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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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
5001 | 2^403363-113635 | 121425 | Enzo Doria | 08/2014 |
5002 | 25531^27552-27552^25531 | 121424 | Frank Doornink | 02/2024 |
5003 | (17*10^121418-113)/3 | 121419 | Robert Price | 06/2021 |
5004 | 2^403336-1861469 | 121417 | Enzo Doria | 03/2016 |
5005 | 27929^22186+22186^27929 | 121382 | Hans Havermann | 02/2021 |
5006 | p(24442)#/2-64 | 121381 | Robert Price | 04/2017 |
5007 | 11^116555-720 | 121380 | Enzo Doria | 11/2012 |
5008 | 2^403100-461267 | 121346 | Enzo Doria | 07/2015 |
5009 | 2^403093-112213 | 121344 | Enzo Doria | 06/2014 |
5010 | 29404^13385+13385^29404 | 121340 | Hans Havermann | 02/2021 |
5011 | 28106^20745+20745^28106 | 121332 | Hans Havermann | 02/2021 |
5012 | (316^48539+1)/317 | 121330 | Eric Chen | 10/2017 |
5013 | (23*10^121320-71)/3 | 121321 | Robert Price | 07/2020 |
5014 | 2^403004+1866361 | 121317 | Enzo Doria | 03/2016 |
5015 | 2^402953+89 | 121301 | Lelio R Paula | 10/2013 |
5016 | 2^402944-2788319 | 121299 | Enzo Doria | 03/2016 |
5017 | (44*10^121297-719)/9 | 121298 | Robert Price | 12/2018 |
5018 | (27*2^402865+1)/5 | 121276 | Lelio R Paula | 04/2014 |
5019 | 2^402828-113183 | 121264 | Enzo Doria | 07/2014 |
5020 | (17*10^121242+1)/9 | 121243 | Serge Batalov | 05/2010 |
5021 | (15*2^402757+1)/101 | 121242 | Lelio R Paula | 05/2014 |
5023 | 2^402715+1874223 | 121230 | Enzo Doria | 06/2016 |
5022 | (35*10^121229-593)/9 | 121230 | Robert Price | 07/2018 |
5024 | (91^61879+1)/92 | 121222 | Paul Bourdelais | 09/2017 |
5025 | 28719^16568+16568^28719 | 121174 | Hans Havermann | 02/2021 |
5026 | 7*10^121144+9 | 121145 | Robert Price | 09/2015 |
5027 | 27490^25467+25467^27490 | 121121 | Hans Havermann | 02/2021 |
5028 | 34575^3182+3182^34575 | 121106 | Hans Havermann | 02/2021 |
5029 | 5*10^121100-37 | 121101 | Robert Price | 11/2021 |
5030 | 25592^27467-27467^25592 | 121078 | Frank Doornink | 02/2024 |
5031 | 29954^10935+10935^29954 | 120979 | Hans Havermann | 02/2021 |
5032 | 33585^3992+3992^33585 | 120946 | Hans Havermann | 02/2021 |
5033 | 40296^1003+1003^40296 | 120941 | Hans Havermann | 02/2021 |
5034 | 2^401725-113251 | 120932 | Enzo Doria | 07/2014 |
5035 | (15*2^401677-1)/19 | 120917 | Lelio R Paula | 05/2014 |
5036 | 2^401652+73711 | 120910 | Enzo Doria | 04/2016 |
5037 | (2^401632+3)/79 | 120902 | Lelio R Paula | 04/2014 |
5038 | 40450^973+973^40450 | 120870 | Hans Havermann | 01/2021 |
5039 | (8*10^120851-11)/3 | 120852 | Robert Price | 07/2023 |
5040 | 10^120841+88417 | 120842 | Patrick De Geest | 04/2020 |
5041 | 10^120841-123456789 | 120841 | Robert Price | 02/2020 |
5042 | 10^120841-176853 | 120841 | Patrick De Geest | 04/2020 |
5043 | 2^401406-2791331 | 120836 | Enzo Doria | 03/2016 |
5044 | (28^83497+1)/29 | 120832 | Robert Price | 07/2013 |
5045 | (22*10^120828+161)/3 | 120829 | Robert Price | 05/2019 |
5046 | 2^401369+1867367 | 120825 | Enzo Doria | 03/2016 |
5047 | (5*10^120821+43)/3 | 120822 | Robert Price | 12/2021 |
5048 | (10^120782+29)/3 | 120782 | Serge Batalov | 12/2014 |
5049 | 2^401215-1657 | 120778 | Yves Minet | 07/2014 |
5050 | 2^401159+53 | 120761 | Lelio R Paula | 10/2013 |
5051 | 27782^22179+22179^27782 | 120739 | Hans Havermann | 01/2021 |
5052 | 32974^4585+4585^32974 | 120730 | Hans Havermann | 02/2021 |
5053 | 2^401031-113047 | 120723 | Enzo Doria | 07/2014 |
5054 | 30598^8813+8813^30598 | 120713 | Hans Havermann | 02/2021 |
5055 | (71*10^120703-287)/9 | 120704 | Robert Price | 09/2019 |
5056 | 25671^27370-27370^25671 | 120687 | Frank Doornink | 02/2024 |
5057 | (29*2^400909-1)/303 | 120685 | Lelio R Paula | 04/2014 |
5058 | 34793^2940+2940^34793 | 120675 | Hans Havermann | 02/2021 |
5059 | 26028^27329-27329^26028 | 120670 | Frank Doornink | 03/2024 |
5060 | (2^400846+538)/2 | 120667 | Stefano Morozzi | 09/2020 |
5061 | (166*10^120654+11)/3 | 120656 | Robert Price | 03/2021 |
5062 | 34066^3481+3481^34066 | 120652 | Hans Havermann | 02/2021 |
5063 | 8*10^120637-27 | 120638 | Robert Price | 10/2021 |
5064 | (2^400709+3546)/2 | 120626 | Stefano Morozzi | 09/2020 |
5065 | (2^400700+3126)/2 | 120623 | Stefano Morozzi | 09/2020 |
5066 | (2^400693+2634)/2 | 120621 | Stefano Morozzi | 09/2020 |
5067 | 9*10^120617-61 | 120618 | Robert Price | 06/2021 |
5068 | (29*10^120590-71)/3 | 120591 | Robert Price | 07/2021 |
5069 | 2^400571-15 | 120584 | Lelio R Paula | 10/2013 |
5070 | (10^120574+359)/9 | 120574 | Serge Batalov | 12/2014 |
5071 | (8*10^120552-17)/9 | 120552 | Serge Batalov | 11/2022 |
5072 | 27431^24810+24810^27431 | 120550 | Hans Havermann | 02/2021 |
5073 | 2^400424-216413 | 120540 | Enzo Doria | 04/2013 |
5074 | 29090^13911+13911^29090 | 120531 | Hans Havermann | 02/2021 |
5075 | (2^400346+1722)/2 | 120516 | Stefano Morozzi | 09/2020 |
5076 | 27899^20868+20868^27899 | 120510 | Hans Havermann | 02/2021 |
5077 | 33740^3729+3729^33740 | 120506 | Hans Havermann | 02/2021 |
5078 | (17*2^400200-1)/587 | 120471 | Lelio R Paula | 05/2014 |
5079 | 2^400166+1874899 | 120462 | Enzo Doria | 06/2016 |
5080 | (2^400165+1602)/2 | 120462 | Stefano Morozzi | 09/2020 |
5081 | 37078^1771+1771^37078 | 120438 | Hans Havermann | 02/2021 |
5082 | (2^400084+1638)/2 | 120437 | Stefano Morozzi | 09/2020 |
5083 | (3*2^400045-1)/865 | 120424 | Lelio R Paula | 04/2014 |
5084 | 2^399999+54173 | 120412 | Norman Luhn | 08/2023 |
5085 | (2^399974+2790)/2 | 120404 | Stefano Morozzi | 02/2021 |
5086 | 2^399966+73759 | 120402 | Enzo Doria | 04/2016 |
5087 | (2^399961+2306)/2 | 120400 | Stefano Morozzi | 02/2021 |
5088 | (112*10^120395-1)/3 | 120397 | Serge Batalov | 12/2014 |
5089 | 2^399918-95 | 120388 | Lelio R Paula | 04/2013 |
5090 | 2^399918+214009 | 120388 | Enzo Doria | 10/2023 |
5091 | (28*10^120381-67)/3 | 120382 | Robert Price | 10/2020 |
5092 | (49*10^120380-139)/9 | 120381 | Robert Price | 03/2019 |
5093 | (2^399874+2194)/2 | 120374 | Stefano Morozzi | 09/2020 |
5094 | 2^399792-1849259 | 120350 | Enzo Doria | 08/2015 |
5095 | 9*10^120342-7 | 120343 | Robert Price | 09/2015 |
5096 | (2^399751+786)/2 | 120337 | Stefano Morozzi | 09/2020 |
5097 | (331*10^120332-7)/9 | 120334 | Robert Price | 04/2022 |
5098 | (13*10^120306-37)/3 | 120307 | Robert Price | 01/2019 |
5099 | (23*10^120299+37)/3 | 120300 | Robert Price | 02/2022 |
5100 | (2^399604+3070)/2 | 120293 | Stefano Morozzi | 09/2020 |
5101 | (2^399549+1062)/2 | 120276 | Stefano Morozzi | 09/2020 |
5102 | 2^399526-1861721 | 120270 | Enzo Doria | 11/2015 |
5103 | (10^(2*60126+1)+36*10^60126-1)/9 | 120253 | Robert Price | 10/2015 |
5104 | 32016^5687+5687^32016 | 120217 | Hans Havermann | 01/2021 |
5105 | (205*10^120212-1)/3 | 120214 | Robert Price | 11/2021 |
5106 | 2^399322-2798111 | 120208 | Enzo Doria | 04/2016 |
5107 | 30438^8867+8867^30438 | 120163 | Hans Havermann | 02/2021 |
5108 | 3^251841-5*2^251841 | 120159 | Jon Grantham | 08/2023 |
5110 | 72^64693-71^64693 | 120157 | Robert Price | 03/2014 |
5109 | (17*10^120156-161)/9 | 120157 | Robert Price | 02/2021 |
5111 | 2^399111-28489 | 120145 | Enzo Doria | 08/2015 |
5112 | (2^399014+1318)/2 | 120115 | Stefano Morozzi | 02/2021 |
5113 | 30254^9333+9333^30254 | 120110 | Hans Havermann | 02/2021 |
5114 | 30882^7745+7745^30882 | 120101 | Hans Havermann | 02/2021 |
5116 | 2^398877+105 | 120074 | Donovan Johnson | 01/2006 |
5115 | (101*10^120072-87)/7 | 120074 | Hans Havermann | 02/2015 |
5117 | (88^61751+1)/89 | 120072 | Paul Bourdelais | 09/2017 |
5118 | 2^398710+57 | 120024 | Lelio R Paula | 04/2013 |
5119 | (2^398698+1138)/2 | 120020 | Stefano Morozzi | 09/2020 |
5120 | 2^398691-115057 | 120018 | Enzo Doria | 06/2015 |
5121 | L(574219) | 120005 | Renaud Lifchitz | 03/2004 |
5122 | 2^398571+60413 | 119982 | Yves Minet | 03/2011 |
5123 | 28623^15538+15538^28623 | 119971 | Hans Havermann | 02/2021 |
5124 | p(24179)#/2-64 | 119949 | Robert Price | 04/2017 |
5125 | 2^398448+1872001 | 119945 | Enzo Doria | 05/2016 |
5126 | (10^119946*19-91)/6093 | 119944 | Alfred Reich | 10/2023 |
5127 | (19*10^119946-91)/9/677 | 119944 | Alfred Reich | 11/2023 |
5128 | (191*10^119941-17)/3 | 119943 | Robert Price | 11/2021 |
5129 | 634^42803+42803^634 | 119938 | Norbert Schneider | 07/2019 |
5130 | 31083^7220+7220^31083 | 119935 | Hans Havermann | 01/2021 |
5131 | (68*10^119931-11)/3 | 119933 | Robert Price | 01/2020 |
5132 | 8*10^119930-3 | 119931 | Ray Chandler | 04/2011 |
5133 | (2^398398+774)/2 | 119930 | Stefano Morozzi | 09/2020 |
5134 | (10^119880+179)/9 | 119880 | Serge Batalov | 12/2014 |
5135 | (9*2^398145+1)/73 | 119853 | Lelio R Paula | 04/2014 |
5136 | (10^119836+77)/3 | 119836 | Robert Price | 01/2018 |
5137 | 28179^17870+17870^28179 | 119821 | Hans Havermann | 02/2021 |
5138 | 2^398029+1872527 | 119819 | Enzo Doria | 05/2016 |
5139 | 33142^4119+4119^33142 | 119802 | Hans Havermann | 01/2021 |
5140 | 2^397897-113541 | 119779 | Enzo Doria | 08/2014 |
5141 | 28636^15171+15171^28636 | 119728 | Hans Havermann | 02/2021 |
5142 | (10556^29929-1)/(10556^173-1) | 119724 | Ryan Propper | 11/2023 |
5143 | (2^397696+1042)/2 | 119719 | Stefano Morozzi | 09/2020 |
5145 | (19*10^119716+101)/3 | 119717 | Robert Price | 09/2019 |
5144 | 29563^11208+11208^29563 | 119717 | Hans Havermann | 02/2021 |
5146 | 2^397655-933075 | 119707 | Paul Bourdelais | 06/2021 |
5147 | (21*2^397661-1)/27593 | 119705 | Lelio R Paula | 04/2014 |
5148 | 28243^17308+17308^28243 | 119701 | Hans Havermann | 02/2021 |
5149 | 77*10^119688+3 | 119690 | Robert Price | 06/2020 |
5150 | 586*25^85601+3717 | 119668 | Eric Chen | 10/2023 |
5151 | (2^397504+1698)/2 | 119661 | Stefano Morozzi | 09/2020 |
5152 | (58^67853-1)/57 | 119653 | Paul Bourdelais | 09/2017 |
5153 | 2^397426+73849 | 119638 | Enzo Doria | 04/2016 |
5154 | 8*10^119509+29 | 119510 | Robert Price | 11/2021 |
5155 | 2^396933-112723 | 119489 | Enzo Doria | 06/2014 |
5156 | 11^114738-150 | 119488 | Enzo Doria | 10/2012 |
5157 | (4*10^119474+149)/9 | 119474 | Robert Price | 04/2018 |
5158 | 2^396790-21 | 119446 | Lelio R Paula | 04/2013 |
5159 | 32061^5300+5300^32061 | 119405 | Hans Havermann | 01/2021 |
5160 | (2^396633-7)/5 | 119398 | Lelio R Paula | 04/2014 |
5161 | 27382^22913+22913^27382 | 119388 | Hans Havermann | 03/2021 |
5162 | (2^396577+2522)/2 | 119382 | Stefano Morozzi | 09/2020 |
5163 | (2^396492+2230)/2 | 119356 | Stefano Morozzi | 01/2021 |
5164 | (47*10^119354+259)/9 | 119355 | Robert Price | 03/2022 |
5166 | 105^59050+104 | 119352 | Norbert Schneider | 11/2016 |
5165 | 126^56824-125 | 119352 | Norbert Schneider | 12/2018 |
5167 | 2^396469+111546435 | 119350 | Paul Bourdelais | 10/2021 |
5168 | 139^55690-138 | 119345 | Norbert Schneider | 04/2019 |
5169 | 790^41179+41179^790 | 119322 | Norbert Schneider | 04/2019 |
5170 | 2^396374+73729 | 119321 | Enzo Doria | 04/2016 |
5171 | 88*10^119295+3 | 119297 | Robert Price | 05/2020 |
5172 | 2^396258-459491 | 119286 | Enzo Doria | 05/2015 |
5173 | (2^396248+3126)/2 | 119283 | Stefano Morozzi | 09/2020 |
5174 | 2^396128-396128-1 | 119247 | Karsten Bonath | 06/2018 |
5176 | (893*10^119228+7)/9 | 119230 | Robert Price | 06/2021 |
5175 | (31*10^119229+257)/9 | 119230 | Robert Price | 12/2021 |
5177 | (28*10^119206-67)/3 | 119207 | Robert Price | 10/2020 |
5178 | (2^395986+5)/76881 | 119199 | Lelio R Paula | 04/2014 |
5179 | 11^114458+6 | 119196 | Paul Bourdelais | 02/2021 |
5180 | (23*2^395942-1)/91 | 119190 | Lelio R Paula | 04/2014 |
5181 | (2^395902+202)/2 | 119179 | Stefano Morozzi | 09/2020 |
5182 | (2^395825+582)/2 | 119155 | Stefano Morozzi | 09/2020 |
5183 | (2^395733+1130)/2 | 119128 | Stefano Morozzi | 09/2020 |
5184 | 29548^10725+10725^29548 | 119091 | Hans Havermann | 02/2021 |
5185 | (11*2^395548+1)/3 | 119073 | Lelio R Paula | 04/2014 |
5186 | (30^80599+1)/31 | 119054 | Robert Price | 07/2013 |
5187 | (232*10^119047+17)/3 | 119049 | Robert Price | 04/2021 |
5188 | (43*10^119024-403)/9 | 119025 | Robert Price | 01/2019 |
5189 | (4*10^119021+47)/3 | 119022 | Robert Price | 01/2022 |
5190 | fibonacci(569433)+3 | 119005 | Jon Grantham | 08/2023 |
5191 | 26603^26888-26888^26603 | 118978 | Norbert Schneider | 07/2021 |
5192 | 6*10^118964+43 | 118965 | Robert Price | 07/2020 |
5193 | (8*10^118960+49)/3 | 118961 | Robert Price | 05/2020 |
5194 | 31253^6402+6402^31253 | 118959 | Hans Havermann | 02/2021 |
5195 | (194*10^118925-17)/3 | 118927 | Robert Price | 09/2020 |
5196 | 2^395062-109121 | 118926 | Enzo Doria | 04/2014 |
5197 | 2^395055-4627 | 118924 | Yves Minet | 05/2019 |
5198 | (2^395054+702)/2 | 118923 | Stefano Morozzi | 09/2020 |
5199 | 2^395018-224141 | 118913 | Harrison Mesh | 06/2022 |
5200 | (2^395011+2526)/2 | 118910 | Stefano Morozzi | 09/2020 |
5201 | (2^394918+78557)/3 | 118882 | Lelio R Paula | 01/2015 |
5202 | 25771^26948-26948^25771 | 118872 | Frank Doornink | 02/2024 |
5203 | (2^394858+1018)/2 | 118864 | Stefano Morozzi | 09/2020 |
5204 | (77*10^118862-149)/9 | 118863 | Robert Price | 03/2022 |
5205 | (16*10^118852+77)/3 | 118853 | Robert Price | 03/2019 |
5206 | fibonacci(568658)-2 | 118843 | Jon Grantham | 08/2023 |
5207 | (2^394739+3)/1883 | 118826 | Lelio R Paula | 04/2014 |
5208 | 10^118772+163599 | 118773 | Patrick De Geest | 02/2021 |
5210 | 10^118772-40000000001 | 118772 | Robert Price | 09/2020 |
5209 | 10^118772-207603 | 118772 | Patrick De Geest | 02/2021 |
5211 | 26842^26577+26577^26842 | 118763 | Hans Havermann | 02/2021 |
5212 | (2^394513+2034)/2 | 118760 | Stefano Morozzi | 09/2020 |
5213 | (2^394473+2774)/2 | 118748 | Stefano Morozzi | 02/2021 |
5214 | 27949^17710+17710^27949 | 118734 | Hans Havermann | 02/2021 |
5215 | 2^394266+71389 | 118686 | Enzo Doria | 04/2016 |
5216 | (10^118681-3^118681)/7 | 118681 | Jon Grantham | 08/2023 |
5217 | 2^394215-51261 | 118671 | Tony Prest / Never Odd Or Even | 04/2018 |
5218 | (2^394215-48793)/5/5 | 118670 | Tony Prest / Never Odd Or Even | 04/2018 |
5219 | (2^394215-17063)/3/3/5 | 118669 | Tony Prest / Never Odd Or Even | 04/2018 |
5220 | (2^394215-24393)/5/5/5/5/5 | 118668 | Tony Prest / Never Odd Or Even | 04/2018 |
5221 | (2^394215-35885)/3/71/173 | 118666 | Tony Prest / Never Odd Or Even | 04/2018 |
5222 | (2^394215-47925)/353/2269 | 118665 | Tony Prest / Never Odd Or Even | 04/2018 |
5223 | 29201^11568+11568^29201 | 118652 | Hans Havermann | 02/2021 |
5224 | (2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673 | 118650 | Tony Prest / Never Odd Or Even | 04/2018 |
5225 | (2^394131+2214)/2 | 118645 | Stefano Morozzi | 09/2020 |
5226 | (17*10^118635+13)/3 | 118636 | Robert Price | 01/2019 |
5227 | 5^169727+2 | 118635 | Lelio R Paula | 08/2013 |
5228 | 2^394034-3 | 118617 | M. Frind & P. Underwood | 09/2002 |
5229 | (7*10^118607+179)/3 | 118608 | Robert Price | 09/2018 |
5230 | 3^248572-6242 | 118599 | Enzo Doria | 05/2014 |
5231 | (3*2^393964-1)/181 | 118594 | Lelio R Paula | 04/2014 |
5232 | (49*10^118576-319)/9 | 118577 | Robert Price | 10/2021 |
5233 | 7^140303-6 | 118570 | Robert Price | 11/2014 |
5234 | (2^393864+2686)/2 | 118565 | Stefano Morozzi | 09/2020 |
5235 | (2^393862+3150)/2 | 118564 | Stefano Morozzi | 09/2020 |
5236 | (2^393849+3762)/2 | 118561 | Stefano Morozzi | 01/2021 |
5237 | (529*10^118554-7)/9 | 118556 | Robert Price | 08/2021 |
5238 | 26712^26777-26777^26712 | 118534 | Norbert Schneider | 07/2021 |
5239 | (2^393661+2666)/2 | 118504 | Stefano Morozzi | 09/2020 |
5240 | (2^393650+1614)/2 | 118501 | Stefano Morozzi | 09/2020 |
5241 | 27655^19264+19264^27655 | 118495 | Hans Havermann | 02/2021 |
5242 | 10^118485+469413 | 118486 | Patrick De Geest | 05/2021 |
5243 | 10^118485-50001 | 118485 | Robert Price | 08/2020 |
5244 | (2^393528+1030)/2 | 118464 | Stefano Morozzi | 09/2020 |
5245 | 2^393427+75683 | 118434 | Enzo Doria | 04/2016 |
5246 | 2^393376-114749 | 118418 | Enzo Doria | 04/2015 |
5247 | (65*10^118417+493)/9 | 118418 | Robert Price | 08/2021 |
5248 | 30960^6671+6671^30960 | 118397 | Hans Havermann | 02/2021 |
5249 | (2^393234+2010)/2 | 118375 | Stefano Morozzi | 09/2020 |
5250 | (2^393205+3030)/2 | 118367 | Stefano Morozzi | 09/2020 |