## PRP Records

### Probable Primes Top 10000

#### (295765 PRPs in the top)

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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See the Latest PRPs
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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 5001 2^416773-25 125462 Lelio R Paula 09/2015 5002 33889^5032+5032^33889 125449 Hans Havermann 03/2021 5003 (289511#+292834)/(2^3*146417) 125444 Makoto Morimoto 10/2017 5004 (2861^36481+1)/(2861^191+1) 125438 Martin Hopf 12/2023 5005 (11*2^416691+1)/43 125436 Lelio R Paula 05/2014 5006 (289511#+1896)/(2*3^3*79*780193*9911849) 125434 Makoto Morimoto 06/2019 5007 2^416641-2*416641+1 125422 Robert Price 05/2018 5008 33392^5697+5697^33392 125409 Hans Havermann 03/2021 5009 (21*2^416566-1)/17 125399 Lelio R Paula 05/2014 5010 2^416530+1870429 125389 Enzo Doria 05/2016 5011 (56*10^125385+691)/9 125386 Robert Price 05/2019 5012 27953^28198+28198^27953 125381 Norbert Schneider 01/2021 5013 31074^10837+10837^31074 125381 Hans Havermann 03/2021 5014 33745^5194+5194^33745 125380 Hans Havermann 03/2021 5015 2^416490+1875109 125376 Enzo Doria 09/2016 5016 28360^26331+26331^28360 125365 Hans Havermann 03/2021 5017 2^416416-114929 125354 Enzo Doria 05/2015 5018 25805^28412-28412^25805 125346 Frank Doornink 03/2024 5019 (77*10^125330-293)/9 125331 Robert Price 09/2019 5020 (172*10^125292-1)/9 125294 Serge Batalov 12/2014 5021 2^416134+1865899 125269 Enzo Doria 03/2016 5022 153^57337-152 125264 Norbert Schneider 12/2018 5023 (599*10^125224+13)/9 125226 Robert Price 02/2022 5024 (9*2^415992+1)/13560845 125220 Lelio R Paula 05/2014 5025 30054^14657+14657^30054 125207 Hans Havermann 03/2021 5026 (23^91943-1)/22 125201 Robert Price 01/2012 5027 2^415884-933075 125194 Paul Bourdelais 06/2021 5028 43125^27010-106 125185 Enzo Doria 08/2012 5029 (38*10^125166+349)/9 125167 Robert Price 10/2018 5030 10^125166-5001 125166 Robert Price 12/2021 5031 2^415765-112603 125158 Enzo Doria 06/2014 5032 8*10^125088-13 125089 Robert Price 08/2019 5033 (25*10^125076-13)/3 125077 Robert Price 09/2019 5034 (11*10^125054+73)/3 125055 Robert Price 08/2021 5035 (29*10^125021-113)/3 125022 Robert Price 10/2019 5036 2^415290-113591 125015 Enzo Doria 08/2014 5037 2^415276-460919 125011 Enzo Doria 06/2015 5038 2^415259+77243 125006 Enzo Doria 05/2016 5039 (67*10^124990+77)/9 124991 Robert Price 10/2021 5040 2^415144-3683 124971 Yves Minet 10/2011 5041 2^415092+111546435 124956 Paul Bourdelais 10/2021 5042 31936^8173+8173^31936 124946 Hans Havermann 03/2021 5043 27458^28145-28145^27458 124927 Frank Doornink 03/2024 5044 5^178715-4 124917 Tyler NeSmith 07/2021 5045 29767^15700+15700^29767 124900 Hans Havermann 03/2021 5046 (310^50131-1)/309 124892 Tom Wu 07/2024 5047 2^414874+79 124890 Lelio R Paula 01/2015 5048 25292^28361-28361^25292 124874 Frank Doornink 01/2024 5049 (2^414765+7)/1389 124854 Lelio R Paula 05/2014 5050 2^414618+79459 124813 Enzo Doria 06/2016 5051 (61*10^124809-1)/3 124811 Robert Price 01/2020 5052 (29*10^124765-71)/3 124766 Robert Price 07/2021 5053 2^414432-1846709 124757 Enzo Doria 07/2015 5054 2*10^124751-51 124752 Robert Price 04/2018 5055 (56*10^124735+367)/9 124736 Robert Price 06/2019 5056 27362^28111-28111^27362 124733 Frank Doornink 03/2024 5057 (13*2^414274-1)/153 124708 Lelio R Paula 05/2014 5058 (23*10^124690+37)/3 124691 Robert Price 02/2022 5059 56*10^124656-3 124658 Robert Price 03/2020 5060 (7*10^124648+197)/3 124649 Robert Price 07/2018 5062 2^414032-5 124637 Henri Lifchitz 07/2006 5061 2^414032+1872331 124637 Enzo Doria 05/2016 5063 37373^2158+2158^37373 124604 Hans Havermann 03/2021 5064 29811^15112+15112^29811 124590 Hans Havermann 03/2021 5065 F(596093)/36870605281541 124563 Serge Batalov 07/2024 5066 2^413781-2023 124561 Riley Fisher 09/2023 5067 14120^30009-30009^14120 124533 Norbert Schneider 02/2015 5068 29757^15296+15296^29757 124521 Hans Havermann 03/2021 5069 35056^3561+3561^35056 124504 Hans Havermann 03/2021 5070 40588^1167+1167^40588 124487 Hans Havermann 02/2021 5071 (85*10^124485-49)/9 124486 Robert Price 12/2020 5072 64^68909-63^68909 124463 Robert Price 07/2013 5073 35016^3581+3581^35016 124448 Hans Havermann 03/2021 5074 2^413387+76253 124442 Enzo Doria 04/2016 5075 28749^21298+21298^28749 124436 Hans Havermann 03/2021 5076 2^413352+524287 124432 Paul Underwood 09/2018 5077 287117#+391613 124424 Nicolas PALAU 01/2017 5078 (4*10^124420+83)/3 124421 Robert Price 02/2018 5079 34578^3965+3965^34578 124421 Hans Havermann 03/2021 5080 (68*10^124392-329)/9 124393 Robert Price 03/2021 5081 (27*2^413207-1)/108335 124385 Lelio R Paula 05/2014 5082 10^124383+58407 124384 Patrick De Geest 08/2021 5084 10^124383-8000001 124383 Robert Price 04/2021 5083 10^124383-5801 124383 Patrick De Geest 08/2021 5085 26091^28154-28154^26091 124342 Frank Doornink 03/2024 5086 (41*10^124335-383)/9 124336 Robert Price 11/2018 5087 (304*10^124329-43)/9 124331 Robert Price 02/2020 5088 34716^3811+3811^34716 124320 Hans Havermann 03/2021 5089 26892^28063-28063^26892 124309 Frank Doornink 03/2024 5090 2^412868-120599 124286 Paul Bourdelais 02/2012 5091 10^124248+899089 124249 Patrick De Geest 05/2021 5093 10^124248-1000001 124248 Robert Price 08/2020 5092 10^124248-501903 124248 Patrick De Geest 05/2021 5094 45^75145-2 124231 Lelio R Paula 08/2015 5095 29901^14272+14272^29901 124224 Hans Havermann 03/2021 5096 2^412645-112213 124219 Enzo Doria 06/2014 5097 29837^14500+14500^29837 124163 Hans Havermann 03/2021 5098 28074^26455+26455^28074 124158 Hans Havermann 03/2021 5099 2^412285+213317 124111 Enzo Doria 09/2023 5100 2^412248+74611 124100 Enzo Doria 04/2016 5101 (22*10^124096-13)/9 124097 Robert Price 06/2018 5102 (455*10^124093+31)/9 124095 Robert Price 06/2021 5103 2^412192-3329 124083 Yves Minet 12/2014 5104 (25*2^412191-1)/23 124082 Lelio R Paula 05/2014 5106 (25*10^124076-67)/3 124077 Robert Price 06/2019 5105 28132^25735+25735^28132 124077 Hans Havermann 03/2021 5107 F(593689) 124074 Henri Lifchitz 01/2005 5108 (11*2^412161+1)/19 124073 Lelio R Paula 05/2014 5109 26372^28057-28057^26372 124045 Frank Doornink 03/2024 5110 27528^27937-27937^27528 124034 Frank Doornink 03/2024 5111 35364^3215+3215^35364 124028 Hans Havermann 03/2021 5113 (266*10^124022-11)/3 124024 Robert Price 04/2020 5112 29987^13674+13674^29987 124024 Hans Havermann 03/2021 5114 2^411932-111546435 124004 Paul Bourdelais 10/2021 5115 2^411884-113279 123990 Enzo Doria 07/2014 5116 (2^411832+1)/257 123972 Lelio R Paula 05/2014 5117 (2^411833+2)/514 123972 Stefano Morozzi 03/2020 5118 (26*10^123970-89)/9 123971 Robert Price 06/2018 5119 2^411790-1853531 123962 Enzo Doria 08/2015 5120 (5^177337+1)/6 123953 Paul Bourdelais 11/2008 5121 (101*10^123950+7)/9 123952 Robert Price 02/2022 5122 2^411711-113257 123938 Enzo Doria 07/2014 5123 (23*2^411675-1)/3 123928 Lelio R Paula 05/2014 5124 36289^2598+2598^36289 123914 Hans Havermann 03/2021 5125 (11*10^123899-179)/3 123900 Robert Price 09/2018 5126 32276^6879+6879^32276 123860 Hans Havermann 02/2021 5127 2^411325-351103 123822 Enzo Doria 06/2015 5128 (646*10^123817+11)/9 123819 Robert Price 10/2021 5129 30738^10643+10643^30738 123784 Hans Havermann 03/2021 5130 31074^9607+9607^31074 123755 Hans Havermann 03/2021 5131 2^411052+1872481 123739 Enzo Doria 05/2016 5132 34365^3986+3986^34365 123733 Hans Havermann 03/2021 5133 2^410997+39 123723 Lelio R Paula 05/2014 5134 (649^43987-1)/648 123700 Michael Stocker 05/2020 5135 (148*10^123688-1)/3 123690 Robert Price 03/2020 5136 36825^2284+2284^36825 123684 Hans Havermann 03/2021 5137 29582^15171+15171^29582 123683 Hans Havermann 03/2021 5138 10^123671+3593037 123672 Paul Bourdelais 10/2021 5139 8*10^123657+87 123658 Robert Price 10/2019 5140 30505^11302+11302^30505 123642 Hans Havermann 03/2021 5141 29956^13401+13401^29956 123633 Hans Havermann 03/2021 5142 155^56438+154 123618 Norbert Schneider 01/2019 5143 2^410596-39 123602 Lelio R Paula 05/2014 5144 (41*10^123600-221)/9 123601 Robert Price 10/2021 5145 28995^18302+18302^28995 123592 Hans Havermann 03/2021 5146 28302^23269+23269^28302 123589 Hans Havermann 03/2021 5147 (41^76630+40)/37 123587 Alfred Reich 06/2024 5148 2^410540-115079 123585 Enzo Doria 06/2015 5149 (7*10^123563+107)/3 123564 Robert Price 02/2018 5150 9*10^123549+89 123550 Robert Price 11/2019 5151 (197*10^123545+7)/3 123547 Robert Price 12/2020 5152 (3*2^410392-1)/9229 123537 Lelio R Paula 05/2014 5153 2^410342+212449 123526 Enzo Doria 08/2023 5154 (29*10^123510+277)/9 123511 Robert Price 11/2021 5155 28118^24687+24687^28118 123508 Hans Havermann 03/2021 5156 39994^1225+1225^39994 123507 Hans Havermann 03/2021 5157 2^410206-113081 123485 Enzo Doria 07/2014 5158 (25*2^410192+1)/10397 123478 Lelio R Paula 04/2014 5159 28974^18215+18215^28974 123442 Hans Havermann 03/2021 5160 28901^18618+18618^28901 123406 Hans Havermann 03/2021 5161 2^409909-189 123395 Enzo Doria 05/2014 5162 2^409896-109043 123391 Enzo Doria 04/2014 5163 2^409890+75409 123390 Enzo Doria 04/2016 5164 81254^33+33^81254 123386 Hans Havermann 03/2021 5165 33463^4854+4854^33463 123348 Hans Havermann 03/2021 5166 34061^4182+4182^34061 123348 Hans Havermann 03/2021 5167 133^58076-2 123345 Lelio R Paula 10/2017 5168 F(590041) 123311 Henri Lifchitz 01/2005 5169 (82*10^123299+377)/9 123300 Robert Price 03/2022 5170 2^409566-113501 123292 Enzo Doria 08/2014 5171 2^409533+77747 123282 Enzo Doria 05/2016 5172 2^409436-112799 123253 Enzo Doria 06/2014 5173 28212^23321+23321^28212 123223 Hans Havermann 03/2021 5174 2^409225+1873787 123189 Enzo Doria 06/2016 5175 2^409174+73009 123174 Enzo Doria 04/2016 5176 2^409058-112685 123139 Enzo Doria 06/2014 5177 (13*10^123137-61)/3 123138 Robert Price 11/2018 5178 4*10^123113+21 123114 Robert Price 12/2018 5179 2^408778+77689 123055 Enzo Doria 05/2016 5180 2^408690-75 123028 Lelio R Paula 11/2013 5181 28327^22032+22032^28327 123026 Hans Havermann 03/2021 5182 (29*10^122996+673)/9 122997 Robert Price 12/2018 5183 (65*10^122994-101)/9 122995 Robert Price 01/2022 5184 2^408574-2787341 122994 Enzo Doria 03/2016 5185 3*10^122977+37 122978 Robert Price 08/2018 5186 (7*10^122976-67)/3 122977 Robert Price 10/2021 5187 Phi(157825,10) 122961 Maksym Voznyy 06/2015 5188 25493^27902-27902^25493 122948 Frank Doornink 02/2024 5189 26749^27768-27768^26749 122938 Frank Doornink 03/2024 5190 (68*10^122933-419)/9 122934 Robert Price 07/2019 5191 29712^13721+13721^29712 122931 Hans Havermann 03/2021 5192 (13*2^408283+1)/1665 122904 Lelio R Paula 05/2014 5193 (266*10^122872-17)/3 122874 Robert Price 07/2020 5194 (16*10^122871+77)/3 122872 Robert Price 03/2019 5195 30395^11022+11022^30395 122865 Hans Havermann 03/2021 5196 4*10^122859-69 122860 Robert Price 01/2022 5197 (10^122857+167)/3 122857 Robert Price 05/2021 5198 33331^4852+4852^33331 122856 Hans Havermann 03/2021 5199 (11*2^408100-1)/35 122850 Lelio R Paula 04/2014 5200 (19*10^122836-43)/3 122837 Robert Price 05/2019 5201 28420^20969+20969^28420 122820 Hans Havermann 03/2021 5202 (16*10^122818+179)/3 122819 Robert Price 11/2021 5203 29865^12934+12934^29865 122797 Hans Havermann 03/2021 5204 (2^407821-lucasV(1,2,407821)+1)/2 122767 Mike Oakes 11/2016 5205 (32*10^122733-77)/9 122734 Robert Price 06/2018 5206 (21*2^407604-1)/215 122701 Lelio R Paula 04/2014 5208 (22*10^122681+161)/3 122682 Robert Price 05/2019 5207 29513^14350+14350^29513 122682 Hans Havermann 03/2021 5209 (21*2^407433-1)/13 122650 Lelio R Paula 04/2014 5211 (26*10^122625-131)/3 122626 Robert Price 10/2019 5210 (643*33^80753+3709)/32 122626 Eric Chen 12/2023 5212 27925^24562+24562^27925 122599 Hans Havermann 03/2021 5213 (73*10^122592-1)/9 122593 Robert Price 01/2015 5214 (5*10^122592+91)/3 122593 Robert Price 04/2018 5215 36751^2166+2166^36751 122589 Hans Havermann 03/2021 5216 (85*10^122585-1)/3 122587 Robert Price 02/2020 5217 29368^14931+14931^29368 122585 Hans Havermann 03/2021 5218 2^407179-112075 122574 Enzo Doria 06/2014 5219 (21*2^407131+1)/207517523 122552 Lelio R Paula 04/2014 5220 (66^67349+1)/67 122543 Paul Bourdelais 09/2017 5221 (646*10^122533+11)/9 122535 Robert Price 10/2021 5222 2^407008-1867919 122522 Enzo Doria 04/2016 5223 11^117642-300 122512 Enzo Doria 10/2012 5224 (F(3*97700+1)^2+L(3*97700+1)^2)/2 122509 Henri Lifchitz 10/2017 5225 2^406949+72197 122504 Enzo Doria 04/2016 5226 (19*10^122501+149)/3 122502 Robert Price 05/2019 5227 28632^18977+18977^28632 122495 Hans Havermann 03/2021 5228 31815^7076+7076^31815 122481 Hans Havermann 03/2021 5229 2^406826-65 122467 Lelio R Paula 11/2013 5230 2^406821-2797363 122466 Enzo Doria 04/2016 5231 (7*10^122456-331)/9 122456 Robert Price 03/2022 5232 2^406758-17 122447 Lelio R Paula 11/2013 5233 29941^12282+12282^29941 122437 Hans Havermann 03/2021 5234 (30^82883-1)/29 122427 Robert Price 12/2011 5235 27496^27577+27577^27496 122422 Norbert Schneider 12/2020 5236 28732^18215+18215^28732 122411 Hans Havermann 03/2021 5237 (2^406583-1)/813167 122388 Jens K. Andersen 02/2009 5238 4*10^122377+19 122378 Robert Price 10/2018 5239 28227^21634+21634^28227 122368 Hans Havermann 03/2021 5240 Phi(246362,10) 122365 Makoto Kamada 09/2019 5241 3*10^122345-97 122346 Robert Price 07/2018 5242 97^61575-2 122336 Lelio R Paula 12/2014 5243 2*10^122319+47 122320 Robert Price 12/2021 5244 208^52765+52765^208 122313 Norbert Schneider 11/2020 5246 2^406298+2799109 122308 Enzo Doria 04/2016 5245 2^406296+213691 122308 Enzo Doria 09/2023 5247 7*10^122294+57 122295 Robert Price 06/2019 5248 (27*2^406241-1)/10277 122289 Lelio R Paula 04/2014 5249 2^406229-1849993 122288 Enzo Doria 08/2015 5250 3*10^122274+7 122275 Robert Price 07/2015

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 13 2024 17:43 (Time in France)

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