## PRP Records

### Probable Primes Top 10000

#### (293510 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 (88*10^128324-637)/9 128325 Robert Price 11/2020 4002 (491*10^128285+31)/9 128287 Robert Price 04/2022 4003 39103^1908+1908^39103 128281 Hans Havermann 04/2021 4004 2^426043+35 128252 Robert Price 11/2015 4005 (4*10^128244-19)/3 128245 Robert Price 03/2018 4006 35489^4102+4102^35489 128222 Hans Havermann 04/2021 4007 34721^4926+4926^34721 128208 Hans Havermann 04/2021 4008 (305*10^128198+1)/9 128200 Robert Price 02/2020 4009 2^425808-459959 128181 Enzo Doria 06/2015 4010 30632^15291+15291^30632 128178 Hans Havermann 04/2021 4011 35981^3648+3648^35981 128167 Hans Havermann 04/2021 4012 2^425627-113605 128127 Enzo Doria 08/2014 4013 (4*10^128109+119)/3 128110 Robert Price 12/2021 4014 (22*10^128094+53)/3 128095 Robert Price 07/2019 4015 (86*10^128086-221)/9 128087 Robert Price 09/2019 4016 18565^30002-30002^18565 128070 Norbert Schneider 01/2015 4017 (2^425287-9)/2737 128021 Lelio R Paula 05/2015 4018 (3*2^425233-1)/25 128007 Lelio R Paula 05/2014 4019 Phi(149401,10)/30037901719561 128003 Makoto Kamada 07/2022 4020 2^425205+4911 128000 Marek Hubal 02/2017 4021 29241^23836+23836^29241 127995 Hans Havermann 04/2021 4022 2^425118-113663 127974 Enzo Doria 08/2014 4023 (86*10^127967-329)/9 127968 Robert Price 01/2020 4024 2^425061+1869761 127957 Enzo Doria 05/2016 4025 746^44541+44541^746 127955 Norbert Schneider 07/2019 4026 30236^17043+17043^30236 127946 Hans Havermann 03/2021 4027 2^424938+212419 127920 Enzo Doria 08/2023 4028 2^424918-21141 127914 Enzo Doria 07/2013 4029 (62*10^127903+91)/9 127904 Robert Price 07/2021 4030 2^424864-29489 127897 Enzo Doria 08/2015 4031 30438^15893+15893^30438 127877 Hans Havermann 02/2021 4032 (97*10^127858-1)/3 127860 Serge Batalov 12/2014 4033 28929^26258+26258^28929 127845 Hans Havermann 03/2021 4034 30563^15220+15220^30563 127828 Hans Havermann 03/2021 4035 2^424632-2786639 127827 Enzo Doria 03/2016 4036 10^127821-700001 127821 Robert Price 08/2021 4037 2^424577-113755 127811 Enzo Doria 09/2014 4038 (7*2^424512-1)/3 127792 Lelio R Paula 05/2014 4039 (56*10^127752+691)/9 127753 Robert Price 05/2019 4040 11^122629-720 127705 Enzo Doria 11/2012 4041 22*10^127645+3 127647 Robert Price 01/2020 4042 28715^27844+27844^28715 127631 Hans Havermann 03/2021 4043 (56*10^127612+187)/9 127613 Robert Price 10/2021 4044 (5*36^81995+821)/7 127609 Eric Chen 01/2021 4045 4*10^127562-39 127563 Robert Price 09/2020 4046 32595^8186+8186^32595 127547 Hans Havermann 03/2021 4047 2^423696-21429 127546 Enzo Doria 07/2013 4048 2^423664-1864559 127536 Enzo Doria 03/2016 4049 37889^2322+2322^37889 127530 Hans Havermann 03/2021 4050 37668^2429+2429^37668 127523 Hans Havermann 03/2021 4051 3^267267-4 127519 Henri Lifchitz 10/2014 4052 fibonacci(610144)-2 127513 Jon Grantham 08/2023 4053 (103*10^127491+17)/3 127493 Robert Price 08/2020 4054 29376^21869+21869^29376 127487 Hans Havermann 03/2021 4055 31186^12241+12241^31186 127483 Hans Havermann 02/2021 4056 (19^99689+5^99689)/24 127477 Robert Price 09/2013 4057 (21*2^423372+1)/101 127447 Lelio R Paula 05/2014 4058 30594^14645+14645^30594 127446 Hans Havermann 03/2021 4059 2^423328-21537 127435 Enzo Doria 07/2013 4060 (67*10^127413-7)/3 127415 Robert Price 01/2020 4061 (5*34^83193+700233)/11 127408 Eric Chen 08/2023 4062 (2*10^127407+73)/3 127407 Robert Price 09/2020 4063 (2^423165-7)/25 127384 Lelio R Paula 05/2015 4064 (7726^32768+1)/13917994151414876602369 127379 Kellen Shenton 04/2021 4065 (4*10^127349+17)/3 127350 Tyler Busby 01/2023 4066 29512^20647+20647^29512 127341 Hans Havermann 03/2021 4067 2^422987-3001935 127332 Paul Bourdelais 07/2023 4068 (112*10^127324+17)/3 127326 Robert Price 03/2020 4069 29565^20252+20252^29565 127321 Hans Havermann 03/2021 4070 fibonacci(609165)-3 127308 Jon Grantham 08/2023 4072 (F(5)^182099-F(4)^182099)/F(3) 127282 Wayne Halsdorf 08/2013 4071 (5^182099-3^182099)/2 127282 Kellen Shenton 05/2022 4073 (16*10^127259+197)/3 127260 Robert Price 04/2019 4074 (26*10^127240+61)/3 127241 Robert Price 10/2019 4075 (234483*27^88884-145)/26 127230 Curtis Bright 05/2015 4076 2^422515-114997 127190 Enzo Doria 06/2015 4077 5*10^127179-3 127180 Robert Price 07/2015 4078 31678^10343+10343^31678 127176 Hans Havermann 03/2021 4079 (44*10^127169-233)/9 127170 Robert Price 01/2019 4080 34947^4352+4352^34947 127162 Hans Havermann 03/2021 4081 6*10^127158+19 127159 Robert Price 11/2021 4082 30469^14902+14902^30469 127155 Hans Havermann 03/2021 4083 5*10^127153+77 127154 Robert Price 12/2018 4084 29941^17620+17620^29941 127130 Hans Havermann 02/2021 4085 31607^10516+10516^31607 127119 Hans Havermann 03/2021 4086 (19*10^127118-97)/3 127119 Robert Price 10/2021 4087 (29*10^127111+691)/9 127112 Robert Price 08/2021 4088 736^44335+44335^736 127104 Norbert Schneider 07/2019 4089 33040^7023+7023^33040 127090 Hans Havermann 03/2021 4090 (4*10^127081+167)/9 127081 Robert Price 03/2022 4091 29748^18661+18661^29748 127052 Hans Havermann 03/2021 4092 -516776642557847117490*Bern(37960)/34256837217082767928421792453 127042 Thomas Ritschel 06/2017 4093 (78^67141-1)/77 127036 Paul Bourdelais 09/2017 4094 (14*10^127014-137)/3 127015 Robert Price 04/2021 4095 31436^10965+10965^31436 127002 Hans Havermann 03/2021 4096 28905^24758+24758^28905 127001 Hans Havermann 03/2021 4097 2^421860-113285 126993 Enzo Doria 07/2014 4098 (10^127030+7)/81234833/9230384921/6092460488946445358851 126991 Alfred Reich 07/2021 4099 (2^421827-7)/11 126982 Lelio R Paula 05/2015 4100 11^121910-840 126957 Enzo Doria 12/2012 4101 (56*10^126935+187)/9 126936 Robert Price 10/2021 4102 28915^24538+24538^28915 126933 Hans Havermann 03/2021 4103 (29*10^126928-77)/3 126929 Robert Price 02/2020 4104 (259*10^126919-1)/3 126921 Robert Price 12/2020 4105 10^126919+204567 126920 Patrick De Geest 05/2021 4106 (2^421617+100280245065) 126920 Paul Bourdelais 05/2022 4107 10^126919-100001 126919 Robert Price 07/2020 4108 28340^28503+28503^28340 126907 Norbert Schneider 02/2021 4109 2^421534-3001935 126895 Paul Bourdelais 07/2023 4110 (71^68539+1)/72 126882 Paul Bourdelais 09/2017 4111 (5*10^126871-119)/3 126872 Robert Price 03/2018 4112 331^50339-10004 126846 Enzo Doria 07/2012 4113 2^421363-2790757 126843 Enzo Doria 03/2016 4114 (106*10^126839-1)/3 126841 Serge Batalov 12/2014 4115 37938^2203+2203^37938 126828 Hans Havermann 03/2021 4116 (13*10^126819+77)/9 126820 Robert Price 07/2022 4117 (7*2^421243+1)/39 126807 Lelio R Paula 05/2014 4119 (14*10^126784-83)/3 126785 Robert Price 12/2018 4118 2^421169-3001935 126785 Paul Bourdelais 07/2023 4120 2^421161-286183 126783 Enzo Doria 06/2015 4121 (106*10^126726+17)/3 126728 Robert Price 04/2021 4122 30718^13347+13347^30718 126724 Hans Havermann 03/2021 4123 2^420939-113935 126716 Enzo Doria 10/2014 4124 11*23^93048+356 126708 Eric Chen 08/2023 4125 177^56363-2 126703 Lelio R Paula 10/2017 4126 2^420741-113659 126656 Enzo Doria 08/2014 4127 2^420694-21 126642 Lelio R Paula 05/2017 4128 (13*10^126638+437)/9 126639 Robert Price 04/2018 4129 (167*10^126637-17)/3 126639 Robert Price 03/2020 4130 4*10^126625+87 126626 Robert Price 08/2018 4131 (31*2^420556+1)/7 126601 Lelio R Paula 05/2014 4132 7*10^126600-99 126601 Robert Price 06/2019 4133 2^420424-59189 126561 Enzo Doria 10/2015 4134 28717^25534+25534^28717 126560 Hans Havermann 03/2021 4135 (86*10^126542+103)/9 126543 Robert Price 12/2021 4136 28922^23655+23655^28922 126503 Hans Havermann 03/2021 4137 2^420126+71893 126471 Enzo Doria 04/2016 4138 (43*10^126441+47)/9 126442 Robert Price 12/2018 4139 8*10^126408+71 126409 Robert Price 05/2022 4140 2^419866+1877059 126393 Enzo Doria 07/2016 4141 29315^20484+20484^29315 126390 Hans Havermann 03/2021 4142 29433^19676+19676^29433 126384 Hans Havermann 03/2021 4143 F(604711) 126377 Henri Lifchitz 02/2005 4144 2^419757+72707 126360 Enzo Doria 04/2016 4145 2^419720-21569 126349 Enzo Doria 07/2013 4146 2^419637+29 126324 Henri Lifchitz 02/2006 4147 31004^11865+11865^31004 126319 Hans Havermann 03/2021 4148 2^419612+1876741 126316 Enzo Doria 07/2016 4149 2^419520+2793271 126289 Enzo Doria 03/2016 4150 (2^419447-5)/369 126264 Lelio R Paula 05/2014 4151 2^419328-1859939 126231 Enzo Doria 03/2016 4152 2^419282-1851507 126217 Enzo Doria 08/2015 4153 (133*10^126212+17)/3 126214 Robert Price 11/2021 4154 2^419251+1866143 126208 Enzo Doria 03/2016 4155 11^121185+2 126202 Robert Price 05/2014 4156 28203^28352+28352^28203 126175 Norbert Schneider 01/2021 4157 (23*2^419036-1)/1393 126141 Lelio R Paula 05/2014 4158 2^418851+23 126087 Robert Price 09/2015 4159 (2^418849-9)/2681 126083 Lelio R Paula 05/2014 4160 2^418829+167 126081 Lelio R Paula 01/2012 4161 31037^11530+11530^31037 126067 Hans Havermann 03/2021 4162 4*10^126064-69 126065 Robert Price 01/2022 4163 (31*2^418782-1)/75891 126063 Lelio R Paula 05/2014 4164 (19*2^418754-1)/15 126058 Lelio R Paula 05/2014 4165 (35*10^126048-323)/9 126049 Robert Price 10/2021 4166 33016^6551+6551^33016 126000 Hans Havermann 03/2021 4167 2^418548-111546435 125996 Paul Bourdelais 10/2021 4168 34736^4227+4227^34736 125954 Hans Havermann 03/2021 4169 2^418319-109501 125927 Enzo Doria 04/2014 4170 2^418316-112373 125926 Enzo Doria 06/2014 4171 40398^1309+1309^40398 125919 Hans Havermann 03/2021 4172 (8*10^125894-29)/3 125895 Robert Price 07/2018 4173 (26*10^125886-413)/9 125887 Robert Price 05/2018 4174 10^(2*62938+1)-7*10^62938-1 125877 Robert Price 07/2023 4175 55*10^125847+9 125849 Robert Price 03/2022 4176 4*10^125832+57 125833 Robert Price 05/2022 4177 2^417968+1869811 125821 Enzo Doria 06/2016 4178 2^417902+63 125802 Lelio R Paula 09/2015 4179 (10^125792-91)/9 125792 Serge Batalov 12/2014 4180 30438^13573+13573^30438 125791 Hans Havermann 03/2021 4181 32867^6714+6714^32867 125782 Hans Havermann 03/2021 4182 31155^10892+10892^31155 125777 Hans Havermann 03/2021 4183 (35*10^125754-593)/9 125755 Robert Price 07/2018 4184 30455^13464+13464^30455 125754 Hans Havermann 03/2021 4185 (32*10^125751-77)/9 125752 Robert Price 06/2018 4186 2^417704+77011 125742 Enzo Doria 05/2016 4187 29755^16816+16816^29755 125737 Hans Havermann 03/2021 4188 (22*10^125734+203)/9 125735 Robert Price 10/2021 4189 29918^15915+15915^29918 125710 Hans Havermann 03/2021 4190 (10^125706+149)/3 125706 Serge Batalov 12/2014 4191 28531^25368+25368^28531 125659 Hans Havermann 03/2021 4192 2^417419-115309 125656 Enzo Doria 07/2015 4193 (46*10^125642+593)/9 125643 Robert Price 04/2022 4194 2^417300+77281 125620 Enzo Doria 05/2016 4195 30638^12537+12537^30638 125561 Hans Havermann 03/2021 4196 2^417095-1657 125559 Yves Minet 07/2014 4197 30162^14525+14525^30162 125538 Hans Havermann 03/2021 4198 (56*10^125535+583)/9 125536 Robert Price 08/2021 4199 (23*10^125517-179)/3 125518 Robert Price 06/2022 4200 9*10^125516+29 125517 Robert Price 03/2022 4201 (88*10^125492-637)/9 125493 Robert Price 11/2020 4202 28958^21525+21525^28958 125474 Hans Havermann 02/2021 4204 2^416773-25 125462 Lelio R Paula 09/2015 4203 (10^125482+7)/162685667/1639829194459 125462 Alfred Reich 07/2021 4205 33889^5032+5032^33889 125449 Hans Havermann 03/2021 4206 (289511#+292834)/(2^3*146417) 125444 Makoto Morimoto 10/2017 4207 (11*2^416691+1)/43 125436 Lelio R Paula 05/2014 4208 (289511#+1896)/(2*3^3*79*780193*9911849) 125434 Makoto Morimoto 06/2019 4209 2^416641-2*416641+1 125422 Robert Price 05/2018 4210 33392^5697+5697^33392 125409 Hans Havermann 03/2021 4211 (21*2^416566-1)/17 125399 Lelio R Paula 05/2014 4212 2^416530+1870429 125389 Enzo Doria 05/2016 4213 (56*10^125385+691)/9 125386 Robert Price 05/2019 4214 27953^28198+28198^27953 125381 Norbert Schneider 01/2021 4215 31074^10837+10837^31074 125381 Hans Havermann 03/2021 4216 33745^5194+5194^33745 125380 Hans Havermann 03/2021 4217 2^416490+1875109 125376 Enzo Doria 09/2016 4218 28360^26331+26331^28360 125365 Hans Havermann 03/2021 4219 2^416416-114929 125354 Enzo Doria 05/2015 4220 (77*10^125330-293)/9 125331 Robert Price 09/2019 4221 (172*10^125292-1)/9 125294 Serge Batalov 12/2014 4222 2^416134+1865899 125269 Enzo Doria 03/2016 4223 153^57337-152 125264 Norbert Schneider 12/2018 4224 (599*10^125224+13)/9 125226 Robert Price 02/2022 4225 (9*2^415992+1)/13560845 125220 Lelio R Paula 05/2014 4226 30054^14657+14657^30054 125207 Hans Havermann 03/2021 4227 (23^91943-1)/22 125201 Robert Price 01/2012 4228 2^415884-933075 125194 Paul Bourdelais 06/2021 4229 43125^27010-106 125185 Enzo Doria 08/2012 4230 (38*10^125166+349)/9 125167 Robert Price 10/2018 4231 10^125166-5001 125166 Robert Price 12/2021 4232 2^415765-112603 125158 Enzo Doria 06/2014 4233 8*10^125088-13 125089 Robert Price 08/2019 4234 (25*10^125076-13)/3 125077 Robert Price 09/2019 4235 (11*10^125054+73)/3 125055 Robert Price 08/2021 4236 (29*10^125021-113)/3 125022 Robert Price 10/2019 4237 2^415290-113591 125015 Enzo Doria 08/2014 4238 2^415276-460919 125011 Enzo Doria 06/2015 4239 2^415259+77243 125006 Enzo Doria 05/2016 4240 (67*10^124990+77)/9 124991 Robert Price 10/2021 4241 2^415144-3683 124971 Yves Minet 10/2011 4242 2^415092+111546435 124956 Paul Bourdelais 10/2021 4243 31936^8173+8173^31936 124946 Hans Havermann 03/2021 4244 5^178715-4 124916 Tyler NeSmith 07/2021 4245 29767^15700+15700^29767 124900 Hans Havermann 03/2021 4246 2^414874+79 124890 Lelio R Paula 01/2015 4247 (2^414765+7)/1389 124854 Lelio R Paula 05/2014 4248 2^414618+79459 124813 Enzo Doria 06/2016 4249 (61*10^124809-1)/3 124811 Robert Price 01/2020 4250 (29*10^124765-71)/3 124766 Robert Price 07/2021

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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