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
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 5001 | 2^471043+35 | 141799 | Robert Price | 11/2015 |
| 5002 | (11*2^470956-1)/7945 | 141770 | Lelio R Paula | 08/2015 |
| 5003 | 43636^1773+1773^43636 | 141761 | Hans Havermann | 05/2021 |
| 5004 | (2*10^141751-17)/3 | 141751 | Serge Batalov | 11/2022 |
| 5005 | (53*10^141722-611)/9 | 141723 | Robert Price | 02/2022 |
| 5006 | (11*10^141718-131)/3 | 141719 | Robert Price | 09/2018 |
| 5007 | (61*10^141716+47)/9 | 141717 | Robert Price | 07/2022 |
| 5008 | 26057^32088-32088^26057 | 141699 | Frank Doornink | 03/2024 |
| 5009 | 2^470692+76771 | 141693 | Enzo Doria | 05/2016 |
| 5010 | 50160^667+667^50160 | 141659 | Hans Havermann | 05/2021 |
| 5011 | 31522^31181+31181^31522 | 141657 | Hans Havermann | 05/2021 |
| 5012 | 29487^31690-31690^29487 | 141643 | Frank Doornink | 06/2024 |
| 5013 | 33076^19135+19135^33076 | 141626 | Hans Havermann | 04/2021 |
| 5014 | 28237^31818-31818^28237 | 141617 | Frank Doornink | 06/2024 |
| 5015 | Phi(303939,5) | 141617 | Henri Lifchitz | 02/2026 |
| 5016 | (91*10^141610+71)/9 | 141612 | Robert Price | 01/2022 |
| 5017 | (21*2^470391+1)/533 | 141601 | Lelio R Paula | 09/2015 |
| 5018 | (5*10^141594-23)/9 | 141594 | Serge Batalov | 11/2022 |
| 5019 | 31932^27155+27155^31932 | 141582 | Hans Havermann | 05/2021 |
| 5020 | 36449^7660+7660^36449 | 141577 | Hans Havermann | 05/2021 |
| 5021 | 2^470305-459373 | 141576 | Enzo Doria | 05/2015 |
| 5022 | 32195^24936+24936^32195 | 141556 | Hans Havermann | 05/2021 |
| 5023 | 2^470183+72623 | 141540 | Enzo Doria | 04/2016 |
| 5024 | 2^470173-16465 | 141537 | Enzo Doria | 04/2013 |
| 5025 | 37297^6234+6234^37297 | 141534 | Hans Havermann | 05/2021 |
| 5026 | 2^4^117533+117533^4^2 | 141524 | Henri Lifchitz | 03/2025 |
| 5027 | (509*10^141479+13)/9 | 141481 | Robert Price | 05/2022 |
| 5028 | 44*10^141476+9 | 141478 | Robert Price | 10/2020 |
| 5029 | 2^469974-1841 | 141477 | Enzo Doria | 05/2014 |
| 5030 | (23*2^469939+1)/25 | 141466 | Lelio R Paula | 08/2015 |
| 5031 | 312*33^93158+23 | 141465 | Eric Chen | 12/2023 |
| 5032 | 2*10^141448+63 | 141449 | Robert Price | 05/2018 |
| 5033 | 2^469824+43 | 141432 | Lelio R Paula | 09/2017 |
| 5034 | (124750^27751-1)/124749 | 141416 | Anonymous | 09/2025 |
| 5035 | 2*10^141407-27 | 141408 | Robert Price | 05/2018 |
| 5036 | (214*10^141385-1)/3 | 141387 | Robert Price | 01/2021 |
| 5037 | 2^469630-59711 | 141373 | Enzo Doria | 10/2015 |
| 5038 | 35277^10172+10172^35277 | 141370 | Hans Havermann | 04/2021 |
| 5039 | 33397^17100+17100^33397 | 141370 | Hans Havermann | 04/2021 |
| 5040 | (25*10^141366-331)/9 | 141367 | Robert Price | 08/2018 |
| 5041 | 36986^6639+6639^36986 | 141365 | Hans Havermann | 06/2021 |
| 5042 | 34572^12271+12271^34572 | 141361 | Hans Havermann | 06/2021 |
| 5043 | 37179^6338+6338^37179 | 141353 | Hans Havermann | 05/2021 |
| 5044 | (2^469564-3)/611 | 141351 | Lelio R Paula | 08/2015 |
| 5045 | 197^61601+2 | 141342 | Lelio R Paula | 08/2017 |
| 5046 | 33420^16951+16951^33420 | 141340 | Hans Havermann | 05/2021 |
| 5047 | 31623^29458+29458^31623 | 141330 | Hans Havermann | 05/2021 |
| 5048 | 48112^865+865^48112 | 141306 | Hans Havermann | 05/2021 |
| 5049 | 2^469372-112949 | 141296 | Enzo Doria | 07/2014 |
| 5050 | 5*10^141294-63 | 141295 | Robert Price | 04/2021 |
| 5051 | 3^296115+4 | 141283 | Tyler NeSmith | 01/2021 |
| 5052 | (64*10^141256+161)/9 | 141257 | Robert Price | 08/2022 |
| 5053 | 143^(2^16)+106^(2^16) | 141253 | Valeryi Kuryshev | 02/2011 |
| 5054 | 143^65536+106^65536 | 141253 | Serge Batalov | 03/2018 |
| 5055 | (11*10^141243-23)/3 | 141244 | Robert Price | 09/2021 |
| 5057 | 2^469198+782569 | 141243 | Enzo Doria | 10/2016 |
| 5056 | 38129^5062+5062^38129 | 141243 | Hans Havermann | 05/2021 |
| 5058 | (41^87583-1)/192892799240 | 141242 | Paul Vanderveen | 05/2025 |
| 5059 | 2^469076-2786939 | 141206 | Enzo Doria | 11/2015 |
| 5060 | 38630^4521+4521^38630 | 141202 | Hans Havermann | 05/2021 |
| 5061 | Phi(143337,-5#) | 141148 | Henri Lifchitz | 12/2025 |
| 5062 | 31755^27836+27836^31755 | 141139 | Hans Havermann | 05/2021 |
| 5063 | 35554^9325+9325^35554 | 141137 | Hans Havermann | 05/2021 |
| 5064 | 2^468804+1874941 | 141125 | Enzo Doria | 06/2016 |
| 5065 | 2^468787+81353 | 141119 | Enzo Doria | 08/2016 |
| 5066 | 30204^31493-31493^30204 | 141091 | Frank Doornink | 06/2024 |
| 5067 | 2^468595-350407 | 141062 | Enzo Doria | 06/2015 |
| 5068 | 2^468564+87855 | 141052 | Lelio R Paula | 01/2016 |
| 5069 | 2^468551-21987 | 141048 | Enzo Doria | 07/2013 |
| 5070 | 2^468523-7 | 141040 | Lelio R Paula | 08/2015 |
| 5071 | (25*10^141019-13)/3 | 141020 | Robert Price | 09/2019 |
| 5072 | 2^468405+87855 | 141004 | Lelio R Paula | 01/2016 |
| 5073 | 39338^3831+3831^39338 | 140961 | Hans Havermann | 05/2021 |
| 5074 | 31458^30239+30239^31458 | 140950 | Hans Havermann | 05/2021 |
| 5075 | 8*10^140932+29 | 140933 | Robert Price | 11/2021 |
| 5076 | 33166^17691+17691^33166 | 140881 | Hans Havermann | 06/2021 |
| 5077 | 2^467978-113051 | 140876 | Enzo Doria | 07/2014 |
| 5078 | 2^467780-344429 | 140816 | Enzo Doria | 07/2015 |
| 5079 | 9*10^140802-89 | 140803 | Robert Price | 04/2020 |
| 5080 | 2^467605-1855603 | 140764 | Enzo Doria | 09/2015 |
| 5081 | (9^147503-5^147503)/4 | 140754 | Jon Grantham | 07/2023 |
| 5082 | 5*10^140744-7 | 140745 | Robert Price | 09/2015 |
| 5084 | (5^201359-1)/4 | 140744 | Paul Bourdelais | 12/2008 |
| 5083 | Phi(201359,5) | 140744 | Henri Lifchitz | 12/2025 |
| 5085 | 2^467401-1850023 | 140702 | Enzo Doria | 08/2015 |
| 5086 | (14*10^140693+13)/9 | 140694 | Tyler Busby | 02/2023 |
| 5087 | (266*10^140681-17)/3 | 140683 | Robert Price | 07/2020 |
| 5088 | (2^467270+78557)/23247 | 140658 | Lelio R Paula | 07/2015 |
| 5089 | 32138^23781+23781^32138 | 140644 | Hans Havermann | 05/2021 |
| 5090 | 31654^27735+27735^31654 | 140640 | Hans Havermann | 05/2021 |
| 5091 | (29*2^467205+1)/2780517107 | 140635 | Lelio R Paula | 08/2015 |
| 5092 | 2^467166-1854941 | 140631 | Enzo Doria | 09/2015 |
| 5093 | (203*10^140615-11)/3 | 140617 | Robert Price | 12/2020 |
| 5094 | (85*10^140609+473)/9 | 140610 | Robert Price | 01/2020 |
| 5095 | (3^672799)%L(672799) | 140607 | Henri Lifchitz | 06/2025 |
| 5096 | 39231^3836+3836^39231 | 140600 | Hans Havermann | 06/2021 |
| 5097 | 5*3^294676+2^294676 | 140597 | Jon Grantham | 08/2023 |
| 5098 | (5^672618)%L(672618) | 140569 | Henri Lifchitz | 07/2025 |
| 5099 | 2^466866-1840571 | 140541 | Enzo Doria | 06/2015 |
| 5100 | 2^466829-459523 | 140530 | Enzo Doria | 05/2015 |
| 5101 | 2^466692-113213 | 140489 | Enzo Doria | 07/2014 |
| 5102 | 23*10^140464-3 | 140466 | Robert Price | 10/2021 |
| 5103 | (2*10^140461-17)/3 | 140461 | Serge Batalov | 11/2022 |
| 5104 | 29^96047-30 | 140459 | Anonymous | 09/2024 |
| 5105 | 31335^30364+30364^31335 | 140455 | Hans Havermann | 05/2021 |
| 5106 | 28511^31524-31524^28511 | 140440 | Frank Doornink | 06/2024 |
| 5107 | 32795^19126+19126^32795 | 140416 | Hans Havermann | 05/2021 |
| 5108 | (44*10^140410-503)/9 | 140411 | Robert Price | 12/2018 |
| 5109 | 28332^31535-31535^28332 | 140403 | Frank Doornink | 06/2024 |
| 5110 | 153^64265-2 | 140400 | Lelio R Paula | 11/2017 |
| 5111 | 30323^31322-31322^30323 | 140379 | Frank Doornink | 06/2024 |
| 5112 | (112*10^140357-1)/3 | 140359 | Serge Batalov | 12/2014 |
| 5113 | (29*10^140337-17)/3 | 140338 | Robert Price | 09/2019 |
| 5114 | 2^466181-112735 | 140335 | Enzo Doria | 07/2014 |
| 5115 | (16*10^140290-37)/3 | 140291 | Robert Price | 05/2021 |
| 5116 | (5*10^140281-119)/3 | 140282 | Robert Price | 03/2018 |
| 5117 | 34568^11415+11415^34568 | 140259 | Hans Havermann | 05/2021 |
| 5118 | (27*2^465872+1)/691 | 140241 | Lelio R Paula | 08/2015 |
| 5119 | 33632^14781+14781^33632 | 140236 | Hans Havermann | 05/2021 |
| 5120 | 31803^25670+25670^31803 | 140233 | Hans Havermann | 05/2021 |
| 5121 | 2^465803-114817 | 140221 | Enzo Doria | 05/2015 |
| 5122 | Phi(213305,-7) | 140192 | Henri Lifchitz | 12/2025 |
| 5123 | floor(Pi*10^140344)%10^140165 | 140165 | Serge Batalov | 08/2012 |
| 5124 | 2^465503-112735 | 140131 | Enzo Doria | 07/2014 |
| 5125 | (16*10^140091+167)/3 | 140092 | Robert Price | 06/2019 |
| 5126 | (8*10^140087-137)/3 | 140088 | Robert Price | 03/2022 |
| 5127 | 6^179964+179964^6-1 | 140040 | Robert Price | 04/2014 |
| 5128 | (89*10^140008-179)/9 | 140009 | Robert Price | 12/2019 |
| 5129 | (29*2^465077-1)/9 | 140003 | Lelio R Paula | 08/2015 |
| 5130 | 2^465072-344789 | 140001 | Enzo Doria | 07/2015 |
| 5131 | 34742^10683+10683^34742 | 139965 | Hans Havermann | 05/2021 |
| 5132 | 5*10^139945+81 | 139946 | Robert Price | 03/2019 |
| 5133 | 32648^19335+19335^32648 | 139941 | Hans Havermann | 05/2021 |
| 5134 | 2^464864-17 | 139939 | Lelio R Paula | 09/2017 |
| 5135 | 8*10^139920+51 | 139921 | Robert Price | 08/2019 |
| 5136 | (85*10^139913-1)/3 | 139915 | Robert Price | 02/2020 |
| 5137 | 31203^30436+30436^31203 | 139896 | Hans Havermann | 04/2021 |
| 5138 | 2^464642+22189 | 139872 | Enzo Doria | 09/2023 |
| 5139 | 26138^31663-31663^26138 | 139865 | Frank Doornink | 03/2024 |
| 5140 | (47^83641-5^83641)/42 | 139855 | Robert Price | 05/2026 |
| 5141 | (16^116139+619)/5 | 139845 | Anonymous | 08/2022 |
| 5142 | (2^464556+619)/5 | 139845 | Eric Chen | 10/2023 |
| 5143 | 4*10^139839-27 | 139840 | Robert Price | 08/2021 |
| 5144 | 33582^14573+14573^33582 | 139821 | Hans Havermann | 05/2021 |
| 5145 | (17^113621+1)/18 | 139804 | Paul Bourdelais | 09/2011 |
| 5147 | 2*10^139800-21 | 139801 | Robert Price | 09/2020 |
| 5146 | 32628^19261+19261^32628 | 139801 | Hans Havermann | 04/2021 |
| 5148 | (13*10^139782+191)/3 | 139783 | Robert Price | 11/2018 |
| 5149 | (64*10^139776+791)/9 | 139777 | Robert Price | 01/2022 |
| 5150 | (695*10^139772+7)/9 | 139774 | Robert Price | 12/2021 |
| 5151 | (19*2^464312-1)/3 | 139773 | Lelio R Paula | 08/2015 |
| 5152 | (74*10^139723+133)/9 | 139724 | Robert Price | 06/2019 |
| 5153 | 3*10^139722+13 | 139723 | Robert Price | 07/2018 |
| 5154 | 31577^26592+26592^31577 | 139721 | Hans Havermann | 05/2021 |
| 5155 | 77*10^139692+3 | 139694 | Robert Price | 06/2020 |
| 5156 | (31*2^463970+1)/5 | 139670 | Lelio R Paula | 08/2015 |
| 5157 | (18203^(2^15)+(18201)^(2^15))/2 | 139597 | Robert Price | 05/2018 |
| 5158 | 39640^3321+3321^39640 | 139584 | Hans Havermann | 05/2021 |
| 5159 | 36663^6410+6410^36663 | 139571 | Hans Havermann | 05/2021 |
| 5160 | 2^463633-2788423 | 139568 | Enzo Doria | 11/2015 |
| 5161 | 33659^13978+13978^33659 | 139532 | Hans Havermann | 05/2021 |
| 5162 | 31811^24318+24318^31811 | 139521 | Hans Havermann | 04/2021 |
| 5163 | 34149^12172+12172^34149 | 139512 | Hans Havermann | 04/2021 |
| 5164 | (29*10^139476+313)/9 | 139477 | Robert Price | 04/2021 |
| 5165 | 31721^24940+24940^31721 | 139474 | Hans Havermann | 05/2021 |
| 5166 | 32833^17698+17698^32833 | 139473 | Hans Havermann | 05/2021 |
| 5167 | 2^463271-109501 | 139459 | Enzo Doria | 04/2014 |
| 5168 | (5*10^139457+79)/3 | 139458 | Robert Price | 03/2018 |
| 5169 | 2^463237-99 | 139449 | Lelio R Paula | 09/2017 |
| 5170 | (49*10^139442+383)/9 | 139443 | Robert Price | 04/2019 |
| 5171 | 31155^29902+29902^31155 | 139441 | Hans Havermann | 05/2021 |
| 5172 | (7*10^139417-547)/9 | 139417 | Robert Price | 01/2018 |
| 5173 | 29636^31175-31175^29636 | 139409 | Frank Doornink | 05/2024 |
| 5174 | (10^139398+191)/3 | 139398 | Robert Price | 02/2018 |
| 5175 | 23*10^139386-3 | 139388 | Robert Price | 10/2021 |
| 5176 | 2^463019+79463 | 139383 | Enzo Doria | 06/2016 |
| 5177 | 3^292129-112756 | 139381 | Enzo Doria | 07/2014 |
| 5178 | (15*2^462951+1)/527 | 139361 | Lelio R Paula | 08/2015 |
| 5179 | 31922^23205+23205^31922 | 139359 | Hans Havermann | 05/2021 |
| 5180 | (19*10^139336+503)/9 | 139337 | Alfred Reich | 11/2023 |
| 5182 | 2^462855-1865707 | 139334 | Enzo Doria | 02/2016 |
| 5181 | 31237^28876+28876^31237 | 139334 | Hans Havermann | 05/2021 |
| 5183 | (86*10^139315+121)/9 | 139316 | Robert Price | 08/2019 |
| 5184 | 2^462786-292043 | 139313 | Enzo Doria | 08/2015 |
| 5185 | 38915^3798+3798^38915 | 139299 | Hans Havermann | 05/2021 |
| 5187 | (26*10^139289+1)/9 | 139290 | Serge Batalov | 05/2010 |
| 5186 | (17*10^139289+7)/3 | 139290 | Robert Price | 06/2023 |
| 5188 | 34065^12248+12248^34065 | 139260 | Hans Havermann | 05/2021 |
| 5189 | 36425^6654+6654^36425 | 139256 | Hans Havermann | 05/2021 |
| 5190 | 39252^3527+3527^39252 | 139243 | Hans Havermann | 05/2021 |
| 5191 | (17*10^139239+67)/3 | 139240 | Robert Price | 01/2019 |
| 5192 | 31887^23248+23248^31887 | 139231 | Hans Havermann | 05/2021 |
| 5193 | (25*10^139210-97)/9 | 139211 | Robert Price | 01/2022 |
| 5194 | 2^462238-935 | 139148 | Yves Minet | 02/2014 |
| 5195 | (29*10^139134-119)/9 | 139135 | Robert Price | 12/2021 |
| 5196 | U(687859)/4127153 | 139105 | Serge Batalov | 07/2024 |
| 5197 | (109*10^139100-7)/3 | 139102 | Robert Price | 03/2021 |
| 5198 | 38744^3885+3885^38744 | 139068 | Hans Havermann | 05/2021 |
| 5199 | 31112^29499+29499^31112 | 139065 | Hans Havermann | 05/2021 |
| 5200 | 2*10^139043-63 | 139044 | Robert Price | 01/2022 |
| 5201 | 36390^6613+6613^36390 | 139025 | Hans Havermann | 04/2021 |
| 5202 | 30554^30989-30989^30554 | 138988 | Frank Doornink | 05/2024 |
| 5203 | 2*10^138975+33 | 138976 | Robert Price | 11/2021 |
| 5204 | 42437^1882+1882^42437 | 138966 | Hans Havermann | 05/2021 |
| 5205 | 32151^20990+20990^32151 | 138958 | Hans Havermann | 05/2021 |
| 5206 | 32154^20933+20933^32154 | 138933 | Hans Havermann | 04/2021 |
| 5207 | 31082^29499+29499^31082 | 138931 | Hans Havermann | 04/2021 |
| 5208 | 30573^30962-30962^30573 | 138876 | Frank Doornink | 05/2024 |
| 5209 | 2^461228+1870441 | 138844 | Enzo Doria | 05/2016 |
| 5210 | 2^461204-113675 | 138837 | Enzo Doria | 08/2014 |
| 5211 | (397227*29^94935-19)/28 | 138837 | Eric Chen | 06/2025 |
| 5212 | (2^461139-7)/47 | 138815 | Lelio R Paula | 08/2015 |
| 5213 | (17*10^138812-521)/9 | 138813 | Robert Price | 04/2018 |
| 5214 | 3*10^138811-11 | 138812 | Robert Price | 07/2018 |
| 5215 | 29109^31088-31088^29109 | 138778 | Frank Doornink | 05/2024 |
| 5216 | (28*10^138768+173)/3 | 138769 | Robert Price | 12/2019 |
| 5217 | (17*2^460963+1)/124051613 | 138757 | Lelio R Paula | 08/2015 |
| 5218 | (379*10^138737-1)/9 | 138739 | Robert Price | 02/2020 |
| 5219 | (43*10^138648+101)/9 | 138649 | Robert Price | 11/2018 |
| 5220 | 2^460567-113541 | 138645 | Enzo Doria | 08/2014 |
| 5221 | 2^460539+224789 | 138637 | Enzo Doria | 07/2024 |
| 5222 | (10^138622+161)/9 | 138622 | Robert Price | 09/2021 |
| 5223 | 7*10^138604+3 | 138605 | Robert Price | 08/2015 |
| 5224 | (133*10^138600+17)/3 | 138602 | Robert Price | 11/2021 |
| 5225 | 33912^12203+12203^33912 | 138581 | Hans Havermann | 05/2021 |
| 5226 | 2^460330+69 | 138574 | Lelio R Paula | 09/2017 |
| 5227 | (17*10^138569-77)/3 | 138570 | Robert Price | 08/2019 |
| 5228 | 31186^27725+27725^31186 | 138556 | Hans Havermann | 05/2021 |
| 5229 | (41^85909-3^85909)/38 | 138552 | Robert Price | 09/2025 |
| 5230 | (16*10^138545+89)/3 | 138546 | Robert Price | 03/2021 |
| 5231 | 39753^3056+3056^39753 | 138546 | Hans Havermann | 05/2021 |
| 5232 | 31282^26847+26847^31282 | 138545 | Hans Havermann | 05/2021 |
| 5233 | 6*10^138520-37 | 138521 | Robert Price | 02/2021 |
| 5236 | 2^460078-69581 | 138498 | Enzo Doria | 12/2015 |
| 5234 | 31830^22447+22447^31830 | 138498 | Hans Havermann | 05/2021 |
| 5235 | Phi(237987,2^3) | 138498 | Henri Lifchitz | 12/2025 |
| 5237 | 37384^5065+5065^37384 | 138492 | Hans Havermann | 05/2021 |
| 5238 | 28736^31055-31055^28736 | 138457 | Frank Doornink | 05/2024 |
| 5239 | 34774^9585+9585^34774 | 138456 | Hans Havermann | 05/2021 |
| 5240 | 10^138444-5001 | 138444 | Robert Price | 12/2021 |
| 5241 | 2^459768+1531 | 138404 | Lelio R Paula | 06/2012 |
| 5242 | (266*10^138328-17)/3 | 138330 | Robert Price | 07/2020 |
| 5243 | 27200^31193-31193^27200 | 138328 | Frank Doornink | 01/2024 |
| 5244 | 2024^41836+2025 | 138319 | Henri Lifchitz | 01/2025 |
| 5245 | 28782^31019-31019^28782 | 138318 | Frank Doornink | 05/2024 |
| 5246 | 32963^15696+15696^32963 | 138306 | Hans Havermann | 05/2021 |
| 5247 | 2^459343-113611 | 138277 | Enzo Doria | 08/2014 |
| 5248 | (28*10^138240+113)/3 | 138241 | Robert Price | 03/2020 |
| 5249 | 2^459199+1874393 | 138233 | Enzo Doria | 06/2016 |
| 5250 | 33339^14002+14002^33339 | 138230 | Hans Havermann | 05/2021 |
