PrimeGrid
Please visit donation page to help the project cover running costs for this month

Toggle Menu

Join PrimeGrid

Returning Participants

Community

Leader Boards

Results

Other

drummers-lowrise

Advanced search

Message boards : Sierpinski/Riesel Base 5 Problem : Chance of SR5 Prime

Author Message
Profile Roger
Volunteer moderator
Project administrator
Volunteer developer
Volunteer tester
Project scientist
Avatar
Send message
Joined: 27 Nov 11
Posts: 1112
ID: 120786
Credit: 261,594,669
RAC: 13,550
Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,012,522)Cullen LLR Amethyst: Earned 1,000,000 credits (1,359,862)ESP LLR Ruby: Earned 2,000,000 credits (2,232,391)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,617,785)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,780,064)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (2,139,392)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Amethyst: Earned 1,000,000 credits (1,311,937)321 Sieve Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,049,697)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,295,860)GFN Emerald: Earned 50,000,000 credits (56,560,659)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 66471 - Posted: 9 Jun 2013 | 2:06:44 UTC

For all the SR5 k's I calculated their Nash weight and the probability of there being a prime from the PRPNet leading edge 938,000 to 1M and for BOINC from 1M to 2M.

form ; Nash ; w ; Chance to 1M ; Chance to 2M 100186*5^n-1 ; 430 ; 0.2454979669 ; 0.96% ; 10.57% 102818*5^n-1 ; 396 ; 0.2260864998 ; 0.89% ; 9.74% 102952*5^n-1 ; 244 ; 0.1393058231 ; 0.54% ; 6.00% 102976*5^n-1 ; 421 ; 0.2403596374 104944*5^n-1 ; 679 ; 0.3876584176 ; 1.52% ; 16.70% 105464*5^n+1 ; 566 ; 0.3231438355 ; 1.27% ; 13.92% 10918*5^n+1 ; 305 ; 0.1741322789 ; 0.68% ; 7.50% 109208*5^n+1 ; 225 ; 0.1284582385 ; 0.51% ; 5.53% 109238*5^n-1 ; 202 ; 0.1153269519 ; 0.45% ; 4.97% 109838*5^n-1 ; 155 ; 0.0884934532 ; 0.34% ; 3.81% 109862*5^n-1 ; 261 ; 0.1490115567 ; 0.58% ; 6.42% 110488*5^n+1 ; 565 ; 0.32257291 114986*5^n-1 ; 259 ; 0.1478697057 ; 0.58% ; 0.47% chance to 1,052,966 11812*5^n-1 ; 198 ; 0.1130432499 118568*5^n+1 ; 382 ; 0.2180935427 ; 0.86% ; 9.39% 119878*5^n-1 ; 291 ; 0.1661393218 ; 0.65% ; 0.20% chance to 1,019,645 126134*5^n+1 ; 175 ; 0.0999119633 ; 0.39% ; 4.30% 127174*5^n-1 ; 413 ; 0.2357922334 ; 0.92% ; 10.15% 130484*5^n-1 ; 464 ; 0.2649094341 ; 1.03% ; 11.41% 131848*5^n-1 ; 413 ; 0.2357922334 ; 0.92% ; 10.15% 133778*5^n+1 ; 477 ; 0.2723314656 ; 1.07% ; 11.73% 134266*5^n-1 ; 393 ; 0.2243737233 ; 0.88% ; 9.66% 136804*5^n-1 ; 663 ; 0.3785236095 ; 1.48% ; 16.30% 138172*5^n-1 ; 302 ; 0.1724195024 ; 0.68% ; 7.43% 138514*5^n+1 ; 250 ; 0.1427313761 ; 0.56% ; 6.15% 139196*5^n+1 ; 274 ; 0.1564335882 ; 0.61% ; 6.74% 1396*5^n-1 ; 320 ; 0.1826961614 ; 0.72% ; 7.87% 143632*5^n-1 ; 503 ; 0.2871755288 ; 1.12% ; 12.37% 144052*5^n+1 ; 253 ; 0.1444441526 ; 0.57% ; 6.22% 145462*5^n-1 ; 428 ; 0.2443561159 ; 0.96% ; 10.52% 145484*5^n-1 ; 366 ; 0.2089587346 ; 0.82% ; 9.00% 146264*5^n-1 ; 1118 ; 0.638294714 ; 2.51% ; 27.49% 146756*5^n-1 ; 722 ; 0.4122082142 ; 1.62% ; 17.75% 147844*5^n-1 ; 436 ; 0.2489235200 ; 0.98% ; 10.72% 150344*5^n-1 ; 420 ; 0.2397887119 ; 0.94% ; 10.33% 151042*5^n-1 ; 191 ; 0.1090467714 ; 0.43% ; 4.70% 152428*5^n-1 ; 462 ; 0.2637675831 ; 1.03% ; 11.36% 152588*5^n+1 ; 537 ; 0.3065869959 ; 1.20% ; 13.20% 154222*5^n+1 ; 956 ; 0.5458047823 ; 2.14% ; 23.51% 154844*5^n-1 ; 576 ; 0.3288530906 ; 1.29% ; 14.16% 159388*5^n-1 ; 478 ; 0.2729023912 ; 1.07% ; 11.75% 162434*5^n-1 ; 454 ; 0.259200179 162668*5^n-1 ; 494 ; 0.2820371992 164852*5^n-1 ; 593 ; 0.3385588242 ; 1.33% ; 14.58% 170386*5^n-1 ; 585 ; 0.3339914201 ; 1.31% ; 14.38% 170908*5^n-1 ; 435 ; 0.2483525945 ; 0.98% ; 10.70% 171362*5^n-1 ; 447 ; 0.2552037005 ; 1.00% ; 10.99% 17152*5^n-1 ; 756 ; 0.4316196814 ; 1.69% ; 18.59% 173198*5^n-1 ; 394 ; 0.2249446488 ; 0.88% ; 9.69% 174344*5^n-1 ; 494 ; 0.2820371992 175124*5^n-1 ; 661 ; 0.3773817585 ; 1.48% ; 16.25% 177742*5^n-1 ; 1027 ; 0.586340493 ; 2.30% ; 25.25% 178658*5^n-1 ; 496 ; 0.2831790502 ; 1.11% ; 12.20% 180062*5^n-1 ; 718 ; 0.4099245122 ; 1.61% ; 17.65% 182398*5^n-1 ; 289 ; 0.1649974708 ; 0.65% ; 7.11% 18656*5^n-1 ; 279 ; 0.1592882158 187916*5^n-1 ; 126 ; 0.0719366136 ; 0.28% ; 3.10% 189766*5^n-1 ; 507 ; 0.2894592308 ; 1.14% ; 12.47% 190334*5^n-1 ; 281 ; 0.1604300668 ; 0.63% ; 6.91% 194368*5^n-1 ; 488 ; 0.2786116462 ; 1.09% ; 12.00% 195872*5^n-1 ; 753 ; 0.4299069049 ; 1.69% ; 18.51% 201778*5^n-1 ; 657 ; 0.3750980565 ; 1.47% ; 16.15% 204394*5^n-1 ; 182 ; 0.1039084418 ; 0.41% ; 4.48% 206894*5^n-1 ; 291 ; 0.1661393218 ; 0.65% ; 7.16% 207394*5^n-1 ; 266 ; 0.1518661842 ; 0.60% ; 6.54% 207494*5^n-1 ; 296 ; 0.1689939493 ; 0.66% ; 7.28% 213988*5^n-1 ; 393 ; 0.2243737233 ; 0.88% ; 9.66% 22478*5^n-1 ; 717 ; 0.4093535867 ; 1.61% ; 17.63% 22934*5^n-1 ; 420 ; 0.2397887119 ; 0.94% ; 10.33% 231674*5^n-1 ; 255 ; 0.1455860036 ; 0.57% ; 6.27% 238694*5^n-1 ; 194 ; 0.1107595479 ; 0.43% ; 4.77% 23906*5^n-1 ; 218 ; 0.1244617600 ; 0.49% ; 5.36% 239062*5^n-1 ; 294 ; 0.1678520983 ; 0.66% ; 7.23% 239342*5^n-1 ; 399 ; 0.2277992763 ; 0.89% ; 9.81% 24032*5^n+1 ; 526 ; 0.3003068154 ; 1.18% ; 12.93% 243686*5^n-1 ; 368 ; 0.2101005857 ; 0.82% ; 9.05% 243944*5^n-1 ; 496 ; 0.2831790502 ; 1.11% ; 12.20% 245114*5^n-1 ; 349 ; 0.1992530011 ; 0.78% ; 8.58% 246238*5^n-1 ; 251 ; 0.1433023016 ; 0.56% ; 6.17% 248546*5^n-1 ; 571 ; 0.3259984631 ; 1.28% ; 14.04% 2488*5^n-1 ; 563 ; 0.321431059 256612*5^n-1 ; 234 ; 0.1335965681 ; 0.52% ; 5.75% 259072*5^n-1 ; 586 ; 0.3345623456 ; 1.31% ; 14.41% 262172*5^n-1 ; 272 ; 0.1552917372 26222*5^n-1 ; 589 ; 0.3362751221 ; 1.32% ; 14.48% 265702*5^n-1 ; 228 ; 0.1301710150 ; 0.51% ; 5.61% 267298*5^n-1 ; 333 ; 0.1901181930 ; 0.74% ; 8.19% 26798*5^n+1 ; 413 ; 0.2357922334 ; 0.93% ; 10.15% 268514*5^n-1 ; 425 ; 0.2426433394 ; 0.95% ; 10.45% 271162*5^n-1 ; 236 ; 0.1347384191 ; 0.52% ; 5.80% 273662*5^n-1 ; 331 ; 0.1889763420 ; 0.74% ; 8.14% 27994*5^n-1 ; 635 ; 0.3625376954 285598*5^n-1 ; 840 ; 0.4795774238 ; 1.88% ; 20.65% 285728*5^n-1 ; 81 ;: 0.0462449659 ; 0.18% ; 1.99% 289184*5^n-1 ; 582 ; 0.3322786436 296024*5^n-1 ; 210 ; 0.1198943559 ; 0.47% ; 5.16% 298442*5^n-1 ; 310 ; 0.1769869064 ; 0.69% ; 7.62% 29914*5^n+1 ; 353 ; 0.2015367031 ; 0.79% ; 8.68% 301562*5^n-1 ; 272 ; 0.1552917372 ; 0.61% ; 6.69% 304004*5^n-1 ; 509 ; 0.2906010818 ; 1.14% ; 12.52% 305716*5^n-1 ; 291 ; 0.1661393218 ; 0.65% ; 7.16% 306398*5^n-1 ; 323 ; 0.1844089380 ; 0.72% ; 7.94% 313126*5^n-1 ; 895 ; 0.5109783265 ; 2.01% ; 22.01% 316594*5^n-1 ; 353 ; 0.2015367031 31712*5^n+1 ; 374 ; 0.2135261387 ; 0.84% ; 9.20% 318278*5^n-1 ; 193 ; 0.1101886224 ; 0.43% ; 4.75% 322498*5^n-1 ; 1150 ; 0.656564330 ; 2.58% ; 28.28% 325918*5^n-1 ; 577 ; 0.3294240161 ; 1.29% ; 14.19% 325922*5^n-1 ; 493 ; 0.2814662737 ; 1.10% ; 12.12% 326834*5^n-1 ; 305 ; 0.1741322789 ; 0.68% ; 7.50% 327926*5^n-1 ; 409 ; 0.2335085313 ; 0.92% ; 10.06% 329584*5^n-1 ; 148 ; 0.0844969747 ; 0.33% ; 3.64% 330286*5^n-1 ; 608 ; 0.3471227067 ; 1.36% ; 14.95% 331882*5^n-1 ; 434 ; 0.247781669 335414*5^n-1 ; 377 ; 0.2152389152 ; 0.84% ; 9.27% 338866*5^n-1 ; 191 ; 0.1090467714 ; 0.43% ; 4.70% 338948*5^n-1 ; 276 ; 0.1575754392 340168*5^n-1 ; 435 ; 0.2483525945 35248*5^n-1 ; 113 ; 0.0645145820 ; 0.25% ; 2.78% 35816*5^n-1 ; 559 ; 0.3191473570 ; 1.25% ; 13.74% 3622*5^n-1 ; 526 ; 0.3003068154 ; 1.17% ; 12.93% 36412*5^n+1 ; 514 ; 0.2934557093 ; 1.15% ; 12.64% 37292*5^n+1 ; 291 ; 0.1661393218 ; 0.65% ; 7.16% 41738*5^n+1 ; 652 ; 0.3722434289 ; 1.46% ; 16.03% 44348*5^n+1 ; 556 ; 0.3174345805 ; 1.24% ; 13.67% 44738*5^n+1 ; 751 ; 0.4287650539 ; 1.68% ; 18.47% 45748*5^n+1 ; 557 ; 0.3180055060 ; 1.25% ; 13.70% 48764*5^n-1 ; 212 ; 0.121036207 4906*5^n-1 ; 478 ; 0.2729023912 ; 1.07% ; 11.75% 49568*5^n-1 ; 503 ; 0.2871755288 51208*5^n+1 ; 490 ; 0.2797534972 ; 1.10% ; 12.05% 52922*5^n-1 ; 352 ; 0.2009657776 ; 0.79% ; 8.66% 53546*5^n-1 ; 650 ; 0.3711015779 ; 1.46% ; 15.98% 5374*5^n-1 ; 673 ; 0.3842328645 55154*5^n+1 ; 518 ; 0.2957394113 ; 1.16% ; 12.74% 57406*5^n-1 ; 411 ; 0.2346503823 58642*5^n+1 ; 333 ; 0.1901181930 ; 0.75% ; 8.19% 59912*5^n+1 ; 1065 ; 0.608035662 ; 2.38% ; 26.19% 60394*5^n+1 ; 402 ; 0.2295120528 ; 0.90% ; 9.88% 62698*5^n+1 ; 753 ; 0.4299069049 ; 1.69% ; 18.51% 63838*5^n-1 ; 505 ; 0.2883173798 ; 1.13% ; 12.42% 64258*5^n+1 ; 435 ; 0.2483525945 ; 0.97% ; 10.70% 6436*5^n+1 ; 571 ; 0.3259984631 ; 1.28% ; 14.04% 64598*5^n-1 ; 384 ; 0.2192353937 ; 0.86% ; 9.44% 66916*5^n-1 ; 515 ; 0.2940266348 ; 1.15% ; 12.66% 67612*5^n+1 ; 464 ; 0.2649094341 ; 1.04% ; 11.41% 67748*5^n+1 ; 331 ; 0.1889763420 ; 0.74% ; 8.14% 68132*5^n-1 ; 143 ; 0.0816423471 ; 0.32% ; 3.52% 70082*5^n-1 ; 752 ; 0.4293359794 71146*5^n-1 ; 397 ; 0.2266574253 ; 0.89% ; 9.76% 71492*5^n+1 ; 221 ; 0.1261745365 ; 0.50% ; 5.43% 72532*5^n-1 ; 383 ; 0.2186644682 74632*5^n+1 ; 565 ; 0.3225729100 ; 1.27% ; 13.89% 7528*5^n+1 ; 313 ; 0.1786996829 ; 0.70% ; 7.70% 76354*5^n-1 ; 168 ; 0.0959154848 ; 0.37% ; 4.13% 76724*5^n+1 ; 438 ; 0.2500653710 ; 0.98% ; 10.77% 77072*5^n+1 ; 159 ; 0.0907771552 ; 0.36% ; 3.91% 81134*5^n-1 ; 552 ; 0.3151508785 ; 1.23% ; 13.57% 81556*5^n+1 ; 527 ; 0.3008777409 ; 1.18% ; 12.96% 83936*5^n+1 ; 428 ; 0.2443561159 ; 0.96% ; 10.52% 84284*5^n+1 ; 359 ; 0.2049622561 ; 0.80% ; 8.83% 84466*5^n-1 ; 924 ; 0.5275351662 ; 2.07% ; 22.72% 88444*5^n-1 ; 704 ; 0.4019315552 ; 1.58% ; 17.31% 90056*5^n+1 ; 398 ; 0.2272283508 ; 0.89% ; 9.79% 92158*5^n+1 ; 203 ; 0.1158978774 ; 0.45% ; 4.99% 92182*5^n+1 ; 354 ; 0.2021076286 ; 0.80% ; 8.70% 92906*5^n+1 ; 347 ; 0.1981111501 ; 0.77% ; 8.53% 92936*5^n-1 ; 740 ; 0.4224848733 ; 1.66% ; 18.20% 93484*5^n+1 ; 655 ; 0.3739562054 ; 1.47% ; 16.11% 97366*5^n-1 ; 676 ; 0.3859456410 ; 1.52% ; 16.62% 97768*5^n-1 ; 320 ; 0.1826961614 ; 0.72% ; 7.87%

According to this we will, on average, find primes for 1.5 k's in PRPNet to 1M and 16.3 k's in BOINC to 2M.
Those k's with no % chance are ones where primes have already been found in PRPNet.

The tools I used previously only covers base 2. You can use srsieve to find weights for any base, for example:
srsieve -n 100001 -N 110000 -P 511 "97768*5^n-1"

Reference: http://www.mersenneforum.org/showthread.php?t=14303
Software: http://www.mersenneforum.org/showthread.php?t=9742

The number of primes, or fraction thereof, expected in a given range n = A to B for a given k, k*b^n+/-1 is:
w * (log(log k + B*log b) - log(log k + A*log b))/log b


Note that odd k's have all terms divisible by 2, that's why we only have even k's in SR5.
I also created a batch file that can calulate weights for k's over a range:
set /a num=1 del output.txt :next set /a kvalue=%num%+%num% REM echo Finding Nash weight for %kvalue%*5^n-1: srsieve-x86_64-windows.exe -q -n 100001 -N 110000 -P 511 "%kvalue%*5^n-1" >> output.txt findstr /R /N "^" srsieve.out | find /C ":" > tmpfile.txt set /p weight= < tmpfile.txt del tmpfile.txt set /a weight=%weight%-2 echo Nash weight for %kvalue%*5^^n-1: %weight% >> output.txt set /a num=%num%+1 if %num% LEQ %1 goto next


First 500 k*5^n-1 weights average: 2204
First 500 k*5^n+1 weights average: 2235
Base 2 weights average: 1751, so base 5 should be easier overall
____________

Profile Roger
Volunteer moderator
Project administrator
Volunteer developer
Volunteer tester
Project scientist
Avatar
Send message
Joined: 27 Nov 11
Posts: 1112
ID: 120786
Credit: 261,594,669
RAC: 13,550
Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,012,522)Cullen LLR Amethyst: Earned 1,000,000 credits (1,359,862)ESP LLR Ruby: Earned 2,000,000 credits (2,232,391)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,617,785)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,780,064)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (2,139,392)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Amethyst: Earned 1,000,000 credits (1,311,937)321 Sieve Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,049,697)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,295,860)GFN Emerald: Earned 50,000,000 credits (56,560,659)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 73431 - Posted: 12 Feb 2014 | 14:42:43 UTC

My old chance of prime equation used weight w as the Nash weight divided by 1751.542 giving a coefficient of 1.00 for the average k of base 2.
The trouble was it assumed base 2 had the same density of primes as a randomly chosen set of odd numbers of the same magnitude.

I started from the basics. To find the weight of the term b*k*n-1 I used Prime Number Theory which says that the chance of a random integer x being prime is about 1/log x
For x = b*k*n-1, chance is about 1/log (b*k*n-1)

To find the probability for a fixed k over a given range we integrate from n = A to n = B.
Integrating 1/log (b*k*n-1) gives li(b*k*n-1)/(k*b), where li() is the logarithmic integral.
So the number of primes, or fraction thereof, expected in a given range n = A to B for b*k*n-1 is:
(li(b*k*B-1)-li(b*k*A-1))/(k*b)
To calculate our weight we're going to sieve test A=100001 and B=110000:
w = k*b*P1e6 / (li(110,000*k*b)-li(100,001*k*b))

Where P1e6 is the number of candidates remaining after testing the range n=100001 to 110000 for factors up to 1 million.
> srsieve -n 100001 -N 110000 -P 1e6 "k*b^n+/-1"
It is similar to the Nash weight but sieved to a deeper depth to be more accurate and not skewed toward small factors.

li(X) is the logarithmic integral.
li(x) ∼ x/ln(x) + x/ln(x)² + 2x/ln(x)³ + 6x/ln(x)⁴ + 24x/ln(x)⁵ + ...

The weight is fixed for a fixed k. To use it we plug it into the same formula:
#Primes = w * (ln(ln k + B*ln b) - ln(ln k + A*ln b))/ln b

I've used this improved weight to calculate the chance of primes for the SR5 project from n=1M to 2M: http://rogerkarpin.wix.com/thecount123ks#!sr5/cy5b
Chances are improved compared to the old weight formula. If we sum the chances we're now expecting 31 primes in the n=1M to 2M range.

I checked the values coming out of my formula for a number of bases and their about 98% correlated with the method they use on CRUS.
Advantage of my method is you don't need the sieve results to calculate the chance of primes.

Want to know more? Yves Gallot did a paper on the subject: http://yves.gallot.pagesperso-orange.fr/papers/weight.pdf

Profile Michael GoetzProject donor
Volunteer moderator
Project administrator
Project scientist
Avatar
Send message
Joined: 21 Jan 10
Posts: 12673
ID: 53948
Credit: 184,533,682
RAC: 116,079
The "Shut up already!" badge:  This loud mouth has mansplained on the forums over 10 thousand times!  Sheesh!!!Discovered the World's First GFN-19 prime!!!Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,063,182)Cullen LLR Ruby: Earned 2,000,000 credits (2,005,249)ESP LLR Ruby: Earned 2,000,000 credits (4,146,403)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,145,754)PPS LLR Ruby: Earned 2,000,000 credits (2,773,744)PSP LLR Ruby: Earned 2,000,000 credits (2,632,269)SoB LLR Sapphire: Earned 20,000,000 credits (34,158,496)SR5 LLR Turquoise: Earned 5,000,000 credits (8,293,415)SGS LLR Ruby: Earned 2,000,000 credits (2,012,222)TRP LLR Ruby: Earned 2,000,000 credits (2,737,347)Woodall LLR Ruby: Earned 2,000,000 credits (2,195,123)321 Sieve Turquoise: Earned 5,000,000 credits (5,046,112)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,059,304)PPS Sieve Sapphire: Earned 20,000,000 credits (20,110,788)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,035,522)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,051,121)AP 26/27 Turquoise: Earned 5,000,000 credits (7,090,096)GFN Emerald: Earned 50,000,000 credits (64,594,991)PSA Jade: Earned 10,000,000 credits (10,212,287)
Message 73433 - Posted: 12 Feb 2014 | 15:09:24 UTC - in response to Message 73431.

If we sum the chances we're now expecting 31 primes in the n=1M to 2M range.


We found 17 primes between n=1M and n=1.5M, which correlates very closely with your result.

One thing I think you left out of your calculations, however, is that unlike, say, the PPS Proth search, every time we find a prime we stop searching that k. Therefore, as primes are found, the odds of finding more primes within a specific n range will drop because we're searching fewer numbers in that range. There are likely primes we're "missing" (because we're not interested in finding them) at higher n's for k's we've already eliminated.

As more and more k's are eliminated this will become a larger factor. With one k out of 100 k's eliminated, the number of tests drops by ~1%. When the next to last k is eliminated, the number of tests drops by ~50%.

____________
Please do not PM me with support questions. Ask on the forums instead. Thank you!

My lucky number is 75898524288+1

Profile Roger
Volunteer moderator
Project administrator
Volunteer developer
Volunteer tester
Project scientist
Avatar
Send message
Joined: 27 Nov 11
Posts: 1112
ID: 120786
Credit: 261,594,669
RAC: 13,550
Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,012,522)Cullen LLR Amethyst: Earned 1,000,000 credits (1,359,862)ESP LLR Ruby: Earned 2,000,000 credits (2,232,391)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,617,785)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,780,064)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (2,139,392)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Amethyst: Earned 1,000,000 credits (1,311,937)321 Sieve Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,049,697)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,295,860)GFN Emerald: Earned 50,000,000 credits (56,560,659)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 73462 - Posted: 13 Feb 2014 | 14:22:45 UTC

31.2 is the average amount that will be found. We could find more, we could find less.
Agreed that we could find more than 1 prime for a k if we tested all 1-2M regardless of prime being found. 31.2 is based on continued testing.
Realise that we will find more in the 1-1.5 range than 1.5-2M.
Plugging the numbers in and assuming and we keep testing all the 150 k's regardless of prime find we should expect:
18.2 primes in the range 1-1.5M on average;
12.9 in the 1.5-2M range;
18.2 in the 2-3M range;
12.9 in the 3-4M range;
...

Now if you reduce the fraction of the k's by stopping testing we should expect:
18.2 primes in the range 1-1.5M on average; 131.8 k's left
12.9*131.8/150 = 11.3 in the 1.5-2M range; 120.5k's left
18.2*120.5/150 = 14.6 in the 2-3M range; 105.9k's left
12.9*105.9/150 = 9.1 in the 3-4M range; 96.8k's left
...
Simplistic but you get the idea.

Profile Roger
Volunteer moderator
Project administrator
Volunteer developer
Volunteer tester
Project scientist
Avatar
Send message
Joined: 27 Nov 11
Posts: 1112
ID: 120786
Credit: 261,594,669
RAC: 13,550
Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,012,522)Cullen LLR Amethyst: Earned 1,000,000 credits (1,359,862)ESP LLR Ruby: Earned 2,000,000 credits (2,232,391)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,617,785)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,780,064)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (2,139,392)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Amethyst: Earned 1,000,000 credits (1,311,937)321 Sieve Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,049,697)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,295,860)GFN Emerald: Earned 50,000,000 credits (56,560,659)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 73529 - Posted: 15 Feb 2014 | 23:57:00 UTC

Removing k's at 0.5M/1M boundary is arbitrary. In reality a k is removed once a prime is found.
So I tested a range size until average chance of prime = 1.00, then removed a k and repeated.
I removed k's starting from the top of the list because I want a method that assumes no prior knowledge of the results.
Using this I found:
17 primes in the 1-1.5M range;
11 in the 1.5-2M range;
14 in the 2-3M range; and
9 in the 3-4M range.

Happy Crunching!

KEPProject donor
Send message
Joined: 10 Aug 05
Posts: 258
ID: 110
Credit: 8,297,330
RAC: 40,690
Found 1 prime in the 2019 Tour de PrimesESP LLR Amethyst: Earned 1,000,000 credits (1,571,826)PPS LLR Amethyst: Earned 1,000,000 credits (1,327,204)PSP LLR Silver: Earned 100,000 credits (273,295)SoB LLR Amethyst: Earned 1,000,000 credits (1,209,000)SR5 LLR Silver: Earned 100,000 credits (112,905)TRP LLR Amethyst: Earned 1,000,000 credits (1,370,887)321 Sieve Amethyst: Earned 1,000,000 credits (1,633,882)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (64,186)TRP Sieve (suspended) Silver: Earned 100,000 credits (259,649)PSA Silver: Earned 100,000 credits (456,059)
Message 73535 - Posted: 16 Feb 2014 | 13:46:35 UTC - in response to Message 73529.
Last modified: 16 Feb 2014 | 13:49:21 UTC

Removing k's at 0.5M/1M boundary is arbitrary. In reality a k is removed once a prime is found.
So I tested a range size until average chance of prime = 1.00, then removed a k and repeated.
I removed k's starting from the top of the list because I want a method that assumes no prior knowledge of the results.
Using this I found:
17 primes in the 1-1.5M range;
11 in the 1.5-2M range;
14 in the 2-3M range; and
9 in the 3-4M range.

Happy Crunching!


I can tell you, that using the percent of k's removed on both Sierpinski aswell as the Riesel side (in the n=750K to n=1.5M range), I came out with a total removal of ~26.x primed k's in the range from n=1.5M to n=3.0M and I can see that you have an expectancy of 25, so despite doing this independent of one another, we came back with very similar results :)

Take care

Kenneth

Message boards : Sierpinski/Riesel Base 5 Problem : Chance of SR5 Prime

[Return to PrimeGrid main page]
DNS Powered by DNSEXIT.COM
Copyright © 2005 - 2019 Rytis Slatkevičius (contact) and PrimeGrid community. Server load 0.77, 0.85, 0.96
Generated 19 Aug 2019 | 1:59:53 UTC