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) !!!
Submit your PRPs
See the Top discoverers
See the Latest PRPs
Search by form
| 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 |
