## PRP Records

### Probable Primes Top 10000

#### (295148 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 ? 4001 2^458248-21815 137947 Enzo Doria 07/2013 4002 2^458194+1876549 137931 Enzo Doria 07/2016 4003 (318259#+325270)/(2^2*5*11*2957) 137907 Makoto Morimoto 10/2017 4004 (318259#+2625)/(3^2*5*7^5*22965193) 137899 Makoto Morimoto 06/2019 4005 (793*10^137887+53)/9 137889 Robert Price 01/2022 4006 2^457937+57 137853 Lelio R Paula 09/2017 4007 28714^30921-30921^28714 137849 Frank Doornink 05/2024 4008 (8*10^137845+13)/3 137846 Robert Price 06/2018 4009 2^457822+105 137819 Donovan Johnson 06/2006 4010 2^457754-113711 137798 Enzo Doria 09/2014 4011 11^132315-360 137792 Enzo Doria 09/2012 4012 32072^19689+19689^32072 137725 Hans Havermann 06/2021 4013 26529^31132-31132^26529 137720 Frank Doornink 03/2024 4014 44592^1225+1225^44592 137707 Hans Havermann 05/2021 4015 28986^30857-30857^28986 137690 Frank Doornink 05/2024 4016 2^457347-37 137676 Lelio R Paula 09/2017 4017 2^457322-2786393 137668 Enzo Doria 10/2015 4018 gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901) 137664 Serge Batalov 04/2015 4019 34015^11134+11134^34015 137647 Hans Havermann 06/2021 4020 2^457240-59939 137643 Enzo Doria 10/2015 4021 (856*10^137633-1)/9 137635 Robert Price 03/2020 4022 36232^6289+6289^36232 137631 Hans Havermann 05/2021 4023 2^457120-21575 137607 Enzo Doria 07/2013 4025 (11*2^456978+1)/15 137564 Lelio R Paula 07/2015 4024 30963^27722+27722^30963 137564 Hans Havermann 04/2021 4026 33722^12003+12003^33722 137562 Hans Havermann 06/2021 4027 (7*25^98399+10613)/12 137556 Curtis Bright 05/2015 4028 41901^1918+1918^41901 137555 Hans Havermann 06/2021 4029 (7*10^137551-1)/3 137552 Robert Price 08/2022 4030 32930^15021+15021^32930 137539 Hans Havermann 05/2021 4031 31178^25785+25785^31178 137538 Hans Havermann 05/2021 4032 419^52446+52446^419 137525 Norbert Schneider 11/2020 4033 2^456813+214175 137515 Enzo Doria 10/2023 4034 2^456796-113513 137510 Enzo Doria 08/2014 4035 31788^21137+21137^31788 137485 Hans Havermann 04/2021 4036 (7*2^456655+1)/39 137467 Lelio R Paula 07/2015 4037 27151^31004-31004^27151 137466 Frank Doornink 01/2024 4038 2^456503-114361 137422 Enzo Doria 01/2015 4039 (11*2^456387+1)/19 137386 Lelio R Paula 07/2015 4040 30618^30618-5^5 137352 Serge Batalov 04/2024 4041 36248^6147+6147^36248 137332 Hans Havermann 05/2021 4042 31986^19651+19651^31986 137329 Hans Havermann 05/2021 4043 2^456167+22313 137320 Enzo Doria 09/2023 4044 31817^20656+20656^31817 137292 Hans Havermann 05/2021 4045 (71*10^137250+1)/9 137251 Serge Batalov 05/2010 4046 2^455922+76249 137247 Enzo Doria 05/2016 4047 31310^24171+24171^31310 137241 Hans Havermann 05/2021 4048 14^119741-119741^14 137239 Serge Batalov 04/2016 4049 35014^8297+8297^35014 137218 Hans Havermann 05/2021 4050 (19*2^455760+1)/3455 137196 Lelio R Paula 07/2015 4052 124^(2^16)+57^(2^16) 137195 Valeryi Kuryshev 02/2011 4051 124^65536+57^65536 137195 Serge Batalov 03/2018 4053 2^455689+72677 137177 Enzo Doria 04/2016 4054 (17948!)^2+Prime(17948) 137118 Robert Price 08/2014 4055 31287^24128+24128^31287 137116 Hans Havermann 05/2021 4056 (37^87421-1)/36 137093 Robert Price 03/2012 4057 36233^6070+6070^36233 137077 Hans Havermann 05/2021 4058 (8*10^137073-17)/9 137073 Serge Batalov 11/2022 4059 38418^3697+3697^38418 137070 Hans Havermann 04/2021 4060 2^455323-57 137066 Lelio R Paula 09/2017 4061 (56*10^137019+583)/9 137020 Robert Price 08/2021 4062 25017^31148-31148^25017 136997 Frank Doornink 12/2023 4063 (73*17^111333-9)/16 136991 Curtis Bright 05/2015 4064 2^455025-112723 136977 Enzo Doria 06/2014 4065 33876^11039+11039^33876 136959 Hans Havermann 05/2021 4066 (19860^32041-1)/(19860^179-1) 136943 Ryan Propper 11/2023 4067 (251^57059-1)/250 136921 Anonymous 04/2024 4068 35142^7873+7873^35142 136919 Hans Havermann 05/2021 4069 (4997*31^91805-1)/2 136918 Eric Chen 05/2024 4070 66*10^136894+7 136896 Robert Price 07/2020 4071 28766^30697-30697^28766 136875 Frank Doornink 05/2024 4072 2^454675-1777 136871 Yves Minet 10/2011 4073 31676^20931+20931^31676 136866 Hans Havermann 05/2021 4074 3*10^136829+29 136830 Robert Price 05/2018 4075 4*10^136813-57 136814 Robert Price 10/2018 4076 (6092*28^94536-143)/9 136812 Curtis Bright 05/2015 4077 fibonacci(654572)-2 136798 Jon Grantham 08/2023 4078 37359^4588+4588^37359 136795 Hans Havermann 05/2021 4079 2^454348-53 136773 Lelio R Paula 09/2017 4080 31^91680-2 136729 Lelio R Paula 05/2017 4081 2^454199-113697 136728 Enzo Doria 09/2014 4082 30785^27622+27622^30785 136725 Hans Havermann 05/2021 4083 32973^14014+14014^32973 136725 Hans Havermann 05/2021 4085 7*10^136716+69 136717 Robert Price 07/2019 4084 36002^6273+6273^36002 136717 Hans Havermann 05/2021 4086 6*10^136692+53 136693 Robert Price 05/2020 4087 (13*10^136687+47)/3 136688 Robert Price 10/2018 4088 2^453935-2791357 136649 Enzo Doria 01/2016 4089 2^453906-69131 136640 Enzo Doria 11/2015 4090 33232^12915+12915^33232 136620 Hans Havermann 05/2021 4091 2^453791+1873913 136605 Enzo Doria 06/2016 4092 34166^9951+9951^34166 136592 Hans Havermann 05/2021 4093 (21*2^453740-1)/2735 136588 Lelio R Paula 07/2015 4094 31102^24635+24635^31102 136587 Hans Havermann 05/2021 4095 580^49413+49413^580 136550 Norbert Schneider 02/2019 4096 2^453503-2788297 136519 Enzo Doria 11/2015 4097 34989^7958+7958^34989 136486 Hans Havermann 12/2020 4098 (2*10^136484+187)/9 136484 Robert Price 06/2022 4099 31007^25158+25158^31007 136452 Hans Havermann 11/2020 4100 2^453267-113827 136447 Enzo Doria 09/2014 4101 32234^17085+17085^32234 136435 Hans Havermann 12/2020 4102 2^453102+1877629 136398 Enzo Doria 08/2016 4103 31016^24981+24981^31016 136397 Hans Havermann 12/2020 4104 (62*10^136384-791)/9 136385 Robert Price 06/2019 4105 34171^9798+9798^34171 136382 Hans Havermann 12/2020 4106 (17*10^136354-113)/3 136355 Robert Price 06/2021 4107 32756^14541+14541^32756 136350 Hans Havermann 11/2020 4108 32205^17086+17086^32205 136313 Hans Havermann 12/2020 4109 (25*10^136303+161)/3 136304 Robert Price 09/2019 4110 35337^7196+7196^35337 136299 Hans Havermann 12/2020 4111 (182*10^136291+1)/3 136293 Robert Price 02/2020 4112 (88*10^136234+83)/9 136235 Robert Price 03/2022 4113 23*10^136225-7 136227 Robert Price 02/2020 4114 L(651821) 136223 Henri Lifchitz 09/2008 4115 25519^30908-30908^25519 136208 Frank Doornink 02/2024 4116 2^452460+77701 136205 Enzo Doria 05/2016 4117 2^452440-114755 136199 Enzo Doria 04/2015 4118 28625^30558-30558^28625 136190 Frank Doornink 05/2024 4119 32286^16489+16489^32286 136157 Hans Havermann 11/2020 4120 (47*10^136141+493)/9 136142 Robert Price 03/2019 4121 27140^30699-30699^27140 136108 Frank Doornink 01/2024 4122 40392^2339+2339^40392 136082 Hans Havermann 12/2020 4123 2*10^136057-43 136058 Robert Price 04/2018 4124 2^451971+21563 136057 Enzo Doria 08/2023 4125 (2^451956-5)/181 136051 Lelio R Paula 07/2015 4126 2^451947-22165 136050 Enzo Doria 07/2013 4127 2^451787-21805 136002 Enzo Doria 07/2013 4128 2^451734-112817 135986 Enzo Doria 06/2014 4129 (11*2^451714+1)/75 135979 Lelio R Paula 07/2015 4130 2^451705-21879 135977 Enzo Doria 07/2013 4131 (4666^37249-1)/(4666^193-1) 135957 Ryan Propper 11/2023 4132 2^451560-112349 135934 Enzo Doria 06/2014 4133 2^451530+45 135925 Lelio R Paula 08/2017 4134 26594^30719-30719^26594 135925 Frank Doornink 03/2024 4135 31622^19875+19875^31622 135922 Hans Havermann 11/2020 4136 (25*10^135906-73)/3 135907 Robert Price 09/2019 4137 2^451450-21743 135900 Enzo Doria 07/2013 4138 (7*10^135879+11)/9 135879 Tyler Busby 01/2023 4139 35218^7199+7199^35218 135846 Hans Havermann 11/2020 4140 35661^6446+6446^35661 135844 Hans Havermann 11/2020 4141 (7*33^89453-4743239)/32 135835 Eric Chen 12/2023 4142 31869^18248+18248^31869 135801 Hans Havermann 12/2020 4143 (77*10^135789+157)/9 135790 Robert Price 05/2022 4144 2^450958+60529 135752 Enzo Doria 08/2023 4145 2^450805+65 135706 Lelio R Paula 08/2017 4146 30761^25728+25728^30761 135669 Hans Havermann 12/2020 4147 2*10^135663+69 135664 Robert Price 06/2020 4148 33962^9867+9867^33962 135651 Hans Havermann 11/2020 4149 34474^8605+8605^34474 135647 Hans Havermann 11/2020 4150 34501^8508+8508^34501 135583 Hans Havermann 12/2020 4151 35487^6614+6614^35487 135577 Hans Havermann 12/2020 4152 (13725^32768+1)/131074 135573 Lelio R Paula 03/2012 4153 (313007#+121876)/(2*30469*424867) 135559 Makoto Morimoto 08/2020 4154 (5^193939+1)/6 135557 Paul Bourdelais 12/2008 4155 (76*10^135553-49)/9 135554 Robert Price 07/2022 4156 5*3^284077+2^284077 135540 Jon Grantham 08/2023 4157 (844*10^135527-7)/9 135529 Robert Price 05/2021 4158 27191^30560-30560^27191 135517 Frank Doornink 01/2024 4159 40387^2260+2260^40387 135463 Hans Havermann 12/2020 4160 2^449944-113247 135447 Enzo Doria 07/2014 4161 2^449770-113247 135395 Enzo Doria 07/2014 4162 2^449637-21471 135355 Enzo Doria 07/2013 4163 26061^30650-30650^26061 135351 Frank Doornink 03/2024 4164 2^449571-75 135335 Lelio R Paula 08/2017 4165 (14*10^135301-53)/3 135302 Robert Price 12/2018 4166 (3*2^449494+1)/61340334013 135301 Lelio R Paula 07/2015 4167 (13*10^135279+437)/9 135280 Robert Price 04/2018 4168 2^449330-35 135262 Lelio R Paula 08/2017 4169 (19*2^449325+1)/9 135261 Lelio R Paula 07/2015 4170 (2709^39601+1)/(2709^199+1) 135260 Martin Hopf 12/2023 4171 (13*10^135184-43)/3 135185 Robert Price 11/2018 4172 2^449049-115309 135178 Enzo Doria 07/2015 4173 (10^135174+191)/3 135174 Robert Price 02/2018 4174 2^449030-15 135172 Lelio R Paula 08/2017 4175 (157*10^135151-1)/3 135153 Robert Price 01/2022 4176 (2^448966+100280245065) 135153 Paul Bourdelais 05/2022 4177 (27*2^448936-1)/11 135144 Lelio R Paula 07/2015 4178 (37*10^135099+251)/9 135100 Robert Price 09/2021 4179 32221^15586+15586^32221 135095 Hans Havermann 12/2020 4180 2^448762-351401 135091 Enzo Doria 07/2015 4181 2*10^135083-43 135084 Robert Price 04/2018 4182 31357^20278+20278^31357 135056 Hans Havermann 12/2020 4183 32242^15445+15445^32242 135055 Hans Havermann 12/2020 4184 k(198476) 135054 Robert Price 07/2020 4185 32461^14470+14470^32461 135053 Hans Havermann 12/2020 4186 31353^20288+20288^31353 135045 Hans Havermann 12/2020 4187 5*10^135019+77 135020 Robert Price 12/2018 4188 (10^135011+719)/9 135011 Serge Batalov 12/2014 4189 (197*10^134978+7)/3 134980 Robert Price 12/2020 4190 2^448386-2786261 134978 Enzo Doria 03/2016 4191 26480^30517-30517^26480 134975 Frank Doornink 03/2024 4192 (73*10^134939+143)/9 134940 Robert Price 07/2019 4193 33957^9392+9392^33957 134903 Hans Havermann 12/2020 4194 2^448122+20809 134899 Enzo Doria 08/2023 4195 2^448113-113949 134896 Enzo Doria 11/2014 4196 30958^22755+22755^30958 134887 Hans Havermann 12/2020 4197 2^447888-2786639 134828 Enzo Doria 03/2016 4198 2^447870-396765 134823 Enzo Doria 07/2013 4199 10^(2*67404+1)-10^67404-1 134809 Robert Price 07/2023 4200 2^447766-21791 134791 Enzo Doria 07/2013 4201 (19*10^134786-49)/3 134787 Robert Price 05/2019 4202 Phi(202173,10)/10064306514895399941409 134758 Makoto Kamada 05/2019 4203 (23*2^447647+1)/155 134755 Lelio R Paula 07/2015 4204 2^447552-1019 134727 Yves Minet 02/2014 4205 (2*10^134720-41)/3 134720 Robert Price 02/2018 4206 (25*10^134695-97)/9 134696 Robert Price 01/2022 4207 2^447437-113569 134692 Enzo Doria 08/2014 4208 2^447426-65 134689 Lelio R Paula 08/2017 4209 2^447357-2797573 134668 Enzo Doria 04/2016 4210 2^447278+93 134645 Lelio R Paula 08/2017 4211 33193^11370+11370^33193 134623 Hans Havermann 12/2020 4212 30736^23979+23979^30736 134619 Hans Havermann 11/2020 4213 2^447094-113193 134589 Enzo Doria 07/2014 4214 3^282041-9934 134568 Enzo Doria 05/2014 4215 2^447019-109039 134567 Enzo Doria 04/2014 4216 31376^19437+19437^31376 134561 Hans Havermann 12/2020 4217 2^446990-22041 134558 Enzo Doria 07/2013 4218 123^64370+122 134528 Karsten Bonath 04/2018 4219 30100^29461+29461^30100 134525 Hans Havermann 11/2020 4220 31251^20158+20158^31251 134519 Hans Havermann 11/2020 4221 2^446782-39701 134495 Enzo Doria 09/2015 4222 31817^16858+16858^31817 134485 Hans Havermann 12/2020 4223 32448^13937+13937^32448 134471 Hans Havermann 12/2020 4224 5^192321+3^192321-1 134427 Jon Grantham 08/2023 4225 2^446494-16485 134409 Enzo Doria 04/2013 4226 30042^29785+29785^30042 134408 Hans Havermann 12/2020 4227 29504^30069-30069^29504 134405 Norbert Schneider 12/2014 4228 2^446441+65 134393 Lelio R Paula 08/2017 4229 (10^134385+719)/9 134385 Serge Batalov 12/2014 4230 30043^29688+29688^30043 134370 Hans Havermann 12/2020 4231 (2*10^134364+529)/9 134364 Robert Price 01/2018 4232 34657^7512+7512^34657 134323 Hans Havermann 11/2020 4233 (13*2^446187-1)/661 134314 Lelio R Paula 07/2015 4234 5^192103+3^192103+2^192103+1 134275 Matthias Baur 12/2019 4235 42035^1564+1564^42035 134270 Hans Havermann 12/2020 4237 (2^446022-7)/339 134264 Lelio R Paula 07/2015 4236 30621^24248+24248^30621 134264 Hans Havermann 12/2020 4238 30341^26562+26562^30341 134237 Hans Havermann 11/2020 4239 10^134209+99867 134210 Patrick De Geest 05/2021 4240 10^134209-80000001 134209 Robert Price 04/2021 4241 10^134209-323283 134209 Patrick De Geest 05/2021 4242 29976^29953+29953^29976 134186 Hans Havermann 12/2020 4243 35038^6755+6755^35038 134183 Hans Havermann 12/2020 4244 63^74568+2 134174 Lelio R Paula 06/2017 4245 2^445671-22071 134161 Enzo Doria 07/2013 4246 532^49205+49205^532 134129 Norbert Schneider 02/2019 4247 36453^4780+4780^36453 134127 Hans Havermann 04/2021 4248 (28*10^134122-1)/9 134123 Serge Batalov 10/2014 4249 2^445515-113859 134114 Enzo Doria 10/2014 4250 31083^20636+20636^31083 134112 Hans Havermann 04/2021

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 20 2024 09:22 (Time in France)

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