## PRP Records

### Probable Primes Top 10000

#### (295583 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 ? 1 (10^8177207-1)/9 8177207 Ryan Propper + Sergey Batalov 05/2021 2 (10^5794777-1)/9 5794777 Ryan Propper + Sergey Batalov 04/2021 3 (2^15135397+1)/3 4556209 Ryan Propper 06/2021 4 (3^8530117-1)/2 4069900 Ryan Propper 11/2023 5 2^13380298-27 4027872 Jeff Gilchrist /Diepeveen-Reix-Underwood-Gilchrist 03/2021 6 (2^13372531+1)/3 4025533 Ryan Propper 09/2013 7 (2^13347311+1)/3 4017941 Ryan Propper 09/2013 8 (2^12720787-1)/1119429257/175573124547437977/8480999878421106991 3829294 Anonymous 10/2022 9 (3^7973131-1)/2 3804150 Ryan Propper 11/2023 10 (2^12588091-1)/32075464348897282169539424801 3789365 Eden Avidan / Naegi Makoto 05/2023 11 (2^12503723-2^6251862+1)/5 3763995 Ryan Propper + Sergey Batalov 07/2020 12 (5^5154509-1)/4 3602847 Ryan Propper 02/2024 13 (5^4939471-1)/4 3452542 Ryan Propper 01/2024 14 (2^10443557-1)/37289325994807 3143811 GIMPS-fre_games 07/2020 15 2^9092392+40291 2737083 Engracio Esmenda / Five or Bust 02/2011 16 (6^3360347-1)/5 2614858 Ryan Propper 10/2023 17 (2^8247949-1)/10623358313/23839855293703/179607668296296461174489 2482834 Anonymous 06/2024 18 (17^1990523-1)/16 2449236 Paul Bourdelais 08/2020 19 (35963^524288+1)/2 2388581 Ryan Propper 08/2022 20 (11^2264611+1)/12 2358349 Paul Bourdelais 07/2021 21 (5^3300593-1)/4 2307015 Anonymous 02/2022 22 (3^4694803+2^4694803)/5 2239990 Ryan Propper 12/2023 23 (2^7313983-1)/305492080276193 2201714 Oliver Kruse 03/2018 24 (3^4571447+2^4571447)/5 2181134 Ryan Propper 12/2023 25 (15^1848811+1)/16 2174370 Paul Bourdelais 07/2024 26 F(10367321) 2166642 Ryan Propper 08/2024 27 (15^1841911+1)/16 2166255 Paul Bourdelais 07/2024 28 4532794^3+3^4532794 2162693 Ryan Propper 10/2023 29 F(10317107) 2156148 Ryan Propper 07/2024 30 (2^7080247-1)/156822217506727/11283326312536321/9632940548330339593 2131318 Gord Palameta 10/2017 31 360834^356345+356345^360834 2003304 Ryan Propper 02/2024 32 360339^356572+356572^360339 2000656 Ryan Propper 05/2024 33 (11^1868983-1)/10 1946345 Paul Bourdelais 06/2021 34 (36^1145393+1)/37 1782577 Paul Bourdelais 11/2023 35 1343238^19+19^1343238 1717671 Ryan Propper 05/2023 36 (3^3598867-1)/2 1717096 Ryan Propper 12/2021 37 (13^1503503-1)/12 1674817 Paul Bourdelais 04/2020 38 Mills(3,30,6,80,12,450,894,3636,70756,97220,66768,300840,1623568,8436308) 1665461 Ryan Propper + Sergey Batalov 05/2024 39 F(7789819) 1627976 Ryan Propper 07/2024 40 (10^1600787+1)/11 1600786 Paul Bourdelais 05/2020 41 (18^1270141-1)/17 1594372 Paul Bourdelais 12/2021 42 (14^1385203+1)/15 1587619 Paul Bourdelais 02/2022 43 (2^5243339-2^2621670+1)/5 1578402 Ryan Propper + Sergey Batalov 06/2020 44 (2^5240707-1)/75392810903 1577600 Tony Prest / Never Odd Or Even 07/2016 45 2^5146295+41693 1549190 Engracio Esmenda / Five or Bust 11/2009 46 (2^4834891-1)/1701881633/70659688575577 1455425 Gord Palameta 01/2017 47 300102^59935+59935^300102 1433792 Ryan Propper 05/2023 48 (187503^262144+1)/2 1382288 Ryan Propper 08/2022 49 2^4583176+2131 1379674 Ben Maloney / Five or Bust 09/2009 50 F(6530879) 1364873 Ryan Propper 08/2022 51 (2^4533073+2^2266537+1)/5 1364591 Serge Batalov 03/2014 52 (13^1199467+1)/14 1336138 Paul Bourdelais 12/2015 53 (5^1888279-1)/4 1319850 Paul Bourdelais 04/2018 54 (5^1856147+1)/6 1297391 Paul Bourdelais 02/2019 55 (3^2704981-1)/2 1290604 Ryan Propper 12/2021 56 (20^984349-1)/19 1280667 Paul Bourdelais 09/2021 57 (3^2674381+1)/4 1276004 Paul Bourdelais 03/2024 58 1139148^13+13^1139148 1268947 Ryan Propper 07/2023 59 (2^4194304+1026473)/3 1262611 Tony Prest / Never Odd Or Even 07/2017 60 (2^4187251-1)/72234342371519 1260475 Tony Prest / Never Odd Or Even 05/2016 61 (14^1091401+1)/15 1250885 Paul Bourdelais 03/2014 62 (16^1025393+1)/17 1234695 Paul Bourdelais 08/2014 63 11^1181716+1181716 1230631 Kellen Shenton 07/2023 64 (2^4031399+1)/3 1213572 Tony Reix / Diepeveen-Underwood -Reix 02/2010 65 (3^2533963+1)/4 1209008 Paul Bourdelais 03/2020 66 L(5466311) 1142392 Ryan Propper 08/2022 67 (34^735439+1)/35 1126308 Paul Bourdelais 10/2023 68 (67*10^1116676+23)/9 1116677 Ryan Propper + Sergey Batalov 01/2023 69 2^3690839-1868407 1111054 Enzo Doria 03/2021 70 2^3678448+384541 1107324 Enzo Doria 03/2022 71 2^3668660+1888801 1104377 Enzo Doria 03/2020 72 (106*23^800873-7)/11 1090573 Curtis Bright 05/2015 73 (7^1264699-1)/6 1068794 Paul Bourdelais 01/2014 74 (6^1365019-1)/5 1062191 Paul Bourdelais 12/2019 75 2^3511529-15 1057076 Stefano Morozzi 06/2023 76 (3^2215303-1)/2 1056968 Paul Bourdelais 02/2019 77 2^3480081-9 1047609 Stefano Morozzi 05/2023 78 10^1043372+7 1043373 Alfred Reich 12/2021 79 (2^3464473-1)/604874508299177 1042896 Anand Nair 10/2014 80 202628^128217+128217^202628 1035013 Ryan Propper 12/2023 81 202688^125163+125163^202688 1033198 Ryan Propper 12/2023 82 201868^129567+129567^201868 1032050 Ryan Propper 11/2023 83 202168^126585+126585^202168 1031539 Ryan Propper 11/2023 84 202336^124213+124213^202336 1030734 Ryan Propper 11/2023 85 201754^125605+125605^201754 1028746 Ryan Propper 10/2023 86 (6^1313371+1)/7 1022001 Paul Bourdelais 01/2019 87 200307^126128+126128^200307 1021729 Ryan Propper 10/2023 88 193143^193143+214^214 1020931 Ryan Propper + Sergey Batalov 05/2024 89 200026^126791+126791^200026 1020751 Ryan Propper 09/2023 90 200068^125561+125561^200068 1020118 Ryan Propper 09/2023 91 192223^192223+166^166 1015669 Ryan Propper + Sergey Batalov 05/2024 92 (2^3352132+9)/5 1009092 Tony Prest / Never Odd Or Even 06/2018 93 (2^3351958+191)/3/3/5/17/67/207061/11066359/1608561247/67472994221 1009003 Tony Prest / Never Odd Or Even 08/2019 94 (2^3351556+159)/5/7/7/2927/14552647/117615601/706874075837 1008886 Tony Prest / Never Odd Or Even 08/2019 95 (2^3351346+113)/3/548533/39539021/94650838127 1008831 Tony Prest / Never Odd Or Even 11/2022 96 (2^3350899+115)/3/3/11/409 1008717 Tony Prest / Never Odd Or Even 04/2020 97 (2^3350068+183)/953/15761231 1008461 Tony Prest / Never Odd Or Even 03/2020 98 (2^3349565+57)/23/263/77893 1008311 Tony Prest / Never Odd Or Even 03/2020 99 (2^3349080+137)/3/79/8060419099 1008162 Tony Prest / Never Odd Or Even 07/2020 100 (2^3349027+183)/23/1277/11638321/5044848527 1008137 Tony Prest / Never Odd Or Even 09/2022 101 (2^3348456+23)/3/41 1007984 Tony Prest / Never Odd Or Even 01/2019 102 (2^3348338+213)/7 1007950 Tony Prest / Never Odd Or Even 10/2018 103 (2^3348184+123)/12491/322944263 1007892 Tony Prest / Never Odd Or Even 01/2021 104 (2^3348131+207)/5/11/41/43/12661193081/86868416749 1007862 Tony Prest / Never Odd Or Even 05/2021 105 (2^3348111+245)/9721/215412555797/19870494524087 1007854 Tony Prest / Never Odd Or Even 05/2021 106 (2^3347690+143)/3/7/167/585877 1007746 Tony Prest / Never Odd Or Even 06/2020 107 (2^3347613+103)/3/5/194809 1007726 Tony Prest / Never Odd Or Even 02/2020 108 (2^3347274+143)/3/3/3/234786457/3484003557569 1007608 Tony Prest / Never Odd Or Even 07/2022 109 (2^3346590+185)/3/31/83/2201765933/326210984543 1007400 Tony Prest / Never Odd Or Even 04/2021 110 (2^3346468+257)/3/7/13/71/10847 1007379 Tony Prest / Never Odd Or Even 05/2020 111 L(4819961) 1007313 Ryan Propper 07/2022 112 (2^3346066+139)/168803/7120527205063 1007249 Tony Prest / Never Odd Or Even 05/2023 113 (2^3345946+187)/7/3122957 1007223 Tony Prest / Never Odd Or Even 03/2019 114 2^3345603+63 1007127 Tony Prest / Never Odd Or Even 05/2018 115 (2^3345474+255)/19/29/2557 1007082 Tony Prest / Never Odd Or Even 12/2019 116 (2^3345364+43)/53/79/109/2389/10889/16838309 1007035 Tony Prest / Never Odd Or Even 07/2022 117 (2^3345080+247)/31/3967 1006965 Tony Prest / Never Odd Or Even 03/2019 118 (2^3343888+209)/3/3/5/31/179 1006606 Tony Prest / Never Odd Or Even 11/2019 119 (2^3343774+115)/12239 1006573 Tony Prest / Never Odd Or Even 10/2018 120 (2^3343633+105)/137 1006532 Tony Prest / Never Odd Or Even 10/2018 121 (2^3343714+149)/3/11/17/6047/23869/3993469/171388950721 1006530 Tony Prest / Never Odd Or Even 01/2021 122 (2^3343629+183)/5/35107/2154259/28212829709 1006511 Tony Prest / Never Odd Or Even 05/2022 123 (2^3343142+13)/587/212195573363/3775970066719 1006360 Tony Prest / Never Odd Or Even 05/2018 124 (2^3342880+215)/3/7/157/239/821 1006299 Tony Prest / Never Odd Or Even 04/2020 125 (2^3342804+51)/13/13/43/2069/149173 1006272 Tony Prest / Never Odd Or Even 01/2023 126 (2^3342732+41)/3/7/28513800139379 1006248 Tony Prest / Never Odd Or Even 03/2023 127 (2^3342588+95)/3/619/13174671553/22761066847 1006196 Tony Prest / Never Odd Or Even 08/2018 128 194968^136197+136197^194968 1000999 Hans Havermann 12/2023 129 191319^170462+170462^191319 1000910 Hans Havermann 07/2023 130 197180^119151+119151^197180 1000905 Hans Havermann 08/2023 131 202818^85523+85523^202818 1000316 Gabor Levai 08/2023 132 (2^3322799+505)/3 1000262 Stefano Morozzi 08/2022 133 2^3322627-525 1000211 Stefano Morozzi 07/2024 134 265341^5882+5882^265341 1000210 Gabor Levai 04/2024 135 218767^37314+37314^218767 1000175 Gabor Levai 03/2023 136 2^3322077+659 1000045 Stefano Morozzi 04/2022 137 211185^54364+54364^211185 1000027 Gabor Levai 05/2022 144 10^999999+593499 1000000 Peter Kaiser 02/2013 138 10^999999+308267*10^292000+1 1000000 Sergey Batalov 09/2021 139 138159533888769035882147()973433052122012098003208^4096+1 1000000 Anonymous 11/2021 140 138159533888769035882147()973433052122012098115876^4096+1 1000000 Anonymous 11/2021 141 190880568043619196745858()064791100275825910782112^2048+1 1000000 Anonymous 05/2023 142 190880568043619196745858()064791100275825910980374^2048+1 1000000 Anonymous 05/2023 143 (sqrtnint(10^999999,1024)+407852)^1024+1 1000000 Anonymous 06/2024 145 10^999999-172473 999999 Patrick De Geest 12/2016 146 10^999999-1087604*10^287000-1 999999 Ryan Propper + Sergey Batalov 09/2021 147 10^999999-1022306*10^287000-1 999999 Ryan Propper + Sergey Batalov 09/2021 148 (7^1178033+1)/8 995553 Paul Bourdelais 01/2019 149 10^995256+7 995257 Alfred Reich 11/2021 150 F(4740217) 990647 Ryan Propper 07/2022 151 (3^2052329+2^2052329)/5 979210 Ryan Propper 12/2023 152 2^3223639+74333 970413 Enzo Doria 10/2021 153 2^3118435+73793 938743 Enzo Doria 01/2021 154 2^3037438+1885789 914360 Enzo Doria 05/2019 155 2^3032354+74209 912830 Enzo Doria 01/2020 156 2^3018556+31 908676 Robert Price 09/2019 157 (3^1896463+1)/4 904843 Paul Bourdelais 01/2020 158 Tau(181^72558) 900969 Nik Lygeros / Olivier Rozier / LR team 07/2018 159 2^2976221+2041857 895932 Makoto Morimoto 09/2014 160 1839730^3+3^1839730 877775 Ryan Propper 06/2023 161 (35^568453-1)/34 877729 Paul Bourdelais 10/2021 162 L(4161629) 869730 Ryan Propper 07/2022 163 (2^2860553+1)/(3*1528891204123*11630352659013691) 861084 Gord Palameta 03/2019 164 2^2843446+1885789 855963 Enzo Doria 05/2019 165 3^1753088+2 836436 Paul Bourdelais 03/2022 166 (12^769543-1)/11 830476 Paul Bourdelais 12/2014 167 2^2740174+1884385 824875 Enzo Doria 01/2019 168 Tau(229^63498) 824146 Nik Lygeros / Olivier Rozier / LR team 07/2020 169 (168326^157609-1)/(168326^397-1) 821614 Ryan Propper 11/2023 170 (9^860029+1)/10 820676 Paul Bourdelais 09/2020 171 2^2723045+60227 819719 Enzo Doria 01/2020 172 2^2711746+74179 816317 Enzo Doria 11/2019 173 (2^2687383+1)/(3*440088720954577) 808968 Gord Palameta 03/2019 174 684614^15+15^684614 805169 Ryan Propper 05/2023 175 (31^535571-1)/30 798729 Alexander Zhirkov 08/2019 176 (9^835391-7^835391)/2 797166 Jon Grantham 07/2023 177 (64*10^779465-1)/81 779465 Serge Batalov 09/2014 178 (8^854149-3^854149)/5 771373 Jon Grantham 08/2023 179 (64*10^762811-1)/9 762812 Serge Batalov 09/2014 180 2^2515946+60529 757376 Enzo Doria 10/2018 181 (15^639833-1)/14 752501 Paul Bourdelais 04/2019 182 2^2442546+74209 735280 Enzo Doria 03/2020 183 (110212^143641-1)/(110212^379-1) 722361 Ryan Propper 11/2023 184 (79^379703+1)/80 720533 Paul Bourdelais 10/2023 185 (10^718580+269)/9 718580 Serge Batalov 12/2014 186 (7^846913-2^846913)/5 715724 Jon Grantham 08/2023 187 (99^357779+1)/100 713995 Paul Bourdelais 02/2022 188 558232^19+19^558232 713842 Ryan Propper 05/2023 189 (26^501409+1)/27 709479 Paul Bourdelais 10/2023 190 (81^370421+1)/82 706942 Paul Bourdelais 12/2021 191 (2^2327417-1)/23915387348002001 700606 Anand Nair 08/2014 192 F(3340367) 698096 Henri Lifchitz 03/2018 193 (2^2305781-2^1152891+1)/5 694109 Serge Batalov 01/2014 194 (7^817519-3^817519)/4 690884 Jon Grantham 08/2023 195 2^2291342+73519 689763 Enzo Doria 12/2018 196 (10^685224+89)/9 685224 Serge Batalov 12/2014 197 (65^375017-1)/64 679872 Paul Bourdelais 10/2023 198 F(3244369) 678033 Henri Lifchitz 09/2017 199 2^2249255+28433 677094 Ben Maloney / Five or Bust 01/2009 200 (10^675470+269)/9 675470 Serge Batalov 12/2014 201 Tau(151^56086) 672156 Nik Lygeros / Olivier Rozier / LR team 10/2017 202 (9^703393+1)/10 671207 Paul Bourdelais 08/2015 203 (121^320483+1)/122 667496 Paul Bourdelais 08/2019 204 (10^666903-7)/3 666903 Rytis Slatkevicius 01/2023 205 2^2213586+71389 666356 Enzo Doria 04/2018 206 (9614^167281-1)/(9614^409-1) 664636 Ryan Propper 11/2023 207 2^2205444+3 663905 Paul Bourdelais 08/2020 208 (41*13^592198+27)/4 659677 Eric Chen 11/2023 209 2^2191232+105 659627 Stefano Morozzi 10/2021 210 2^2187054+1886719 658369 Enzo Doria 11/2018 211 (6^840316-11)/5 653893 Paul Bourdelais 06/2020 212 2^2160082+39973 650250 Stefano Morozzi 07/2024 213 2^2160074+41857 650248 Stefano Morozzi 06/2024 214 2^2160054+24817 650242 Stefano Morozzi 06/2024 215 (15^551927+1)/16 649116 Paul Bourdelais 07/2013 216 2^2153756+72181 648346 Enzo Doria 04/2018 217 (3^1353449-3^676725+1)/7 645759 Serge Batalov 03/2014 218 Tau(983^38932) 640784 Nik Lygeros / Olivier Rozier 02/2016 219 2^2119239+684443 637955 Enzo Doria 11/2018 220 2^2117699+89 637491 Stefano Morozzi 10/2021 221 (5*10^636570+31)/9 636570 Rytis Slatkevicius 02/2023 222 2^2114495+20753 636527 Enzo Doria 08/2023 223 2^2107382+105 634386 Stefano Morozzi 10/2021 224 (51*21^479149-1243)/4 633542 Curtis Bright 11/2015 225 2^2099459+71663 632001 Enzo Doria 07/2018 226 (10^631715+53)/9 631715 Rytis Slatkevicius 01/2023 227 Tau(881^38992) 631568 Nik Lygeros / Olivier Rozier 01/2016 228 2^2097791+60563 631499 Enzo Doria 04/2018 229 2^2086750-3 628175 Paul Bourdelais 05/2020 230 2^2083766+73519 627277 Enzo Doria 01/2019 231 (16105^146689-1)/(16105^383-1) 615504 Ryan Propper 11/2023 232 (20^472709-1)/19 615008 Paul Bourdelais 01/2015 233 PIPrime(613373) 613373 Adrian Bondrescu 05/2016 234 124452^80465+80465^124452 610513 Ryan Propper 10/2023 235 11^586020-2 610277 Paul Bourdelais 11/2021 236 (19^476929+1)/20 609874 Paul Bourdelais 03/2015 237 (7^720497-2^720497)/5 608890 Jon Grantham 08/2023 238 2^2019811+1867211 608024 Enzo Doria 04/2018 239 F(2904353) 606974 Henri Lifchitz 07/2014 240 2^2014720+71893 606492 Enzo Doria 04/2018 241 (5^866029-3^866029)/2 605328 Jon Grantham 08/2023 242 L(2894561) 604928 Ryan Propper 06/2022 243 (18^481147+1)/19 603970 Paul Bourdelais 07/2011 244 200^262144+119^262144 603202 Kellen Shenton 08/2022 245 (83467^121801-1)/(83467^349-1) 597728 Ryan Propper 11/2023 246 (61448^124609-1)/(61448^353-1) 595001 Ryan Propper 11/2023 247 (15^505117-1)/14 594063 Paul Bourdelais 01/2015 248 81^310721-80^310721 593007 Paul Bourdelais 07/2023 249 (152^270217-1)/(152-1) 589570 Michael Stocker 06/2015 250 Phi(177147,94259) 587458 Anonymous 09/2022

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 13 2024 19:51 (Time in France)

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