## PRP Records

### Probable Primes Top 10000

#### (295149 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 ? 501 2^1398726+7 421059 Stefano Morozzi 10/2022 502 2^1398269+131595 420921 Makoto Morimoto 10/2013 503 2^1397071+684443 420561 Enzo Doria 07/2017 504 953^141023-952^141023 420121 Jean-Louis Charton 10/2016 505 2^1393111+1867211 419369 Enzo Doria 09/2023 506 (3^877843-1)/2 418838 Paul Bourdelais 07/2010 507 2^1389628+28651 418320 Enzo Doria 03/2024 508 2^1386321+60299 417325 Enzo Doria 02/2018 509 2^1386320+184531 417324 Enzo Doria 09/2017 510 2^1382074+1883587 416046 Enzo Doria 01/2017 511 2^1380651+215843 415618 Enzo Doria 12/2023 512 2^1379907+1885223 415394 Enzo Doria 03/2017 513 2^1379111+29693 415154 Enzo Doria 05/2024 514 2^1376707+25763 414431 Enzo Doria 12/2023 515 2^1375751+24443 414143 Enzo Doria 12/2023 516 2^1375574+1886719 414090 Enzo Doria 04/2017 517 2^1373111+1884833 413348 Enzo Doria 02/2017 518 2^1372996+15 413313 Stefano Morozzi 10/2022 519 2^1372515+32393 413169 Enzo Doria 05/2024 520 2^1369171+216593 412162 Enzo Doria 01/2024 521 2^1368632+1889731 412000 Enzo Doria 10/2017 522 (65245^85849-1)/(65245^293-1) 411914 Ryan Propper 11/2023 523 (89*10^411590+1)/9 411591 Serge Batalov 09/2014 524 F(1968721) 411439 Henri Lifchitz 11/2009 525 2^1366066+683749 411227 Enzo Doria 02/2017 526 2^1364401+217727 410726 Enzo Doria 02/2024 527 2^1364303+219533 410697 Enzo Doria 03/2024 528 2^1363434+27589 410435 Enzo Doria 02/2024 529 2^1359550+25819 409266 Enzo Doria 12/2023 530 2^1355826+15 408145 Stefano Morozzi 10/2022 531 2^1355790+1888939 408134 Enzo Doria 07/2017 532 2^1355635+1884203 408087 Enzo Doria 01/2017 533 (22071^94249-1)/(22071^307-1) 408068 Ryan Propper 11/2023 534 2^1349535+218783 406251 Enzo Doria 03/2024 535 (55766^85849-1)/(55766^293-1) 406081 Ryan Propper 11/2023 536 2^1348956+24241 406077 Enzo Doria 11/2023 537 (88^208739+1)/89 405888 Paul Bourdelais 12/2020 538 (2^1347781-2^673891+1)/5 405722 Borys Jaworski 10/2008 539 2^1347744-3 405712 Paul Bourdelais 07/2019 540 9*10^404644-11 404645 Mischa Rodermond 04/2023 541 1215^131072+242^131072 404302 Kellen Shenton 08/2022 542 2^1341908+212911 403955 Enzo Doria 09/2023 543 1196^131072+595^131072 403405 Kellen Shenton 08/2022 544 2^1339302+29389 403171 Enzo Doria 04/2024 545 2^1330371+28313 400482 Enzo Doria 03/2024 546 10^400000+1415223 400001 Patrick De Geest 10/2020 547 10^400000-339233 400000 Patrick De Geest 10/2020 548 2^1323373+27317 398375 Enzo Doria 01/2024 549 Tau(863^24630) 397727 Nik Lygeros / Olivier Rozier 01/2016 550 2^1320423+24293 397487 Enzo Doria 11/2023 551 2^1320057+211517 397377 Enzo Doria 08/2023 552 2^1319770+1884949 397291 Enzo Doria 06/2017 553 2^1319616+30091 397244 Enzo Doria 04/2024 554 2^1317657+31367 396655 Enzo Doria 04/2024 555 2^1314741+219257 395777 Enzo Doria 03/2024 556 2^1313062+1888849 395272 Enzo Doria 08/2017 557 (1073516^81920+1)/(1073516^16384+1) 395236 Serge Batalov 01/2017 558 2^1312349+221177 395057 Enzo Doria 04/2024 559 (1059995^81920+1)/(1059995^16384+1) 394875 Serge Batalov 01/2017 560 2^1311618+783529 394837 Enzo Doria 01/2017 561 2^1308992+28111 394046 Enzo Doria 02/2024 562 2^1308000+1883521 393748 Enzo Doria 02/2017 563 2^1307262+28759 393526 Enzo Doria 02/2024 564 (1009565^81920+1)/(1009565^16384+1) 393487 Serge Batalov 01/2017 565 (995042^81920+1)/(995042^16384+1) 393075 Serge Batalov 01/2017 566 (988945^81920+1)/(988945^16384+1) 392900 Serge Batalov 01/2017 567 (988823^81920+1)/(988823^16384+1) 392897 Serge Batalov 01/2017 568 (2^1304983-1)/52199321 392832 Tony Prest / Never Odd Or Even 03/2014 569 (978970^81920+1)/(978970^16384+1) 392612 Serge Batalov 01/2017 570 2^1303102+1866409 392273 Enzo Doria 09/2017 571 2^1302818+283429 392188 Enzo Doria 01/2017 572 2^1301430+22669 391770 Enzo Doria 10/2023 573 2^1301229+222467 391709 Enzo Doria 04/2024 574 (934422^81920+1)/(934422^16384+1) 391286 Serge Batalov 01/2017 575 2^1299181+1886867 391093 Enzo Doria 04/2017 576 (37^249341-1)/36 391016 Paul Bourdelais 08/2020 577 2^1298304+1882891 390829 Enzo Doria 01/2017 578 95196^12497+12497^95196 390000 Hans Havermann 12/2021 579 86206^33381+33381^86206 389953 Hans Havermann 05/2023 580 2^1294324+25171 389631 Enzo Doria 12/2023 581 (874207^81920+1)/(874207^16384+1) 389390 Serge Batalov 01/2017 582 2^1289624+32551 388216 Enzo Doria 05/2024 583 (7^457871-5^457871)/2 386946 Jon Grantham 08/2023 584 79455^73828+73828^79455 386805 Hans Havermann 03/2023 585 81650^54369+54369^81650 386642 Yusuf AttarBashi 06/2021 586 80565^62824+62824^80565 386561 Hans Havermann 08/2021 587 83747^41272+41272^83747 386548 Hans Havermann 08/2021 588 15^328574+328574^15 386434 Serge Batalov 05/2014 589 2^1280078+1885099 385342 Enzo Doria 08/2017 590 2^1279921+17 385295 Stefano Morozzi 10/2022 591 2^1276977+71657 384409 Enzo Doria 08/2023 592 (76803^78961-1)/(76803^281-1) 384382 Ryan Propper 11/2023 593 2^1276571+26213 384287 Enzo Doria 12/2023 594 2^1274941+1880717 383796 Enzo Doria 10/2016 595 2^1272632+383431 383101 Enzo Doria 01/2017 596 2^1271346+1889839 382714 Enzo Doria 08/2017 597 2^1271173+219587 382662 Enzo Doria 03/2024 598 5*3^798534-2^798534 380999 Jon Grantham 08/2023 599 (10^380976-7)/3 380976 Leonid Durman 01/2012 600 2^1264748+23221 380728 Enzo Doria 11/2023 601 (4*10^380056+11)/3 380057 Tyler Busby 03/2023 602 2^1257787+1447761 378632 Makoto Morimoto 10/2013 603 (2^1257787+32270)/(2*233*281*2207*3011) 378620 Makoto Morimoto 12/2016 604 2^1257728+20851 378614 Enzo Doria 08/2023 605 (77^200657-1)/76 378536 Paul Bourdelais 08/2020 606 (98^189619+1)/99 377573 Paul Bourdelais 02/2021 607 F(1803059) 376817 Henri Lifchitz 06/2009 608 2^1250590+29389 376466 Enzo Doria 03/2024 609 (10^376417-3^376417)/7 376417 Jon Grantham 08/2023 610 2^1246724+213961 375302 Enzo Doria 10/2023 611 2^1245230+19 374852 Stefano Morozzi 10/2022 612 7^442674+4 374103 Paul Bourdelais 02/2021 613 (97^187393-1)/96 372306 Paul Bourdelais 09/2020 614 10^371696+7 371697 Alfred Reich 05/2021 615 2^1234709+883127 371685 Enzo Doria 12/2016 616 2^1234119+21803 371507 Enzo Doria 09/2023 617 (67^203431+1)/68 371479 Paul Bourdelais 09/2021 618 2^1233971+216593 371463 Enzo Doria 12/2023 619 2^1233212+27301 371234 Enzo Doria 12/2023 620 2^1231466+283819 370709 Enzo Doria 07/2017 621 2^1229766+26659 370197 Enzo Doria 12/2023 622 2^1228899+30713 369936 Enzo Doria 03/2024 623 (49627^78961-1)/(49627^281-1) 369460 Ryan Propper 11/2023 624 2^1226987+28163 369360 Enzo Doria 02/2024 625 2^1226569+30857 369235 Enzo Doria 03/2024 626 73^197880+197880 368715 Kellen Shenton 06/2023 627 5*3^771723-2^771723 368207 Jon Grantham 08/2023 628 2^1222473+221597 368002 Enzo Doria 04/2024 629 2^1222211+22703 367923 Enzo Doria 11/2023 630 (2^1222097+19)/3 367888 Stefano Morozzi 09/2022 631 2^1220335+1881263 367358 Enzo Doria 11/2016 632 2^1218344+215641 366759 Enzo Doria 12/2023 633 2^1217510+220039 366508 Enzo Doria 03/2024 634 2^1216694+1884769 366262 Enzo Doria 02/2017 635 2^1215889-3 366020 Paul Bourdelais 06/2019 636 2^1215296+1885441 365841 Enzo Doria 03/2017 637 (80^192133+1)/81 365645 Paul Bourdelais 01/2021 638 2^1214307+1888115 365543 Enzo Doria 05/2017 639 2^1213815+3 365395 Paul Bourdelais 06/2019 640 (80^191953+1)/81 365302 Paul Bourdelais 01/2021 641 2^1213313+215837 365244 Enzo Doria 11/2023 642 2^1208276+22201 363728 Enzo Doria 09/2023 643 2^1207345+1882577 363448 Enzo Doria 12/2016 644 2^1207336+217801 363445 Enzo Doria 03/2024 645 2^1207073+883727 363366 Enzo Doria 03/2017 646 3^761457-2 363308 Ryan Propper 07/2015 647 (10^363030+7)/337/443 363025 Alfred Reich 12/2021 648 2^1200972+141811 361529 Stefano Morozzi 10/2022 649 (2^1200924+324730)/2 361514 Stefano Morozzi 06/2021 650 (2^1200912+274110)/2 361511 Stefano Morozzi 01/2021 651 2^1200906+165249 361509 Stefano Morozzi 07/2022 652 2^1200890+166339 361504 Stefano Morozzi 01/2023 653 (2^1200887+344126)/2 361503 Stefano Morozzi 10/2020 654 2^1200877+186755 361500 Stefano Morozzi 09/2022 655 2^1200861+198521 361496 Stefano Morozzi 11/2021 656 (2^1200856+305790)/2 361494 Stefano Morozzi 10/2020 657 (2^1200853+372822)/2 361493 Stefano Morozzi 06/2021 658 2^1200812+324178)/2 361481 Stefano Morozzi 06/2021 659 (2^1200768+380458)/2 361467 Stefano Morozzi 01/2021 660 2^1200756+140917 361464 Stefano Morozzi 05/2022 661 2^1200741+184781 361460 Stefano Morozzi 09/2022 662 (2^1200741+293402)/2 361459 Stefano Morozzi 07/2021 663 2^1200734+142653 361457 Stefano Morozzi 02/2023 665 2^1200672+1880881 361439 Enzo Doria 10/2016 664 2^1200672+141535 361439 Stefano Morozzi 09/2022 666 2^1200669+178805 361438 Stefano Morozzi 11/2022 667 2^1200660+198555 361435 Stefano Morozzi 12/2021 668 2^1200657+164837 361434 Stefano Morozzi 05/2022 669 2^1200631+166431 361426 Stefano Morozzi 02/2023 670 2^1200627+150669 361425 Stefano Morozzi 02/2023 671 (2^1200603+356030)/2 361418 Stefano Morozzi 10/2020 672 (2^1200590+275854)/2 361414 Stefano Morozzi 03/2021 673 2^1200550+139297 361402 Stefano Morozzi 10/2021 674 2^1200486+172855 361383 Stefano Morozzi 01/2023 675 (2^1200456+320526)/2 361373 Stefano Morozzi 10/2020 676 2^1200443+142121 361370 Stefano Morozzi 01/2023 677 2^1200416+164065 361362 Stefano Morozzi 01/2022 678 2^1200331+155429 361336 Stefano Morozzi 10/2021 680 (2^1200289+348366)/2 361323 Stefano Morozzi 10/2020 679 2^1200289+141885 361323 Stefano Morozzi 11/2022 681 (2^1200284+273162)/2 361322 Stefano Morozzi 10/2020 682 2^1200252+194535 361312 Stefano Morozzi 11/2021 683 (2^1200250+364230)/2 361311 Stefano Morozzi 10/2020 684 2^1200227+156881 361305 Stefano Morozzi 05/2022 685 (2^1200209+305990)/2 361299 Stefano Morozzi 10/2020 686 (2^1200210+376278)/2 361299 Stefano Morozzi 10/2020 687 2^1200202+216499 361297 Enzo Doria 12/2023 688 (2^1200182+274462)/2 361291 Stefano Morozzi 01/2021 689 2^1200178+149193 361290 Stefano Morozzi 07/2022 690 2^1200168+140403 361287 Stefano Morozzi 03/2022 691 (2^1200162+275910)/2 361285 Stefano Morozzi 03/2021 692 2^1200157+168927 361284 Stefano Morozzi 02/2023 693 2^1200134+141385 361277 Stefano Morozzi 08/2022 694 (2^1200131+360150)/2 361276 Stefano Morozzi 10/2020 695 (2^1200118+290718)/2 361272 Stefano Morozzi 01/2021 696 2^1200022+192777 361243 Stefano Morozzi 09/2022 697 2^1200021+149777 361243 Stefano Morozzi 10/2022 698 (64*10^360173-1)/243 360173 Serge Batalov 09/2014 699 (59^203309+1)/60 360029 Paul Bourdelais 09/2021 700 (2*10^359860-11)/9 359860 Rytis Slatkevicius 01/2023 701 2^1195093+1882577 359759 Enzo Doria 12/2016 702 3^753451+5*2^753451 359488 Jon Grantham 08/2023 703 (6^461108-11)/5 358812 Paul Bourdelais 04/2019 704 2^1191375+8543 358640 Phil Moore 06/2008 705 2^1190972+1880191 358519 Enzo Doria 11/2016 706 2^1189930+28549 358205 Enzo Doria 03/2024 707 (45^216551-1)/44 358004 Paul Bourdelais 08/2020 708 (50^210319-1)/49 357324 Paul Bourdelais 08/2020 709 (531^131072+25^131072)/2 357184 Kellen Shenton 03/2021 710 2^1184565+21227 356590 Enzo Doria 08/2023 711 2^1180159+22823 355264 Enzo Doria 11/2023 712 2^1179836+1885021 355167 Enzo Doria 02/2017 713 2^1178942+32269 354897 Enzo Doria 04/2024 714 2^1177053+28607 354329 Enzo Doria 02/2024 715 (19*10^353884-91)/9 353885 Alfred Reich 02/2023 716 (10^353884*19-91)/9 353885 Alfred Reich 10/2023 717 20^271951+3 353817 Paul Bourdelais 01/2021 718 72722^72722+7^7 353551 Serge Batalov 04/2024 719 2^1173095+21 353137 Stefano Morozzi 10/2022 720 2^1170959+218945 352494 Enzo Doria 03/2024 721 (63^195893-1)/62 352477 Paul Bourdelais 08/2020 722 2^1170331+27293 352305 Enzo Doria 01/2024 723 2^1170326+7 352304 Stefano Morozzi 10/2022 724 numbpart(100000135540) 352269 Serge Batalov 04/2017 725 (10^352237-1)/9/10567111/950335427 352221 Maksym Voznyy 01/2015 726 5*3^737931-2^737931 352084 Jon Grantham 08/2023 727 2^1168554+783529 351770 Enzo Doria 01/2017 728 (2^1168183-1)/54763676838381762583 351639 Matthias Wurtinger 01/2011 729 2^1166950+30409 351287 Enzo Doria 03/2024 730 2^1166152+1882411 351047 Enzo Doria 12/2016 731 2^1163972+20971 350391 Enzo Doria 08/2023 732 2^1163272+22411 350180 Enzo Doria 10/2023 733 10^350071+7 350072 Alfred Reich 05/2021 734 2^1162154+1890207 349844 Enzo Doria 08/2017 735 (7*10^348724-61)/9 348724 Erik Branger 09/2016 736 (4*10^348453+41)/9 348453 Serge Batalov 11/2022 737 (127^165601-1)/126 348390 Alexander Zhirkov 09/2015 738 2^1155085+213377 347716 Enzo Doria 09/2023 739 2^1153083+1883693 347113 Enzo Doria 04/2017 740 (2^1148729+2^574365+1)/5 345802 Borys Jaworski 03/2007 741 2^1145882+80779 344945 Enzo Doria 09/2016 742 2^1143425+221177 344206 Enzo Doria 03/2024 743 2^1141813+27047 343720 Enzo Doria 12/2023 744 2^1141114+221869 343510 Enzo Doria 04/2024 745 2^1138296+27541 342662 Enzo Doria 01/2024 746 2^1136462+1887289 342110 Enzo Doria 05/2017 747 F(1636007) 341905 Henri Lifchitz 03/2009 748 (2^1135567+13)/3 341840 Stefano Morozzi 09/2022 749 2^1133678+782569 341272 Enzo Doria 11/2016 750 (11^327001+1)/12 340536 Paul Bourdelais 09/2013

Find by discoverer :

Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 22 2024 21:19 (Time in France)

Go back