## 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 ? 501 2^1200021+149777 361243 Stefano Morozzi 10/2022 502 (64*10^360173-1)/243 360173 Serge Batalov 09/2014 503 (59^203309+1)/60 360029 Paul Bourdelais 09/2021 504 (2*10^359860-11)/9 359860 Rytis Slatkevicius 01/2023 505 2^1195093+1882577 359759 Enzo Doria 12/2016 506 3^753451+5*2^753451 359488 Jon Grantham 08/2023 507 (6^461108-11)/5 358812 Paul Bourdelais 04/2019 508 2^1191375+8543 358640 Phil Moore 06/2008 509 2^1190972+1880191 358519 Enzo Doria 11/2016 510 (45^216551-1)/44 358004 Paul Bourdelais 08/2020 511 (50^210319-1)/49 357324 Paul Bourdelais 08/2020 512 (531^131072+25^131072)/2 357184 Kellen Shenton 03/2021 513 2^1184565+21227 356590 Enzo Doria 08/2023 514 2^1179836+1885021 355167 Enzo Doria 02/2017 515 (19*10^353884-91)/9 353885 Alfred Reich 02/2023 516 20^271951+3 353817 Paul Bourdelais 01/2021 517 2^1173095+21 353137 Stefano Morozzi 10/2022 518 (63^195893-1)/62 352477 Paul Bourdelais 08/2020 519 2^1170326+7 352304 Stefano Morozzi 10/2022 520 numbpart(100000135540) 352269 Serge Batalov 04/2017 521 (10^352237-1)/9/10567111/950335427 352221 Maksym Voznyy 01/2015 522 5*3^737931-2^737931 352084 Jon Grantham 08/2023 523 2^1168554+783529 351770 Enzo Doria 01/2017 524 (2^1168183-1)/54763676838381762583 351639 Matthias Wurtinger 01/2011 525 2^1166152+1882411 351047 Enzo Doria 12/2016 526 2^1163972+20971 350391 Enzo Doria 08/2023 527 10^350071+7 350072 Alfred Reich 05/2021 528 2^1162154+1890207 349844 Enzo Doria 08/2017 529 (7*10^348724-61)/9 348724 Erik Branger 09/2016 530 (4*10^348453+41)/9 348453 Serge Batalov 11/2022 531 (127^165601-1)/126 348390 Alexander Zhirkov 09/2015 532 2^1155085+213377 347716 Enzo Doria 09/2023 533 2^1153083+1883693 347113 Enzo Doria 04/2017 534 (2^1148729+2^574365+1)/5 345802 Borys Jaworski 03/2007 535 2^1145882+80779 344945 Enzo Doria 09/2016 536 2^1136462+1887289 342110 Enzo Doria 05/2017 537 F(1636007) 341905 Henri Lifchitz 03/2009 538 (2^1135567+13)/3 341840 Stefano Morozzi 09/2022 539 2^1133678+782569 341272 Enzo Doria 11/2016 540 (11^327001+1)/12 340536 Paul Bourdelais 09/2013 541 (2^1127239+2^563620+1)/5 339333 Borys Jaworski 11/2006 542 Tau(907^20848) 339132 Nik Lygeros / Olivier Rozier 01/2016 543 2^1126380-3 339075 Paul Bourdelais 06/2019 544 2^1125446+1885099 338794 Enzo Doria 08/2017 545 (63^188147+1)/64 338539 Paul Bourdelais 12/2020 546 2^1124549+143807 338523 Enzo Doria 10/2016 547 (4*10^338476+23)/9 338476 Serge Batalov 11/2022 548 2^1121187+1886783 337511 Enzo Doria 04/2017 549 (48^200443-1)/47 336992 Paul Bourdelais 08/2020 550 (2*10^336405+43)/9 336405 Rytis Slatkevicius 01/2023 551 (94^170371-1)/93 336162 Paul Bourdelais 09/2020 552 2^1116184+1883521 336005 Enzo Doria 02/2017 553 2^1114517+1880087 335504 Enzo Doria 10/2016 554 (5*10^335480+31)/9 335480 Serge Batalov 11/2022 555 5*3^701688+2^701688 334791 Jon Grantham 08/2023 556 (101^166849+1)/102 334418 Paul Bourdelais 12/2020 557 (3^700897+1)/4 334413 Paul Bourdelais 04/2010 558 2^1104408-114539 332460 Enzo Doria 03/2015 559 2^1101921+82085 331712 Enzo Doria 10/2016 560 2^1100655+683513 331331 Enzo Doria 01/2017 561 (10^330906+71)/9 330906 Serge Batalov 07/2015 562 2^1098346+482899 330636 Enzo Doria 11/2016 563 (2^1096212+19)/5 329992 Stefano Morozzi 09/2022 564 2^1095679+1878713 329833 Enzo Doria 09/2016 565 2^1094740-1851539 329550 Enzo Doria 08/2015 566 2^1092242+19 328798 Stefano Morozzi 10/2022 567 2^1091469-379369 328565 Enzo Doria 03/2014 568 (69^178093-1)/68 327485 Paul Bourdelais 08/2020 569 (10^326884+7)/421 326882 Alfred Reich 12/2021 570 2^1085750+582349 326844 Enzo Doria 11/2016 571 2^1083596+483061 326195 Enzo Doria 12/2016 572 (2^541456-1)*10^162995+2^541455-1 325990 paolo galliani 01/2019 573 2^1082908+583561 325988 Enzo Doria 05/2017 574 30^220411-29^220411 325574 Jean-Louis Charton 10/2018 575 2^1081308+7 325507 Stefano Morozzi 10/2022 576 2^1078242+1881649 324584 Enzo Doria 11/2016 577 2^1077737+1880117 324432 Enzo Doria 10/2016 578 3^679017-5*2^679017 323974 Jon Grantham 08/2023 579 2^1075425+1880117 323736 Enzo Doria 10/2016 580 (28^223381+1)/29 323267 Paul Bourdelais 12/2020 581 10^322999+187071 323000 Stefano Morozzi 03/2019 582 10^322999-143151 322999 Patrick De Geest 05/2020 583 2^1072146+1886869 322749 Enzo Doria 04/2017 584 2^1072118-7321953 322740 Enzo Doria 02/2015 585 2^1071026+1886869 322411 Enzo Doria 04/2017 586 2^1070539+1880633 322265 Enzo Doria 10/2016 587 2^1069293-1147195 321890 Enzo Doria 05/2015 588 2^1065968+1880941 320889 Enzo Doria 10/2016 589 2^1065897-1147195 320867 Enzo Doria 05/2015 590 2^1063427+1882103 320124 Enzo Doria 12/2016 591 2^1061095-1061095 319422 Henri Lifchitz 10/2013 592 2^1060950+653119 319378 Enzo Doria 12/2016 593 2^1060363+782753 319202 Enzo Doria 11/2016 594 (71^172259-1)/70 318895 Paul Bourdelais 08/2020 595 2^1054736+483061 317508 Enzo Doria 12/2016 596 2^1053965+1879667 317276 Enzo Doria 10/2016 597 (43^194119-1)/42 317086 Paul Bourdelais 08/2020 598 2^1052186-458165 316740 Enzo Doria 03/2015 599 11^303909+2 316489 Paul Bourdelais 08/2023 600 2^1046613-114685 315062 Enzo Doria 04/2015 601 2^1045625-459373 314765 Enzo Doria 06/2015 602 10^(2*157363+1)-8*10^157363-1 314727 Robert Price 07/2023 603 (7*10^314564-61)/9 314564 Erik Branger 09/2016 604 2^1044206+7 314338 Stefano Morozzi 10/2022 605 (7^371669-1)/6 314096 Paul Bourdelais 02/2010 606 (53^181981-1)/52 313784 Paul Bourdelais 08/2020 607 (8^347437-5^347437)/3 313767 Jon Grantham 08/2023 608 2^1041944+283051 313657 Enzo Doria 12/2016 609 2^1041153-114391 313419 Enzo Doria 02/2015 610 (2^1039700+9)/5 312981 Stefano Morozzi 09/2022 611 (74^167311+1)/75 312742 Paul Bourdelais 12/2020 612 2^1038871+1866983 312732 Enzo Doria 04/2016 613 2^1038545+71657 312634 Enzo Doria 08/2023 614 (55^179573-1)/54 312521 Paul Bourdelais 08/2020 615 2^1037647+1881263 312363 Enzo Doria 11/2016 616 2^1037226+1879699 312237 Enzo Doria 10/2016 617 2^1036867+1865843 312129 Enzo Doria 02/2016 618 (76^165947+1)/77 312114 Paul Bourdelais 01/2021 619 2^1036020-114539 311874 Enzo Doria 02/2015 620 (90^159463-1)/89 311628 Paul Bourdelais 08/2020 621 2^1032240+1883431 310736 Enzo Doria 01/2017 622 2^1030352+1870021 310167 Enzo Doria 06/2016 623 2^1030046+1882843 310075 Enzo Doria 11/2016 624 3^648872+16 309591 Robert Price 04/2020 625 64221^64366+64366^64221 309451 Norbert Schneider 06/2023 626 2^1026999+20513 309158 Enzo Doria 07/2023 627 5^442281+2 309142 Paul Bourdelais 01/2021 628 2^1026204+22741 308919 Enzo Doria 09/2023 629 2^1026190+15 308914 Stefano Morozzi 10/2022 630 2^1025108+20851 308589 Enzo Doria 08/2023 631 A352736(16) 306985 Kellen Shenton 05/2022 632 (11^293831-1)/10 305993 Paul Bourdelais 03/2010 633 (67^167449-1)/66 305773 Paul Bourdelais 08/2020 634 (62^170539+1)/63 305671 Paul Bourdelais 12/2020 635 2^1015321-1015321 305643 Henri Lifchitz 08/2013 636 2^1014450+7 305380 Stefano Morozzi 10/2022 637 2^1014224-2791229 305312 Enzo Doria 01/2016 638 (10^304986+7)/673 304984 Alfred Reich 11/2021 639 65473^45250+45250^65473 304818 Hans Havermann 02/2022 640 66012^41423+41423^66012 304794 Hans Havermann 03/2022 641 65073^48202+48202^65073 304742 Hans Havermann 04/2022 642 238176^19+19^238176 304569 Hans Havermann 03/2022 643 73122^14615+14615^73122 304539 Hans Havermann 05/2022 644 64492^52639+52639^64492 304487 Hans Havermann 03/2022 645 65955^41288+41288^65955 304437 Hans Havermann 04/2022 646 71729^17530+17530^71729 304403 Hans Havermann 03/2022 647 70170^21733+21733^70170 304336 Hans Havermann 03/2022 648 2^1010751-107709 304267 Enzo Doria 03/2014 649 84473^3994+3994^84473 304222 Hans Havermann 03/2022 650 (2^1010623-1)/12602017578957977 304212 Tony Prest / Never Odd Or Even 02/2014 651 74442^12125+12125^74442 303998 Hans Havermann 02/2022 652 77842^8039+8039^77842 303989 Hans Havermann 01/2022 653 64209^54140+54140^64209 303935 Hans Havermann 02/2022 654 2^1009577+1869587 303913 Enzo Doria 06/2016 655 67389^32338+32338^67389 303906 Hans Havermann 02/2022 656 8^336419-7^336419 303817 Jean-Louis Charton 01/2008 657 2^1009168+15 303790 Stefano Morozzi 10/2022 658 80766^5771+5771^80766 303782 Hans Havermann 01/2022 659 66094^39385+39385^66094 303724 Hans Havermann 01/2022 660 69147^24574+24574^69147 303589 Hans Havermann 02/2022 661 78390^7459+7459^78390 303580 Hans Havermann 01/2022 662 2^1008301+1869377 303529 Enzo Doria 06/2016 663 65008^46615+46615^65008 303492 Hans Havermann 02/2022 664 (2^1007838+5)/3 303389 Serge Batalov 08/2015 665 65018^46293+46293^65018 303343 Hans Havermann 01/2022 666 6^389756+5 303290 Paul Bourdelais 02/2021 667 71016^18649+18649^71016 303285 Hans Havermann 01/2022 668 80160^6047+6047^80160 303129 Hans Havermann 01/2022 669 67434^31237+31237^67434 303094 Hans Havermann 03/2022 670 65537^42102+42102^65537 303063 Hans Havermann 02/2022 671 71790^16553+16553^71790 302874 Hans Havermann 11/2021 672 65208^44129+44129^65208 302874 Hans Havermann 11/2021 673 84181^3960+3960^84181 302858 Hans Havermann 11/2021 674 71956^16087+16087^71956 302682 Hans Havermann 11/2021 675 2^1005326+383059 302634 Enzo Doria 12/2016 676 2^1004929+1877567 302514 Enzo Doria 08/2016 677 69341^22978+22978^69341 302418 Hans Havermann 12/2021 678 111443^516+516^111443 302306 Hans Havermann 12/2021 679 67638^29387+29387^67638 302218 Hans Havermann 11/2021 680 2^1003494+1874899 302082 Enzo Doria 06/2016 681 75189^10400+10400^75189 302037 Hans Havermann 12/2021 682 67237^31042+31042^67237 302026 Hans Havermann 12/2021 683 64540^47791+47791^64540 302005 Hans Havermann 11/2021 684 2^1003046+60529 301947 Enzo Doria 04/2016 685 83278^4209+4209^83278 301815 Hans Havermann 09/2021 686 64431^48250+48250^64431 301763 Hans Havermann 09/2021 687 67237^30714+30714^67237 301716 Hans Havermann 09/2021 688 64641^46288+46288^64641 301581 Hans Havermann 09/2021 689 71513^16482+16482^71513 301572 Hans Havermann 10/2021 690 72017^15396+15396^72017 301565 Hans Havermann 09/2021 691 65534^39927+39927^65534 301540 Hans Havermann 10/2021 692 (23^221411-1)/22 301501 Paul Bourdelais 08/2020 693 63169^59152+59152^63169 301441 Hans Havermann 09/2021 694 75055^10348+10348^75055 301336 Hans Havermann 09/2021 695 2^1000647+1881353 301225 Enzo Doria 11/2016 696 83686^3961+3961^83686 301086 Hans Havermann 10/2021 697 68529^24742+24742^68529 301078 Hans Havermann 09/2021 698 65207^41416+41416^65207 301072 Hans Havermann 10/2021 700 2^1000000+821751 301030 Tony Prest / Never Odd Or Even 10/2015 699 2^999999+77151 301030 Norman Luhn 09/2023 701 90762^2071+2071^90762 300984 Hans Havermann 06/2021 702 63909^51142+51142^63909 300934 Hans Havermann 08/2021 703 2^999646+1874029 300924 Enzo Doria 06/2016 704 66280^34607+34607^66280 300856 Hans Havermann 06/2021 705 65534^38925+38925^65534 300817 Hans Havermann 07/2021 706 63296^56517+56517^63296 300794 Hans Havermann 06/2021 707 110610^523+523^110610 300694 Hans Havermann 06/2021 708 66428^33609+33609^66428 300684 Hans Havermann 06/2021 709 74247^11210+11210^74247 300672 Hans Havermann 06/2021 710 (59^169777-1)/58 300649 Paul Bourdelais 08/2020 711 10^300476+3 300477 Ed Trice 10/2012 712 10^300476-530913 300476 Patrick De Geest 03/2016 713 66703^31960+31960^66703 300471 Hans Havermann 06/2021 714 63722^51915+51915^63722 300468 Hans Havermann 06/2021 715 2^998053+1879667 300444 Enzo Doria 09/2016 716 77018^7959+7959^77018 300437 Hans Havermann 07/2021 717 314738^9+9^314738 300337 Anatoly F. Selevich 02/2011 718 69478^20987+20987^69478 300281 Hans Havermann 07/2021 719 64088^48393+48393^64088 300239 Hans Havermann 07/2021 720 64605^44146+44146^64605 300084 Hans Havermann 08/2021 721 7^355039-6^355039 300043 Jean-Louis Charton 05/2011 722 67594^27465+27465^67594 300035 Hans Havermann 06/2021 723 10^300000+287389 300001 Patrick De Geest 10/2019 724 10^300000-83657 300000 Patrick De Geest 10/2019 725 70599^17756+17756^70599 300000 Hans Havermann 06/2021 726 numbpart(72526161452) 299999 Serge Batalov 04/2017 727 2^996182-114431 299881 Enzo Doria 02/2015 728 3*2^996126+5 299865 Jon Grantham 07/2023 729 2^996034-17 299837 Stefano Morozzi 07/2022 730 (19*10^299640+77)/3 299641 Robert Price 03/2023 731 2^995214-2788361 299590 Enzo Doria 12/2015 732 2^994791-114319 299462 Enzo Doria 01/2015 733 2^994490-1863791 299372 Enzo Doria 01/2016 734 2^993322+1885729 299020 Enzo Doria 03/2017 735 (36395^65536+36393^65536)/2 298913 Kellen Shenton 04/2022 736 2^992711-2788807 298836 Enzo Doria 12/2015 737 2^992525-114199 298780 Enzo Doria 12/2014 738 (7^353501-3^353501)/4 298743 Jon Grantham 08/2023 739 2^992329+1884707 298721 Enzo Doria 02/2017 740 2^991968-23 298613 Stefano Morozzi 07/2022 741 2^991715-19 298536 Stefano Morozzi 07/2022 742 (10^298414+7)/191/823/56921/1334467 298398 Alfred Reich 10/2021 743 2^989562+25 297888 Stefano Morozzi 05/2021 744 (19*10^297497+77)/3 297498 Robert Price 03/2023 745 (2*10^297488-23)/3 297488 Robert Price 10/2022 746 (2^986191+1)/3 296873 Vincent Diepeveen 06/2008 747 2^985217-114553 296580 Enzo Doria 03/2015 748 (76^157649-1)/75 296507 Paul Bourdelais 07/2019 749 2^984650+21529 296410 Enzo Doria 08/2023 750 2^984131-1828009 296253 Enzo Doria 01/2015

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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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