## PRP Records

### Probable Primes Top 10000

#### (295756 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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 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 2^1453419+26783 437523 Enzo Doria 01/2024 502 (67^239053+1)/68 436527 Paul Bourdelais 09/2021 503 2^1448122+74209 435929 Enzo Doria 08/2023 504 2^1446449+221087 435425 Enzo Doria 05/2024 505 2^1446263+74333 435369 Enzo Doria 08/2023 506 2^1444386+221029 434804 Enzo Doria 03/2024 507 (80^228419+1)/81 434701 Paul Bourdelais 02/2021 508 2^1443089+60227 434414 Enzo Doria 10/2017 509 (21^328129-1)/20 433858 Paul Bourdelais 06/2014 510 (35^280979+1)/36 433850 Paul Bourdelais 09/2021 511 2^1438663+214175 433081 Enzo Doria 11/2023 512 2^1434519+215813 431834 Enzo Doria 01/2024 513 2^1434400+3 431798 Paul Bourdelais 06/2019 514 2^1434298+31669 431767 Enzo Doria 08/2024 515 2^1434097+215207 431707 Enzo Doria 11/2023 516 2^1433033+212987 431386 Enzo Doria 10/2023 517 2^1432308+1888801 431168 Enzo Doria 10/2017 518 (2^1430131+1)/(3*356468732537*36519993971459) 430487 Gord Palameta 12/2018 519 (7^508867-2^508867)/5 430042 Jon Grantham 08/2023 520 2^1428489+25097 430019 Enzo Doria 11/2023 521 2^1425483+1886813 429114 Enzo Doria 04/2017 522 (63^238481+1)/64 429107 Paul Bourdelais 12/2020 523 (17^348259+1)/18 428514 Paul Bourdelais 05/2014 524 2^1422688+24391 428272 Enzo Doria 12/2023 525 (10^427912+89)/9 427912 Serge Batalov 12/2014 526 2^1421089+1890167 427791 Enzo Doria 09/2017 527 2^1420902+221149 427735 Enzo Doria 05/2024 528 2^1418388+25771 426978 Enzo Doria 12/2023 529 2^1416724+214981 426477 Enzo Doria 11/2023 530 (96228^85849-1)/(96228^293-1) 426352 Ryan Propper 11/2023 531 20^326600+3 424917 Paul Bourdelais 01/2021 532 (10^424861-7)/3 424861 Leonid Durman 01/2012 533 10^424821-11 424821 Mischa Rodermond 04/2023 534 (2^1411200+13)/7 424813 Stefano Morozzi 09/2022 535 2^1411117+35927 424789 Enzo Doria 09/2024 536 2^1410894+219859 424722 Enzo Doria 03/2024 537 2^1410310+30409 424546 Enzo Doria 05/2024 538 2^1410233+218447 424523 Enzo Doria 03/2024 539 1+3^605376+5^605376 423140 Jon Grantham 08/2023 540 2^1405367+213413 423058 Enzo Doria 10/2023 541 2^1404213+184217 422711 Enzo Doria 09/2017 542 2^1401872+1884385 422006 Enzo Doria 04/2017 543 2^1401257+6077 421821 Enzo Doria 09/2017 544 138^196873-137^196873 421285 Jean-Louis Charton 12/2009 545 2^1398726+7 421059 Stefano Morozzi 10/2022 546 2^1398269+131595 420921 Makoto Morimoto 10/2013 547 2^1397071+684443 420561 Enzo Doria 07/2017 548 953^141023-952^141023 420121 Jean-Louis Charton 10/2016 549 2^1393111+1867211 419369 Enzo Doria 09/2023 550 (3^877843-1)/2 418838 Paul Bourdelais 07/2010 551 2^1389628+28651 418320 Enzo Doria 03/2024 552 2^1386321+60299 417325 Enzo Doria 02/2018 553 2^1386320+184531 417324 Enzo Doria 09/2017 554 2^1382074+1883587 416046 Enzo Doria 01/2017 555 2^1380651+215843 415618 Enzo Doria 12/2023 556 2^1379907+1885223 415394 Enzo Doria 03/2017 557 2^1379111+29693 415154 Enzo Doria 05/2024 558 2^1376707+25763 414431 Enzo Doria 12/2023 559 2^1375751+24443 414143 Enzo Doria 12/2023 560 2^1375574+1886719 414090 Enzo Doria 04/2017 561 2^1373111+1884833 413348 Enzo Doria 02/2017 562 2^1372996+15 413313 Stefano Morozzi 10/2022 563 2^1372515+32393 413169 Enzo Doria 05/2024 564 2^1369171+216593 412162 Enzo Doria 01/2024 565 2^1368632+1889731 412000 Enzo Doria 10/2017 566 (65245^85849-1)/(65245^293-1) 411914 Ryan Propper 11/2023 567 (89*10^411590+1)/9 411591 Serge Batalov 09/2014 568 F(1968721) 411439 Henri Lifchitz 11/2009 569 2^1366066+683749 411227 Enzo Doria 02/2017 570 2^1364401+217727 410726 Enzo Doria 02/2024 571 2^1364303+219533 410697 Enzo Doria 03/2024 572 2^1363434+27589 410435 Enzo Doria 02/2024 573 2^1363068+222631 410325 Enzo Doria 06/2024 574 2^1359550+25819 409266 Enzo Doria 12/2023 575 2^1357392+224401 408616 Enzo Doria 06/2024 576 2^1355826+15 408145 Stefano Morozzi 10/2022 577 2^1355790+1888939 408134 Enzo Doria 07/2017 578 2^1355635+1884203 408087 Enzo Doria 01/2017 579 (22071^94249-1)/(22071^307-1) 408068 Ryan Propper 11/2023 580 2^1355083+221603 407921 Enzo Doria 05/2024 581 2^1349535+218783 406251 Enzo Doria 03/2024 582 (55766^85849-1)/(55766^293-1) 406081 Ryan Propper 11/2023 583 2^1348956+24241 406077 Enzo Doria 11/2023 584 (88^208739+1)/89 405888 Paul Bourdelais 12/2020 585 (2^1347781-2^673891+1)/5 405722 Borys Jaworski 10/2008 586 2^1347744-3 405712 Paul Bourdelais 07/2019 587 2^1346431+691203 405317 Boyan Hu 09/2024 588 9*10^404644-11 404645 Mischa Rodermond 04/2023 589 1215^131072+242^131072 404302 Kellen Shenton 08/2022 590 2^1341908+212911 403955 Enzo Doria 09/2023 591 1196^131072+595^131072 403405 Kellen Shenton 08/2022 592 2^1339302+29389 403171 Enzo Doria 04/2024 593 2^1335130+31669 401915 Enzo Doria 07/2024 594 2^1330371+28313 400482 Enzo Doria 03/2024 595 10^400000+1415223 400001 Patrick De Geest 10/2020 596 10^400000-339233 400000 Patrick De Geest 10/2020 597 2^1323373+27317 398375 Enzo Doria 01/2024 598 Tau(863^24630) 397727 Nik Lygeros / Olivier Rozier 01/2016 599 2^1320423+24293 397487 Enzo Doria 11/2023 600 2^1320057+211517 397377 Enzo Doria 08/2023 601 2^1319770+1884949 397291 Enzo Doria 06/2017 602 2^1319616+30091 397244 Enzo Doria 04/2024 603 2^1317657+31367 396655 Enzo Doria 04/2024 604 2^1314741+219257 395777 Enzo Doria 03/2024 605 2^1313062+1888849 395272 Enzo Doria 08/2017 606 (1073516^81920+1)/(1073516^16384+1) 395236 Serge Batalov 01/2017 607 2^1312349+221177 395057 Enzo Doria 04/2024 608 (1059995^81920+1)/(1059995^16384+1) 394875 Serge Batalov 01/2017 609 2^1311618+783529 394837 Enzo Doria 01/2017 610 2^1308992+28111 394046 Enzo Doria 02/2024 611 2^1308000+1883521 393748 Enzo Doria 02/2017 612 2^1307324+224611 393544 Enzo Doria 07/2024 613 2^1307262+28759 393526 Enzo Doria 02/2024 614 (1009565^81920+1)/(1009565^16384+1) 393487 Serge Batalov 01/2017 615 2^1305860+35461 393104 Enzo Doria 08/2024 616 (995042^81920+1)/(995042^16384+1) 393075 Serge Batalov 01/2017 617 (988945^81920+1)/(988945^16384+1) 392900 Serge Batalov 01/2017 618 (988823^81920+1)/(988823^16384+1) 392897 Serge Batalov 01/2017 619 (2^1304983-1)/52199321 392832 Tony Prest / Never Odd Or Even 03/2014 620 (978970^81920+1)/(978970^16384+1) 392612 Serge Batalov 01/2017 621 2^1303102+1866409 392273 Enzo Doria 09/2017 622 2^1302818+283429 392188 Enzo Doria 01/2017 623 2^1301430+22669 391770 Enzo Doria 10/2023 624 2^1301229+222467 391709 Enzo Doria 04/2024 625 (934422^81920+1)/(934422^16384+1) 391286 Serge Batalov 01/2017 626 2^1299181+1886867 391093 Enzo Doria 04/2017 627 (37^249341-1)/36 391016 Paul Bourdelais 08/2020 628 2^1298304+1882891 390829 Enzo Doria 01/2017 629 95196^12497+12497^95196 390000 Hans Havermann 12/2021 630 2^1295539+35633 389997 Enzo Doria 08/2024 631 86206^33381+33381^86206 389953 Hans Havermann 05/2023 632 2^1294324+25171 389631 Enzo Doria 12/2023 633 (874207^81920+1)/(874207^16384+1) 389390 Serge Batalov 01/2017 634 2^1289624+32551 388216 Enzo Doria 05/2024 635 (7^457871-5^457871)/2 386946 Jon Grantham 08/2023 636 79455^73828+73828^79455 386805 Hans Havermann 03/2023 637 81650^54369+54369^81650 386642 Yusuf AttarBashi 06/2021 638 80565^62824+62824^80565 386561 Hans Havermann 08/2021 639 83747^41272+41272^83747 386548 Hans Havermann 08/2021 640 15^328574+328574^15 386434 Serge Batalov 05/2014 641 2^1280078+1885099 385342 Enzo Doria 08/2017 642 2^1279921+17 385295 Stefano Morozzi 10/2022 643 2^1279245+224087 385092 Enzo Doria 07/2024 644 2^1276977+71657 384409 Enzo Doria 08/2023 645 (76803^78961-1)/(76803^281-1) 384382 Ryan Propper 11/2023 646 2^1276571+26213 384287 Enzo Doria 12/2023 647 MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832,26908) 384166 Sergey Batalov 05/2024 648 2^1274941+1880717 383796 Enzo Doria 10/2016 649 2^1272632+383431 383101 Enzo Doria 01/2017 650 2^1271346+1889839 382714 Enzo Doria 08/2017 651 2^1271173+219587 382662 Enzo Doria 03/2024 652 5*3^798534-2^798534 380999 Jon Grantham 08/2023 653 (10^380976-7)/3 380976 Leonid Durman 01/2012 654 2^1264748+23221 380728 Enzo Doria 11/2023 655 (4*10^380056+11)/3 380057 Tyler Busby 03/2023 656 2^1260859+222683 379557 Enzo Doria 06/2024 657 2^1257787+1447761 378632 Makoto Morimoto 10/2013 658 (2^1257787+32270)/(2*233*281*2207*3011) 378620 Makoto Morimoto 12/2016 659 2^1257728+20851 378614 Enzo Doria 08/2023 660 (77^200657-1)/76 378536 Paul Bourdelais 08/2020 661 (98^189619+1)/99 377573 Paul Bourdelais 02/2021 662 F(1803059) 376817 Henri Lifchitz 06/2009 663 2^1250590+29389 376466 Enzo Doria 03/2024 664 (10^376417-3^376417)/7 376417 Jon Grantham 08/2023 665 2^1250116+34951 376323 Enzo Doria 08/2024 666 2^1246724+213961 375302 Enzo Doria 10/2023 667 2^1245230+19 374852 Stefano Morozzi 10/2022 668 7^442674+4 374103 Paul Bourdelais 02/2021 669 2^1239151+35633 373022 Enzo Doria 08/2024 670 2^1237699+34703 372585 Enzo Doria 07/2024 671 (97^187393-1)/96 372306 Paul Bourdelais 09/2020 672 10^371696+7 371697 Alfred Reich 05/2021 673 2^1234709+883127 371685 Enzo Doria 12/2016 674 2^1234119+21803 371507 Enzo Doria 09/2023 675 (67^203431+1)/68 371479 Paul Bourdelais 09/2021 676 2^1233971+216593 371463 Enzo Doria 12/2023 677 2^1233212+27301 371234 Enzo Doria 12/2023 678 2^1231466+283819 370709 Enzo Doria 07/2017 679 2^1229766+26659 370197 Enzo Doria 12/2023 680 2^1228899+30713 369936 Enzo Doria 03/2024 681 2^1228892+223831 369934 Enzo Doria 06/2024 682 (49627^78961-1)/(49627^281-1) 369460 Ryan Propper 11/2023 683 2^1227060+226663 369382 Enzo Doria 09/2024 684 2^1226987+28163 369360 Enzo Doria 02/2024 685 2^1226569+30857 369235 Enzo Doria 03/2024 686 73^197880+197880 368715 Kellen Shenton 06/2023 687 5*3^771723-2^771723 368207 Jon Grantham 08/2023 688 2^1222473+221597 368002 Enzo Doria 04/2024 689 2^1222211+22703 367923 Enzo Doria 11/2023 690 (2^1222097+19)/3 367888 Stefano Morozzi 09/2022 691 2^1220335+1881263 367358 Enzo Doria 11/2016 692 2^1218344+215641 366759 Enzo Doria 12/2023 693 2^1217510+220039 366508 Enzo Doria 03/2024 694 (233^154787-1)/232 366434 Anonymous 05/2024 695 2^1216694+1884769 366262 Enzo Doria 02/2017 696 2^1215889-3 366020 Paul Bourdelais 06/2019 697 2^1215296+1885441 365841 Enzo Doria 03/2017 698 (80^192133+1)/81 365645 Paul Bourdelais 01/2021 699 2^1214307+1888115 365543 Enzo Doria 05/2017 700 2^1213815+3 365395 Paul Bourdelais 06/2019 701 (80^191953+1)/81 365302 Paul Bourdelais 01/2021 702 2^1213313+215837 365244 Enzo Doria 11/2023 703 2^1208276+22201 363728 Enzo Doria 09/2023 704 2^1207345+1882577 363448 Enzo Doria 12/2016 705 2^1207336+217801 363445 Enzo Doria 03/2024 706 2^1207073+883727 363366 Enzo Doria 03/2017 707 3^761457-2 363308 Ryan Propper 07/2015 708 (10^363030+7)/337/443 363025 Alfred Reich 12/2021 709 2^1204869+224885 362702 Enzo Doria 07/2024 710 2^1200972+141811 361529 Stefano Morozzi 10/2022 711 (2^1200924+324730)/2 361514 Stefano Morozzi 06/2021 712 (2^1200912+274110)/2 361511 Stefano Morozzi 01/2021 713 2^1200906+165249 361509 Stefano Morozzi 07/2022 714 2^1200890+166339 361504 Stefano Morozzi 01/2023 715 (2^1200887+344126)/2 361503 Stefano Morozzi 10/2020 716 2^1200877+186755 361500 Stefano Morozzi 09/2022 717 2^1200861+198521 361496 Stefano Morozzi 11/2021 718 (2^1200856+305790)/2 361494 Stefano Morozzi 10/2020 719 (2^1200853+372822)/2 361493 Stefano Morozzi 06/2021 720 2^1200812+324178)/2 361481 Stefano Morozzi 06/2021 721 (2^1200768+380458)/2 361467 Stefano Morozzi 01/2021 722 2^1200756+140917 361464 Stefano Morozzi 05/2022 723 2^1200741+184781 361460 Stefano Morozzi 09/2022 724 (2^1200741+293402)/2 361459 Stefano Morozzi 07/2021 725 2^1200734+142653 361457 Stefano Morozzi 02/2023 727 2^1200672+1880881 361439 Enzo Doria 10/2016 726 2^1200672+141535 361439 Stefano Morozzi 09/2022 728 2^1200669+178805 361438 Stefano Morozzi 11/2022 729 2^1200660+198555 361435 Stefano Morozzi 12/2021 730 2^1200657+164837 361434 Stefano Morozzi 05/2022 731 2^1200631+166431 361426 Stefano Morozzi 02/2023 732 2^1200627+150669 361425 Stefano Morozzi 02/2023 733 (2^1200603+356030)/2 361418 Stefano Morozzi 10/2020 734 (2^1200590+275854)/2 361414 Stefano Morozzi 03/2021 735 2^1200550+139297 361402 Stefano Morozzi 10/2021 736 2^1200486+172855 361383 Stefano Morozzi 01/2023 737 (2^1200456+320526)/2 361373 Stefano Morozzi 10/2020 738 2^1200443+142121 361370 Stefano Morozzi 01/2023 739 2^1200416+164065 361362 Stefano Morozzi 01/2022 740 2^1200331+155429 361336 Stefano Morozzi 10/2021 742 (2^1200289+348366)/2 361323 Stefano Morozzi 10/2020 741 2^1200289+141885 361323 Stefano Morozzi 11/2022 743 (2^1200284+273162)/2 361322 Stefano Morozzi 10/2020 744 2^1200252+194535 361312 Stefano Morozzi 11/2021 745 (2^1200250+364230)/2 361311 Stefano Morozzi 10/2020 746 2^1200227+156881 361305 Stefano Morozzi 05/2022 747 (2^1200209+305990)/2 361299 Stefano Morozzi 10/2020 748 (2^1200210+376278)/2 361299 Stefano Morozzi 10/2020 749 2^1200202+216499 361297 Enzo Doria 12/2023 750 (2^1200182+274462)/2 361291 Stefano Morozzi 01/2021

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 12 2024 08:27 (Time in France)

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