## PRP Records

### Probable Primes Top 10000

#### (295829 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) !!!

See the Top discoverers
See the Latest PRPs
Search by form

 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 2^466829-459523 140530 Enzo Doria 05/2015 4002 2^466692-113213 140489 Enzo Doria 07/2014 4003 23*10^140464-3 140466 Robert Price 10/2021 4004 (2*10^140461-17)/3 140461 Serge Batalov 11/2022 4005 31335^30364+30364^31335 140455 Hans Havermann 05/2021 4006 28511^31524-31524^28511 140440 Frank Doornink 06/2024 4007 32795^19126+19126^32795 140416 Hans Havermann 05/2021 4008 (44*10^140410-503)/9 140411 Robert Price 12/2018 4009 28332^31535-31535^28332 140403 Frank Doornink 06/2024 4010 153^64265-2 140400 Lelio R Paula 11/2017 4011 30323^31322-31322^30323 140379 Frank Doornink 06/2024 4012 (112*10^140357-1)/3 140359 Serge Batalov 12/2014 4013 (29*10^140337-17)/3 140338 Robert Price 09/2019 4014 2^466181-112735 140335 Enzo Doria 07/2014 4015 (16*10^140290-37)/3 140291 Robert Price 05/2021 4016 (5*10^140281-119)/3 140282 Robert Price 03/2018 4017 34568^11415+11415^34568 140259 Hans Havermann 05/2021 4018 (27*2^465872+1)/691 140241 Lelio R Paula 08/2015 4019 33632^14781+14781^33632 140236 Hans Havermann 05/2021 4020 31803^25670+25670^31803 140233 Hans Havermann 05/2021 4021 2^465803-114817 140221 Enzo Doria 05/2015 4022 floor(Pi*10^140344)%10^140165 140165 Serge Batalov 08/2012 4023 2^465503-112735 140131 Enzo Doria 07/2014 4024 (16*10^140091+167)/3 140092 Robert Price 06/2019 4025 (8*10^140087-137)/3 140088 Robert Price 03/2022 4026 6^179964+179964^6-1 140040 Robert Price 04/2014 4027 (89*10^140008-179)/9 140009 Robert Price 12/2019 4028 (29*2^465077-1)/9 140003 Lelio R Paula 08/2015 4029 2^465072-344789 140001 Enzo Doria 07/2015 4030 34742^10683+10683^34742 139965 Hans Havermann 05/2021 4031 5*10^139945+81 139946 Robert Price 03/2019 4032 32648^19335+19335^32648 139941 Hans Havermann 05/2021 4033 2^464864-17 139939 Lelio R Paula 09/2017 4034 8*10^139920+51 139921 Robert Price 08/2019 4035 (85*10^139913-1)/3 139915 Robert Price 02/2020 4036 31203^30436+30436^31203 139896 Hans Havermann 04/2021 4037 2^464642+22189 139872 Enzo Doria 09/2023 4038 26138^31663-31663^26138 139865 Frank Doornink 03/2024 4039 (16^116139+619)/5 139845 Anonymous 08/2022 4040 (2^464556+619)/5 139845 Eric Chen 10/2023 4041 4*10^139839-27 139840 Robert Price 08/2021 4042 33582^14573+14573^33582 139821 Hans Havermann 05/2021 4043 (17^113621+1)/18 139804 Paul Bourdelais 09/2011 4045 2*10^139800-21 139801 Robert Price 09/2020 4044 32628^19261+19261^32628 139801 Hans Havermann 04/2021 4046 (13*10^139782+191)/3 139783 Robert Price 11/2018 4047 (64*10^139776+791)/9 139777 Robert Price 01/2022 4048 (695*10^139772+7)/9 139774 Robert Price 12/2021 4049 (19*2^464312-1)/3 139773 Lelio R Paula 08/2015 4050 (74*10^139723+133)/9 139724 Robert Price 06/2019 4051 3*10^139722+13 139723 Robert Price 07/2018 4052 31577^26592+26592^31577 139721 Hans Havermann 05/2021 4053 77*10^139692+3 139694 Robert Price 06/2020 4054 (31*2^463970+1)/5 139670 Lelio R Paula 08/2015 4055 (18203^(2^15)+(18201)^(2^15))/2 139597 Robert Price 05/2018 4056 39640^3321+3321^39640 139584 Hans Havermann 05/2021 4057 36663^6410+6410^36663 139571 Hans Havermann 05/2021 4058 2^463633-2788423 139568 Enzo Doria 11/2015 4059 33659^13978+13978^33659 139532 Hans Havermann 05/2021 4060 31811^24318+24318^31811 139521 Hans Havermann 04/2021 4061 34149^12172+12172^34149 139512 Hans Havermann 04/2021 4062 (29*10^139476+313)/9 139477 Robert Price 04/2021 4063 31721^24940+24940^31721 139474 Hans Havermann 05/2021 4064 32833^17698+17698^32833 139473 Hans Havermann 05/2021 4065 2^463271-109501 139459 Enzo Doria 04/2014 4066 (5*10^139457+79)/3 139458 Robert Price 03/2018 4067 2^463237-99 139449 Lelio R Paula 09/2017 4068 (49*10^139442+383)/9 139443 Robert Price 04/2019 4069 31155^29902+29902^31155 139441 Hans Havermann 05/2021 4070 (7*10^139417-547)/9 139417 Robert Price 01/2018 4071 29636^31175-31175^29636 139409 Frank Doornink 05/2024 4072 (10^139398+191)/3 139398 Robert Price 02/2018 4073 23*10^139386-3 139388 Robert Price 10/2021 4074 2^463019+79463 139383 Enzo Doria 06/2016 4075 3^292129-112756 139381 Enzo Doria 07/2014 4076 (15*2^462951+1)/527 139361 Lelio R Paula 08/2015 4077 31922^23205+23205^31922 139359 Hans Havermann 05/2021 4078 (19*10^139336+503)/9 139337 Alfred Reich 11/2023 4080 2^462855-1865707 139334 Enzo Doria 02/2016 4079 31237^28876+28876^31237 139334 Hans Havermann 05/2021 4081 (86*10^139315+121)/9 139316 Robert Price 08/2019 4082 2^462786-292043 139313 Enzo Doria 08/2015 4083 38915^3798+3798^38915 139299 Hans Havermann 05/2021 4085 (26*10^139289+1)/9 139290 Serge Batalov 05/2010 4084 (17*10^139289+7)/3 139290 Robert Price 06/2023 4086 34065^12248+12248^34065 139260 Hans Havermann 05/2021 4087 36425^6654+6654^36425 139256 Hans Havermann 05/2021 4088 39252^3527+3527^39252 139243 Hans Havermann 05/2021 4089 (17*10^139239+67)/3 139240 Robert Price 01/2019 4090 31887^23248+23248^31887 139231 Hans Havermann 05/2021 4091 (25*10^139210-97)/9 139211 Robert Price 01/2022 4092 2^462238-935 139148 Yves Minet 02/2014 4093 (29*10^139134-119)/9 139135 Robert Price 12/2021 4094 U(687859)/4127153 139105 Serge Batalov 07/2024 4095 (109*10^139100-7)/3 139102 Robert Price 03/2021 4096 38744^3885+3885^38744 139068 Hans Havermann 05/2021 4097 31112^29499+29499^31112 139065 Hans Havermann 05/2021 4098 2*10^139043-63 139044 Robert Price 01/2022 4099 36390^6613+6613^36390 139025 Hans Havermann 04/2021 4100 30554^30989-30989^30554 138988 Frank Doornink 05/2024 4101 2*10^138975+33 138976 Robert Price 11/2021 4102 42437^1882+1882^42437 138966 Hans Havermann 05/2021 4103 32151^20990+20990^32151 138958 Hans Havermann 05/2021 4104 32154^20933+20933^32154 138933 Hans Havermann 04/2021 4105 31082^29499+29499^31082 138931 Hans Havermann 04/2021 4106 30573^30962-30962^30573 138876 Frank Doornink 05/2024 4107 2^461228+1870441 138844 Enzo Doria 05/2016 4108 2^461204-113675 138837 Enzo Doria 08/2014 4109 (2^461139-7)/47 138815 Lelio R Paula 08/2015 4110 (17*10^138812-521)/9 138813 Robert Price 04/2018 4111 3*10^138811-11 138812 Robert Price 07/2018 4112 29109^31088-31088^29109 138778 Frank Doornink 05/2024 4113 (28*10^138768+173)/3 138769 Robert Price 12/2019 4114 (17*2^460963+1)/124051613 138757 Lelio R Paula 08/2015 4115 (379*10^138737-1)/9 138739 Robert Price 02/2020 4116 (43*10^138648+101)/9 138649 Robert Price 11/2018 4117 2^460567-113541 138645 Enzo Doria 08/2014 4118 2^460539+224789 138637 Enzo Doria 07/2024 4119 (10^138622+161)/9 138622 Robert Price 09/2021 4120 7*10^138604+3 138605 Robert Price 08/2015 4121 (133*10^138600+17)/3 138602 Robert Price 11/2021 4122 33912^12203+12203^33912 138581 Hans Havermann 05/2021 4123 2^460330+69 138574 Lelio R Paula 09/2017 4124 (17*10^138569-77)/3 138570 Robert Price 08/2019 4125 31186^27725+27725^31186 138556 Hans Havermann 05/2021 4126 (16*10^138545+89)/3 138546 Robert Price 03/2021 4127 39753^3056+3056^39753 138546 Hans Havermann 05/2021 4128 31282^26847+26847^31282 138545 Hans Havermann 05/2021 4129 6*10^138520-37 138521 Robert Price 02/2021 4131 2^460078-69581 138498 Enzo Doria 12/2015 4130 31830^22447+22447^31830 138498 Hans Havermann 05/2021 4132 37384^5065+5065^37384 138492 Hans Havermann 05/2021 4133 28736^31055-31055^28736 138457 Frank Doornink 05/2024 4134 34774^9585+9585^34774 138456 Hans Havermann 05/2021 4135 10^138444-5001 138444 Robert Price 12/2021 4136 2^459768+1531 138404 Lelio R Paula 06/2012 4137 (266*10^138328-17)/3 138330 Robert Price 07/2020 4138 27200^31193-31193^27200 138328 Frank Doornink 01/2024 4139 28782^31019-31019^28782 138318 Frank Doornink 05/2024 4140 32963^15696+15696^32963 138306 Hans Havermann 05/2021 4141 2^459343-113611 138277 Enzo Doria 08/2014 4142 (28*10^138240+113)/3 138241 Robert Price 03/2020 4143 2^459199+1874393 138233 Enzo Doria 06/2016 4144 33339^14002+14002^33339 138230 Hans Havermann 05/2021 4145 30137^30860-30860^30137 138226 Frank Doornink 05/2024 4146 2^459063-345307 138192 Enzo Doria 06/2015 4147 2*10^138162-43 138163 Robert Price 04/2018 4148 2^458927-112747 138151 Enzo Doria 06/2014 4149 2^458927-69217 138151 Enzo Doria 11/2015 4150 30907^29458+29458^30907 138130 Hans Havermann 05/2021 4151 32882^15837+15837^32882 138094 Hans Havermann 05/2021 4152 39252^3295+3295^39252 138083 Hans Havermann 05/2021 4153 33789^12190+12190^33789 138062 Hans Havermann 06/2021 4154 555555*2^458524+1513 138036 Darren Bedwell 08/2009 4155 28095^31028-31028^28095 138033 Frank Doornink 05/2024 4156 30931^29002+29002^30931 138028 Hans Havermann 05/2021 4157 2^458465+2^32+1 138012 T. D. Noe 06/2007 4158 32206^19275+19275^32206 138003 Hans Havermann 05/2021 4159 2^458321-113053 137969 Enzo Doria 07/2014 4160 6^177298+323 137965 Riley Fisher 03/2023 4161 2^458298+79459 137962 Enzo Doria 06/2016 4162 30254^30789-30789^30254 137959 Frank Doornink 05/2024 4163 2^458248-21815 137947 Enzo Doria 07/2013 4164 2^458194+1876549 137931 Enzo Doria 07/2016 4165 (318259#+325270)/(2^2*5*11*2957) 137907 Makoto Morimoto 10/2017 4166 (318259#+2625)/(3^2*5*7^5*22965193) 137899 Makoto Morimoto 06/2019 4167 (793*10^137887+53)/9 137889 Robert Price 01/2022 4168 2^457937+57 137853 Lelio R Paula 09/2017 4169 28714^30921-30921^28714 137849 Frank Doornink 05/2024 4170 (8*10^137845+13)/3 137846 Robert Price 06/2018 4171 2^457822+105 137819 Donovan Johnson 06/2006 4172 2^457754-113711 137798 Enzo Doria 09/2014 4173 11^132315-360 137792 Enzo Doria 09/2012 4174 32072^19689+19689^32072 137725 Hans Havermann 06/2021 4175 26529^31132-31132^26529 137720 Frank Doornink 03/2024 4176 44592^1225+1225^44592 137707 Hans Havermann 05/2021 4177 28986^30857-30857^28986 137690 Frank Doornink 05/2024 4178 2^457347-37 137676 Lelio R Paula 09/2017 4179 2^457322-2786393 137668 Enzo Doria 10/2015 4180 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 4181 34015^11134+11134^34015 137647 Hans Havermann 06/2021 4182 2^457240-59939 137643 Enzo Doria 10/2015 4183 (856*10^137633-1)/9 137635 Robert Price 03/2020 4184 36232^6289+6289^36232 137631 Hans Havermann 05/2021 4185 2^457120-21575 137607 Enzo Doria 07/2013 4186 (11*2^456978+1)/15 137564 Lelio R Paula 07/2015 4187 30963^27722+27722^30963 137564 Hans Havermann 04/2021 4188 33722^12003+12003^33722 137562 Hans Havermann 06/2021 4189 (7*25^98399+10613)/12 137556 Curtis Bright 05/2015 4190 41901^1918+1918^41901 137555 Hans Havermann 06/2021 4191 (7*10^137551-1)/3 137552 Robert Price 08/2022 4192 32930^15021+15021^32930 137539 Hans Havermann 05/2021 4193 31178^25785+25785^31178 137538 Hans Havermann 05/2021 4194 419^52446+52446^419 137525 Norbert Schneider 11/2020 4195 2^456813+214175 137515 Enzo Doria 10/2023 4196 2^456796-113513 137510 Enzo Doria 08/2014 4197 31788^21137+21137^31788 137485 Hans Havermann 04/2021 4198 (7*2^456655+1)/39 137467 Lelio R Paula 07/2015 4199 27151^31004-31004^27151 137466 Frank Doornink 01/2024 4200 2^456503-114361 137422 Enzo Doria 01/2015 4201 (11*2^456387+1)/19 137386 Lelio R Paula 07/2015 4202 30618^30618-5^5 137352 Serge Batalov 04/2024 4203 36248^6147+6147^36248 137332 Hans Havermann 05/2021 4204 31986^19651+19651^31986 137329 Hans Havermann 05/2021 4205 2^456167+22313 137320 Enzo Doria 09/2023 4206 31817^20656+20656^31817 137292 Hans Havermann 05/2021 4207 (71*10^137250+1)/9 137251 Serge Batalov 05/2010 4208 2^455922+76249 137247 Enzo Doria 05/2016 4209 31310^24171+24171^31310 137241 Hans Havermann 05/2021 4210 14^119741-119741^14 137239 Serge Batalov 04/2016 4211 35014^8297+8297^35014 137218 Hans Havermann 05/2021 4212 (19*2^455760+1)/3455 137196 Lelio R Paula 07/2015 4214 124^(2^16)+57^(2^16) 137195 Valeryi Kuryshev 02/2011 4213 124^65536+57^65536 137195 Serge Batalov 03/2018 4215 2^455689+72677 137177 Enzo Doria 04/2016 4216 (17948!)^2+Prime(17948) 137118 Robert Price 08/2014 4217 31287^24128+24128^31287 137116 Hans Havermann 05/2021 4218 (37^87421-1)/36 137093 Robert Price 03/2012 4219 36233^6070+6070^36233 137077 Hans Havermann 05/2021 4220 (8*10^137073-17)/9 137073 Serge Batalov 11/2022 4221 38418^3697+3697^38418 137070 Hans Havermann 04/2021 4222 2^455323-57 137066 Lelio R Paula 09/2017 4223 (56*10^137019+583)/9 137020 Robert Price 08/2021 4224 25017^31148-31148^25017 136997 Frank Doornink 12/2023 4225 (73*17^111333-9)/16 136991 Curtis Bright 05/2015 4226 2^455025-112723 136977 Enzo Doria 06/2014 4227 33876^11039+11039^33876 136959 Hans Havermann 05/2021 4228 (19860^32041-1)/(19860^179-1) 136943 Ryan Propper 11/2023 4229 (251^57059-1)/250 136921 Anonymous 04/2024 4230 35142^7873+7873^35142 136919 Hans Havermann 05/2021 4231 (4997*31^91805-1)/2 136918 Eric Chen 05/2024 4232 66*10^136894+7 136896 Robert Price 07/2020 4233 28766^30697-30697^28766 136875 Frank Doornink 05/2024 4234 2^454675-1777 136871 Yves Minet 10/2011 4235 31676^20931+20931^31676 136866 Hans Havermann 05/2021 4236 3*10^136829+29 136830 Robert Price 05/2018 4237 4*10^136813-57 136814 Robert Price 10/2018 4238 (6092*28^94536-143)/9 136812 Curtis Bright 05/2015 4239 fibonacci(654572)-2 136798 Jon Grantham 08/2023 4240 37359^4588+4588^37359 136795 Hans Havermann 05/2021 4241 2^454348-53 136773 Lelio R Paula 09/2017 4242 31^91680-2 136729 Lelio R Paula 05/2017 4243 2^454199-113697 136728 Enzo Doria 09/2014 4244 30785^27622+27622^30785 136725 Hans Havermann 05/2021 4245 32973^14014+14014^32973 136725 Hans Havermann 05/2021 4247 7*10^136716+69 136717 Robert Price 07/2019 4246 36002^6273+6273^36002 136717 Hans Havermann 05/2021 4248 6*10^136692+53 136693 Robert Price 05/2020 4249 (13*10^136687+47)/3 136688 Robert Price 10/2018 4250 2^453935-2791357 136649 Enzo Doria 01/2016

Find by discoverer :

Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 18 2024 11:41 (Time in France)

Go back