PRP Records

Probable Primes Top 10000

(294113 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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 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 2^390889-115003 117670 Enzo Doria 06/2015 5002 12^109010+35 117642 Riley Fisher 08/2023 5003 2^390779-30337 117637 Paul Bourdelais 02/2012 5004 (2^390735+378)/2 117623 Stefano Morozzi 02/2021 5005 11^112916-780 117590 Enzo Doria 12/2012 5006 27641^17916+17916^27641 117564 Hans Havermann 02/2021 5007 27906^16321+16321^27906 117561 Hans Havermann 02/2021 5008 27294^20275+20275^27294 117555 Hans Havermann 02/2021 5009 (2^390473+1002)/2 117544 Stefano Morozzi 09/2020 5010 35912^1875+1875^35912 117541 Hans Havermann 02/2021 5011 (16^97613-5^97613)/11 117537 Robert Price 07/2013 5012 (2^390438+1774)/2 117534 Stefano Morozzi 01/2021 5013 (2^390418+1722)/2 117528 Stefano Morozzi 09/2020 5014 (2^390403+654)/2 117523 Stefano Morozzi 09/2020 5015 (2^390343+2246)/2 117505 Stefano Morozzi 01/2021 5016 28043^15478+15478^28043 117493 Hans Havermann 02/2021 5017 (17*2^390272+1)/1983 117482 Lelio R Paula 04/2014 5018 37077^1474+1474^37077 117479 Hans Havermann 01/2021 5019 31^78759-30 117459 Theodore Burton 02/2007 5020 (2^390176+1222)/2 117455 Stefano Morozzi 09/2020 5021 (2^390133+1242)/2 117442 Stefano Morozzi 09/2020 5022 (2^390013+2634)/2 117406 Stefano Morozzi 09/2020 5023 3*10^117402+61 117403 Robert Price 09/2020 5024 2^389998+37 117402 Lelio R Paula 03/2013 5025 (2^389977+314)/2 117395 Stefano Morozzi 09/2020 5026 (2^389921+342)/2 117378 Stefano Morozzi 01/2021 5027 71830^43+43^71830 117333 Hans Havermann 01/2021 5028 (2^389768+1582)/2 117332 Stefano Morozzi 09/2020 5029 33802^2951+2951^33802 117292 Hans Havermann 02/2021 5030 26789^23866+23866^26789 117277 Hans Havermann 02/2021 5031 29^80192-1*80192^29 117273 Dylan Delgado 12/2019 5032 (101*10^117260+7)/9 117262 Robert Price 02/2022 5033 (13*10^117249+161)/3 117250 Robert Price 11/2018 5034 2^389478+43 117245 Lelio R Paula 03/2013 5035 (298*10^117229-7)/3 117231 Robert Price 06/2020 5036 (2^389416+342)/2 117226 Stefano Morozzi 01/2021 5037 (29*2^389351-1)/9 117207 Lelio R Paula 04/2014 5038 5*10^117205+23 117206 Robert Price 03/2019 5039 (2^389341-7)/3865 117200 Lelio R Paula 03/2014 5040 27272^19827+19827^27272 117195 Hans Havermann 01/2021 5041 (2^389276+2650)/2 117184 Stefano Morozzi 09/2020 5042 (844*10^117175-7)/9 117177 Robert Price 05/2021 5043 10^117142+209223 117143 Patrick De Geest 04/2018 5045 10^117142-1000000001 117142 Robert Price 03/2018 5044 10^117142-966057 117142 Patrick De Geest 04/2018 5046 10^117135+360577 117136 Patrick De Geest 07/2018 5047 10^117135-401 117135 Robert Price 01/2018 5048 26415^26488-26488^26415 117126 Norbert Schneider 05/2021 5049 4*10^117123+79 117124 Robert Price 08/2018 5050 2^389033-12797413 117111 Enzo Doria 04/2016 5051 (2^388987+2634)/2 117097 Stefano Morozzi 09/2020 5052 2^388960-109505 117089 Enzo Doria 04/2014 5053 7*10^117082-57 117083 Robert Price 06/2020 5054 (2^388928-5)/569 117077 Lelio R Paula 03/2014 5055 2^388888-1529 117067 Yves Minet 01/2013 5056 10^117059+28879 117060 Patrick De Geest 05/2016 5057 (10^117059-71)/1 117059 Serge Batalov 12/2014 5058 (2^388854+3630)/2 117057 Stefano Morozzi 09/2020 5059 (2^388842+2098)/2 117053 Stefano Morozzi 09/2020 5060 (2^388789+3150)/2 117037 Stefano Morozzi 09/2020 5061 (2^388748+378)/2 117025 Stefano Morozzi 02/2021 5062 (693^41189-1)/692 117005 Michael Stocker 05/2020 5063 (26*10^116999-503)/9 117000 Robert Price 07/2018 5064 (2^388609+1554)/2 116983 Stefano Morozzi 09/2020 5065 38496^1093+1093^38496 116975 Hans Havermann 02/2021 5066 3^245154-6256 116969 Enzo Doria 05/2014 5067 5*10^116966-43 116967 Robert Price 01/2019 5068 2^388536-113495 116961 Enzo Doria 08/2014 5069 (2^388512+382)/2 116954 Stefano Morozzi 02/2021 5070 (8*32^77701+271)/31 116952 Eric Chen 11/2023 5071 2^388469-43 116941 Lelio R Paula 03/2013 5072 27417^18416+18416^27417 116939 Hans Havermann 02/2021 5073 (2^388438+1842)/2 116932 Stefano Morozzi 02/2021 5074 (7*2^388372-1)/111 116911 Lelio R Paula 04/2014 5075 (7*2^388335-1)/25 116900 Lelio R Paula 04/2014 5076 2^388180+93 116854 Donovan Johnson 07/2008 5077 (2^388167+2510)/2 116850 Stefano Morozzi 09/2020 5078 (85*10^116842+293)/9 116843 Robert Price 12/2019 5079 35296^2043+2043^35296 116840 Hans Havermann 02/2021 5080 (2^388081+7)/1179 116821 Lelio R Paula 03/2014 5081 38633^1056+1056^38633 116814 Hans Havermann 02/2021 5082 2^387946-113261 116784 Enzo Doria 07/2014 5083 28*36^75009+305 116739 Eric Chen 12/2022 5084 28363^13056+13056^28363 116737 Hans Havermann 02/2021 5085 2^387745+75557 116723 Enzo Doria 04/2016 5086 (29*10^116719+313)/9 116720 Robert Price 04/2021 5087 29622^8699+8699^29622 116695 Hans Havermann 02/2021 5088 (206*10^116687-17)/9 116689 Robert Price 01/2020 5089 (7*10^116684+179)/3 116685 Robert Price 09/2018 5090 2^387554+71455 116666 Enzo Doria 04/2016 5091 (602*10^116647-71)/9 116649 Robert Price 12/2021 5092 3^244461-10 116638 Tyler NeSmith 09/2022 5093 (2^387447+78557)/365 116631 Lelio R Paula 12/2014 5094 (2*10^116620+43)/9 116620 Serge Batalov 11/2022 5095 (19*10^116617+287)/9/12893 116614 Alfred Reich 11/2022 5096 (145*10^116610-1)/9 116612 Serge Batalov 12/2014 5097 (25*10^116601-331)/9 116602 Robert Price 08/2018 5098 (17*2^387284-1)/59 116584 Lelio R Paula 04/2014 5099 (2^387284+3726)/2 116584 Stefano Morozzi 09/2020 5100 2^387211+111546435 116563 Paul Bourdelais 10/2021 5101 10^116557+987654321 116558 Robert Price 12/2019 5102 10^116557+9141 116558 Patrick De Geest 02/2020 5103 10^116557-609431 116557 Patrick De Geest 02/2020 5104 (28*10^116546+41)/3 116547 Robert Price 07/2021 5105 (2^387123+1814)/2 116536 Stefano Morozzi 02/2021 5106 (2^387076+2046)/2 116522 Stefano Morozzi 09/2020 5107 (2^387073+2570)/2 116521 Stefano Morozzi 09/2020 5108 (7*10^116514-1)/3 116515 Robert Price 08/2022 5109 (26*32^77406-390071011)/31 116508 Eric Chen 11/2023 5110 28846^10931+10931^28846 116500 Hans Havermann 02/2021 5111 10^116496+3593037 116497 Paul Bourdelais 10/2021 5112 (31*2^386968+1)/7 116490 Lelio R Paula 03/2014 5113 2^386947+1869143 116483 Enzo Doria 05/2016 5114 (30^78857-1)/29 116480 Robert Price 12/2011 5115 (2^386903-3)/5 116469 Lelio R Paula 03/2014 5116 28107^13892+13892^28107 116441 Hans Havermann 02/2021 5117 29110^9957+9957^29110 116386 Hans Havermann 02/2021 5118 26469^24838+24838^26469 116335 Hans Havermann 01/2021 5119 2^386389-1864783 116315 Enzo Doria 03/2016 5120 (8*32^77250-163)/31 116273 Eric Chen 11/2023 5121 (31*2^386231-1)/1711 116266 Lelio R Paula 03/2014 5122 297^47012+47012^297 116250 Norbert Schneider 07/2018 5123 (35*10^116223-341)/9 116224 Robert Price 08/2021 5124 (2^386087-5)/40959 116220 Lelio R Paula 03/2014 5125 (2^386054+714)/2 116214 Stefano Morozzi 09/2020 5126 (10^116201+7)/39623 116197 Alfred Reich 06/2021 5127 2^385969-823 116189 Yves Minet 05/2012 5128 57^66162+2 116173 Lelio R Paula 08/2013 5129 2^385854+75049 116154 Enzo Doria 04/2016 5130 (2^385832+2590)/2 116147 Stefano Morozzi 09/2020 5131 2^385775-109587 116130 Enzo Doria 04/2014 5132 (14*10^116112-101)/3 116113 Robert Price 02/2019 5133 Phi(236354,10)/24817171 116109 Makoto Kamada 08/2019 5134 3*10^116107+23 116108 Robert Price 03/2022 5135 28729^10990+10990^28729 116094 Hans Havermann 02/2021 5136 2^385622+71839 116084 Enzo Doria 04/2016 5138 2^385564+781 116067 Lelio R Paula 01/2012 5137 (2^385565+1562)/2 116067 Stefano Morozzi 09/2020 5139 (2^385563+378)/2 116066 Stefano Morozzi 02/2021 5140 (2^385557+2214)/2 116064 Stefano Morozzi 09/2020 5141 29431^8776+8776^29431 116056 Hans Havermann 01/2021 5142 (266*10^116024-17)/3 116026 Robert Price 07/2020 5143 30263^6820+6820^30263 116022 Hans Havermann 02/2021 5144 2^385410+71893 116020 Enzo Doria 04/2016 5145 38225^1084+1084^38225 116014 Hans Havermann 02/2021 5146 26548^23433+23433^26548 116011 Hans Havermann 02/2021 5147 (25*2^385091+1)/27 115924 Lelio R Paula 04/2014 5148 (11*10^115910-131)/3 115911 Robert Price 09/2018 5149 2^384953-111943 115883 Paul Bourdelais 02/2012 5150 43^70942-2 115882 Lelio R Paula 04/2014 5151 (94*10^115879-7)/3 115881 Robert Price 03/2020 5152 7*10^115863+3 115864 Robert Price 08/2015 5153 2^384834+93 115847 Donovan Johnson 07/2008 5154 2^384809+71297 115840 Enzo Doria 04/2016 5155 (55*10^115829+323)/9 115830 Robert Price 10/2021 5156 (7*2^384759-1)/5 115825 Lelio R Paula 04/2014 5157 31348^4951+4951^31348 115822 Hans Havermann 02/2021 5158 (793*10^115810+53)/9 115812 Robert Price 01/2022 5159 (71*10^115810-17)/9 115811 Ray Chandler 08/2011 5160 (97*10^115794-1)/3 115796 Serge Batalov 12/2014 5161 31115^5266+5266^31115 115794 Hans Havermann 02/2021 5162 2*10^115784-27 115785 Robert Price 05/2018 5163 10^115773+126739 115774 Patrick De Geest 04/2018 5165 10^115773-1000000001 115773 Robert Price 03/2018 5164 10^115773-396221 115773 Patrick De Geest 04/2018 5166 (2^384582+778)/2 115771 Stefano Morozzi 09/2020 5167 30537^6178+6178^30537 115762 Hans Havermann 01/2021 5168 2^384530+1874305 115756 Enzo Doria 06/2016 5169 (3*2^384524-1)/7631 115750 Lelio R Paula 03/2014 5170 28275^12406+12406^28275 115748 Hans Havermann 01/2021 5171 (44*10^115697-413)/9 115698 Robert Price 03/2019 5172 31408^4825+4825^31408 115692 Hans Havermann 02/2021 5173 (2^384317+1026)/2 115691 Stefano Morozzi 09/2020 5174 2^384312+81091 115690 Yves Minet 02/2010 5175 (2^384265+2150)/2 115675 Stefano Morozzi 09/2020 5176 (2^384246+2182)/2 115670 Stefano Morozzi 09/2020 5177 (4*10^115668-79)/3 115669 Robert Price 02/2018 5178 (2^384193+242)/2 115654 Stefano Morozzi 09/2020 5179 (266947#+1267)/(7^2*181) 115647 Makoto Morimoto 06/2019 5180 (266947#+273808)/(2*109*157) 115646 Makoto Morimoto 10/2017 5181 18^92125-92125^18 115642 Dylan Delgado 08/2019 5182 3^242337-4042 115625 Enzo Doria 05/2014 5183 (2^383931+674)/2 115575 Stefano Morozzi 09/2020 5184 7*10^115561+79 115562 Robert Price 07/2019 5185 (2^383872+3046)/2 115557 Stefano Morozzi 09/2020 5186 (11*2^383859-13)/15 115553 Renaud Lifchitz 03/2011 5187 2^383780-3149 115530 Yves Minet 10/2014 5188 (41*10^115523-383)/9 115524 Robert Price 11/2018 5189 27316^16923+16923^27316 115506 Hans Havermann 02/2021 5190 (2^383618+618)/2 115481 Stefano Morozzi 09/2020 5191 2^383560-455 115464 Yves Minet 03/2012 5192 (2^383544+5)/3 115458 Lelio R Paula 03/2014 5193 (22*10^115454+119)/3 115455 Robert Price 04/2021 5194 89^59221-88^59221 115445 Robert Price 06/2015 5195 (7^136559-5^136559)/2 115406 Jon Grantham 08/2023 5196 2^383347+1869413 115399 Enzo Doria 05/2016 5197 (103*10^115366+17)/3 115368 Robert Price 08/2020 5198 (2^383232+750)/2 115365 Stefano Morozzi 09/2020 5199 (2^383130-7)/131793 115329 Lelio R Paula 03/2014 5200 (12^106859+1)/13 115320 Paul Bourdelais 02/2010 5201 29961^7060+7060^29961 115315 Hans Havermann 01/2021 5203 2^383039+1869509 115307 Enzo Doria 05/2016 5202 32918^3183+3183^32918 115307 Hans Havermann 01/2021 5204 36964^1315+1315^36964 115288 Hans Havermann 02/2021 5205 (13*2^382968+1)/7 115286 Lelio R Paula 04/2014 5206 (22*10^115282+29)/3 115283 Robert Price 02/2021 5207 (2^382945+2046)/2 115278 Stefano Morozzi 09/2020 5208 (2^382789+3182)/2 115231 Stefano Morozzi 09/2020 5209 30416^6141+6141^30416 115224 Hans Havermann 02/2021 5210 6*10^115211+79 115212 Robert Price 09/2020 5211 (2^382722+3598)/2 115211 Stefano Morozzi 09/2020 5212 27987^13078+13078^27987 115210 Hans Havermann 02/2021 5213 (2^382699+2090)/2 115204 Stefano Morozzi 09/2020 5214 (22*10^115188-193)/9 115189 Robert Price 07/2022 5215 2^382633+73697 115185 Enzo Doria 04/2016 5216 2^382509-113593 115147 Enzo Doria 08/2014 5217 2^382502-2791721 115145 Enzo Doria 03/2016 5218 (2^382495+1274)/2 115143 Stefano Morozzi 01/2021 5219 2^382464+22741 115134 Enzo Doria 09/2023 5220 26752^20065+20065^26752 115099 Hans Havermann 02/2021 5221 26383^23008+23008^26383 115080 Hans Havermann 02/2021 5222 9^120590-120590 115073 Robert Price 03/2014 5223 28203^12016+12016^28203 115062 Hans Havermann 02/2021 5224 2^382198+9 115054 Lelio R Paula 03/2013 5225 30101^6630+6630^30101 115032 Hans Havermann 01/2021 5226 (89*10^115030-179)/9 115031 Robert Price 12/2019 5227 (2^381935+2774)/2 114974 Stefano Morozzi 02/2021 5228 27300^16271+16271^27300 114972 Hans Havermann 02/2021 5229 (23*10^114962+7)/3 114963 Robert Price 05/2023 5230 2^381883-59197 114959 Enzo Doria 10/2015 5231 27423^15542+15542^27423 114944 Hans Havermann 02/2021 5232 (2^381820+1626)/2 114939 Stefano Morozzi 09/2020 5234 2^381806-4481 114936 Yves Minet 07/2011 5233 2^381808-1851507 114936 Enzo Doria 08/2015 5235 (2^381792+2502)/2 114931 Stefano Morozzi 09/2020 5236 2^381774-112373 114926 Enzo Doria 06/2014 5237 26341^22980+22980^26341 114883 Hans Havermann 01/2021 5238 2^381555-109051 114860 Enzo Doria 04/2014 5239 2^381551+213683 114859 Enzo Doria 09/2023 5240 2^381546-113501 114857 Enzo Doria 08/2014 5241 (7*10^114845-19)/3 114846 Robert Price 10/2020 5242 26675^20178+20178^26675 114833 Hans Havermann 02/2021 5243 (2^381436+1182)/2 114824 Stefano Morozzi 09/2020 5244 3^240644+16 114817 Robert Price 04/2020 5245 2^381360-110429 114801 Enzo Doria 05/2014 5246 (17*10^114795+79)/3 114796 Robert Price 04/2019 5247 (66^63079+1)/67 114774 Paul Bourdelais 09/2017 5248 2^381252-115079 114769 Enzo Doria 06/2015 5249 (2^381251+3186)/2 114768 Stefano Morozzi 09/2020 5250 2^381209-29323 114756 Enzo Doria 07/2015

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 05 2023 08:12 (Time in France)

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