.02740442 ; 1.98%
250027 ; 0.06736920 ; 4.88%
273809 ; 0.11304324 ; 8.19%
304207 ; 0.03653923 ; 2.64%
315929 ; 0.11703972 ; 8.48%
319511 ; 0.15985914 ; 11.58%
324011 ; 0.08963530 ; 6.49%
325123 ; 0.07307846 ; 5.29%
327671 ; 0.05937625 ; 4.30%
336839 ; 0.22323187 ; 16.18%
342847 ; 0.01998239 ; already at 10M
344759 ; 0.09648641 ; 6.99%
362609 ; 0.15414988 ; 11.17%
363343 ; 0.09020622 ; 6.53%
364903 ; 0.15357896 ; 11.13%
365159 ; 0.14273137 ; 10.34%
368411 ; 0.15414988 ; 11.17%
371893 ; 0.09534455 ; 6.91%
384539 ; 0.10733399 ; 7.78%
386801 ; 0.06908198 ; 5.00%
397027 ; 0.04852866 ; 3.51%
398023 ; 0.07307846 ; 5.29%
402539 ; 0.13416749 ; 9.72%
409753 ; 0.10048288 ; 7.28%
444637 ; 0.02169516 ; already at 10M
470173 ; 0.09134808 ; 6.62%
474491 ; 0.14786970 ; 10.72%
477583 ; 0.03311367 ; 2.40%
485557 ; 0.05252514 ; 3.80%
494743 ; 0.05366699 ; 3.89%
502573 ; 0.06337273 ; 4.59%
According to this we will, on average, find primes for 3.6 k's below n=10M.
342847 and 444637 have already been pushed to 10M, presumably because they have the lowest number of tests remaining after sieving. However they also have the lowest chance of finding a prime.
9221 and 336839 have the highest chance of finding a prime. Does anyone else feel like we should be attacking those k's first?
Note that my chance calculation is based on the Prime Number theory:
http://www.primegrid.com/forum_thread.php?id=4935&nowrap=true#64017
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I think it would be interesting to see which k's you would have preferred if you would have calculated the probabilities of all of the original 64 candidates in the nrange of 3M to 10M. If your prediction would have resulted in more hits than falses with respect to the nine primes we have found so far it could be worthwile to push two of the k's forward at higher speed. But I remember that I have checked how many tests were avoided by the first finds and it were not the biggest numbers of tests for the deleted k so I guess your method has a good chance to fail. Anyway, the target of this TRP excercise is to prove that a prime exists for every remaining k. Therefore it does not really matter when they are found. But yes, it is time for another one as there was for so long no hit... 


RogerVolunteer moderator Project administrator Volunteer developer Volunteer tester Project scientist
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Joined: 27 Nov 11 Posts: 1112 ID: 120786 Credit: 261,530,863 RAC: 0

For the TRP found k of the original 64:
k ; w ; rank(w) of 64 ; n found
65531 ; 0.1130432499 ; 18 ; 3.6M
123547 ; 0.062801805 ; 49 ; 4.2M
141941 ; 0.246068892 ; 01 ; 4.3M
162941 ; 0.073078464 ; 41 ; 5.0M
191249 ; 0.104479367 ; 23 ; 3.4M
252191 ; 0.085638825 ; 33 ; 5.5M
353159 ; 0.079358645 ; 38 ; 4.3M
415267 ; 0.171277651 ; 04 ; 4.2M
428639 ; 0.085638827 ; 34 ; 3.5M
Average rank = 26.7 => 41.8% of range
As a predictor it's not fabulous, but then it's still better than a random k (50% of range).
The first expected prime for k with w below 0.05 is really scary, like n in the billions, and it goes up super fast as w gets smaller. 



Interesting, your first place guess was in the list of found primes.
My curiosity lets me ask one more question: How many primes would you have anticipated at PrimeGrid's start of the TRPproject for the range of n=3M to n=6M? 


RogerVolunteer moderator Project administrator Volunteer developer Volunteer tester Project scientist
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Joined: 27 Nov 11 Posts: 1112 ID: 120786 Credit: 261,530,863 RAC: 0

For the original 64 k's would have expected to find, on average, 6.1 primes in the range 3M<n<6M.
We found 9 within that range.
The probability distribution would be some kind of bell curve and we were on the luckier end. 



If only one k would be pushed forward I would prefer 9221 as those tests run significantly faster on my computers. 



If only one k would be pushed forward I would prefer 9221 as those tests run significantly faster on my computers.
n=6.1M (~6100000 bits)
k=2293 AVX FFT length 448K Time per bit: 1.961 ms.
k=9221 AVX FFT length 480K Time per bit: 2.127 ms.
k=23669 AVX FFT length 512K Time per bit: 2.195 ms.
...
k=107347 AVX FFT length 560K Time per bit: 2.506 ms.
...
k=502573 AVX FFT length 640K Time per bit: 2.894 ms. 

