## PRP Records

### Probable Primes Top 10000

#### (295503 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 ? 2501 (14*10^178822+67)/9 178823 Robert Price 05/2022 2502 (29*10^178732-119)/9 178733 Robert Price 12/2021 2503 2^593631+101381 178701 Jorge Menendez 04/2018 2504 10^178695+136719 178696 Patrick De Geest 05/2016 2505 10^178695-71 178695 Serge Batalov 12/2014 2506 (2*10^178649-161)/3 178649 Robert Price 12/2020 2507 (691^62903-1)/690 178609 Michael Stocker 05/2020 2508 (2^148330+1)^4-2 178608 Cletus Emmanuel 12/2003 2509 2^593242+28309 178584 Enzo Doria 01/2024 2510 2^593222-14145 178578 Jorge Menendez 10/2017 2511 7*10^178566+33 178567 Robert Price 06/2020 2512 2^593178+1867219 178565 Enzo Doria 03/2016 2513 2^593152+22441 178557 Enzo Doria 09/2023 2514 (38*10^178456+151)/9 178457 Robert Price 03/2022 2515 (302*10^178369+13)/9 178371 Robert Price 02/2020 2516 (26*10^178296-113)/3 178297 Robert Price 06/2020 2517 (18^142031-1)/17 178287 Paul Bourdelais 03/2010 2518 (13*10^178233+137)/3 178234 Robert Price 06/2021 2519 (5*10^178206+91)/3 178207 Robert Price 04/2018 2520 2^591872-291929 178172 Enzo Doria 07/2015 2521 2^591682-286871 178115 Enzo Doria 07/2015 2522 (7^210761-5^210761)/2 178114 Jon Grantham 08/2023 2523 4*10^178091+9 178092 Robert Price 05/2015 2524 410747#+478483 178007 Makoto Morimoto 02/2016 2525 3*10^177872+73 177873 Robert Price 08/2018 2526 2^590762-396765 177838 Enzo Doria 08/2013 2527 (136*10^177754-1)/9 177756 Serge Batalov 12/2014 2528 ReverseConsecutiveIntegerPrime(37765) 177719 Eric W. Weisstein 04/2010 2529 Smr(37765) 177719 Eric W. Weisstein 12/2021 2530 (266*10^177577-11)/3 177579 Robert Price 04/2020 2531 (11*10^177466-113)/3 177467 Robert Price 10/2018 2532 3*10^177373-97 177374 Robert Price 07/2018 2533 2^589204+1881151 177369 Enzo Doria 11/2016 2534 2^589132-69479 177347 Enzo Doria 01/2016 2535 (101*10^177302-17)/3 177304 Robert Price 02/2020 2536 2^588912-113519 177281 Enzo Doria 08/2014 2537 (682*10^177266-7)/9 177268 Robert Price 08/2021 2538 15^150706+2 177245 Robert Price 06/2015 2539 (31208^39601-1)/(31208^199-1) 177084 Ryan Propper 11/2023 2540 2^588194-1861001 177065 Enzo Doria 11/2015 2541 5*10^177016-37 177017 Robert Price 11/2021 2542 fibonacci(846926)-4 176997 Jon Grantham 08/2023 2543 (23*10^176964-47)/3 176965 Robert Price 09/2019 2544 20530^41031+41031^20530 176942 Norbert Schneider 07/2022 2545 (19*10^176932+521)/9 176933 Robert Price 05/2018 2546 (8*10^176908+43)/3 176909 Robert Price 06/2018 2547 (85*10^176900+203)/9 176901 Robert Price 09/2020 2548 2^587560-113699 176874 Enzo Doria 09/2014 2549 20596^40995+40995^20596 176844 Norbert Schneider 07/2022 2550 (101*10^176815-17)/3 176817 Robert Price 02/2020 2551 (25*10^176715-37)/3 176716 Robert Price 10/2019 2552 5^252763-12862 176674 Enzo Doria 05/2014 2553 38442^38531+38531^38442 176658 Norbert Schneider 09/2022 2554 2^586829+23961 176654 Enzo Doria 10/2023 2555 2^586804+81721 176646 Enzo Doria 08/2016 2556 (10^176584+77)/3 176584 Robert Price 01/2018 2557 2^586570+1874419 176576 Enzo Doria 06/2016 2558 (157*10^176482-1)/3 176484 Robert Price 01/2022 2559 5*2^586202+3 176466 Jon Grantham 07/2023 2560 27122^39799-39799^27122 176442 Frank Doornink 01/2024 2561 2^585994-3311 176402 Yves Minet 12/2014 2562 8*10^176383-81 176384 Robert Price 02/2021 2563 (23*10^176357+61)/3 176358 Robert Price 01/2022 2564 2^585832-112799 176354 Enzo Doria 07/2014 2565 fibonacci(843383)+4 176257 Jon Grantham 08/2023 2566 (29*10^176240+49)/3 176241 Robert Price 09/2021 2567 (2^585387-11)/3 176219 Stefano Morozzi 08/2022 2568 2^585336-461039 176204 Enzo Doria 06/2015 2569 (25*10^176164+143)/3 176165 Robert Price 08/2020 2570 2^585095-1848127 176132 Enzo Doria 08/2015 2571 (5*10^176101-311)/9 176101 Robert Price 12/2021 2572 6*10^176092+77 176093 Robert Price 06/2020 2573 2^584950-115451 176088 Enzo Doria 07/2015 2574 (646*10^176044+11)/9 176046 Robert Price 10/2021 2575 (7^208283-5^208283)/2 176020 Jon Grantham 08/2023 2576 2^584671-3697 176004 Yves Minet 03/2017 2577 (13*10^175965-37)/3 175966 Robert Price 01/2019 2578 31728^39089-39089^31728 175957 Frank Doornink 01/2024 2579 2*10^175860-87 175861 Robert Price 04/2018 2580 27009^39670-39670^27009 175798 Frank Doornink 01/2024 2581 (86*10^175774-221)/9 175775 Robert Price 09/2019 2582 2^583614+216037 175686 Enzo Doria 11/2023 2583 9*10^175654+47 175655 Robert Price 01/2022 2584 25430^39869-39869^25430 175637 Frank Doornink 01/2024 2585 10^175608+2971 175609 Mike Oakes 05/2010 2586 10^175608-55829 175608 Patrick De Geest 09/2013 2587 2^583051+1879793 175516 Enzo Doria 09/2016 2588 (76*10^175514+491)/9 175515 Robert Price 10/2021 2590 2^582860-23829 175459 Enzo Doria 08/2013 2589 (200^76253-1)/199 175459 Anonymous 06/2024 2591 (8*10^175428-53)/9 175428 Serge Batalov 11/2022 2592 (28*10^175417-67)/3 175418 Robert Price 10/2020 2593 2^582670-23913 175402 Enzo Doria 08/2013 2594 2^582573-29563 175372 Enzo Doria 08/2015 2595 2^582435-1862767 175331 Enzo Doria 12/2015 2596 10^175295-40000001 175295 Robert Price 07/2022 2597 31093^39018-39018^31093 175295 Frank Doornink 01/2024 2598 (11*10^175250-149)/3 175251 Robert Price 09/2018 2599 (29*10^175236+31)/3 175237 Robert Price 04/2021 2600 2^582072-1848599 175222 Enzo Doria 08/2015 2601 (404267#+465)/(3^4*5^2*31) 175208 Makoto Morimoto 06/2019 2602 Phi(262767,10)/259613797 175168 Makoto Kamada 12/2022 2603 (2^581871-15)/7 175160 Stefano Morozzi 08/2022 2604 (5*10^175117-311)/9 175117 Robert Price 12/2021 2605 31193^38966-38966^31193 175116 Frank Doornink 01/2024 2606 10^175093-89 175093 Riley Fisher 10/2023 2607 (220221^32768+1)/2 175075 Serge Batalov 03/2018 2608 2^581560+1874911 175068 Enzo Doria 06/2016 2609 (25*10^174987-97)/9 174988 Robert Price 01/2022 2610 (75^93307-1)/74 174955 Paul Bourdelais 09/2017 2611 26446^39555-39555^26446 174927 Frank Doornink 03/2024 2612 31522^38883-38883^31522 174920 Frank Doornink 01/2024 2613 (27398^39601-1)/(27398^199-1) 174855 Ryan Propper 11/2023 2614 (861^59557-1)/860 174798 Jinyuan Wang 11/2023 2615 31492^38859-38859^31492 174796 Frank Doornink 01/2024 2616 (47*10^174790+493)/9 174791 Robert Price 03/2019 2617 2^580528-114035 174757 Enzo Doria 11/2014 2618 (19*10^174754+737)/9 174755 Robert Price 07/2018 2619 (35*10^174704-377)/9 174705 Robert Price 07/2018 2621 (49*10^174681+293)/9 174682 Robert Price 03/2021 2620 6*10^174681+11 174682 Robert Price 07/2022 2622 3*10^174665-97 174666 Robert Price 07/2018 2623 2^580046-459161 174612 Enzo Doria 05/2015 2624 2^579992-39779 174595 Enzo Doria 09/2015 2625 25613^39582-39582^25613 174496 Frank Doornink 02/2024 2626 (29*10^174481-149)/3 174482 Robert Price 08/2022 2627 (4*10^174423+101)/3 174424 Robert Price 11/2021 2628 (2^579371-17)/3 174408 Stefano Morozzi 08/2022 2629 (2*10^174301-71)/3 174301 Robert Price 12/2017 2630 14^152048+3 174267 Paul Bourdelais 12/2020 2631 (2^578696+1)/257 174203 Lelio R Paula 09/2015 2632 2^578656-1851809 174193 Enzo Doria 08/2015 2633 2^578583-113917 174171 Enzo Doria 10/2014 2634 2^578434-83 174126 Yves Minet 07/2017 2635 15^148048-2 174118 Robert Price 06/2015 2636 5*10^174101+81 174102 Robert Price 03/2019 2637 2^578346+2794249 174100 Enzo Doria 03/2016 2638 10^173947+1372429 173948 Patrick De Geest 08/2021 2640 10^173947-500000001 173947 Robert Price 12/2020 2639 10^173947-286391 173947 Patrick De Geest 08/2021 2641 5*10^173904-13 173905 Robert Price 01/2019 2642 (8*10^173862-59)/3 173863 Robert Price 08/2021 2643 (71*10^173854-287)/9 173855 Robert Price 09/2019 2644 (43*10^173826+101)/9 173827 Robert Price 11/2018 2645 2*10^173809-87 173810 Robert Price 04/2018 2646 (2^577372-23)/7 173806 Stefano Morozzi 08/2022 2647 (L!41532)/2 173772 Serge Batalov 07/2017 2648 2^577146-49877 173739 Enzo Doria 10/2015 2649 2^576889+49727 173661 Enzo Doria 09/2016 2650 (167*10^173571-17)/3 173573 Robert Price 03/2020 2651 37803^37916+37916^37803 173562 Norbert Schneider 06/2022 2652 5*10^173534+29 173535 Robert Price 12/2020 2653 (2^576551-1)/4612409/64758208321/242584327930759 173528 Dario Alpern 06/2014 2654 4*10^173509+99 173510 Robert Price 12/2020 2655 (13*10^173467-37)/3 173468 Robert Price 01/2019 2656 2^576016-113919 173399 Enzo Doria 11/2014 2657 2^575911-1849387 173367 Enzo Doria 08/2015 2658 2^575879+215843 173357 Enzo Doria 11/2023 2659 2^575871+28733 173355 Enzo Doria 01/2024 2660 515^63898+63898^515 173280 Norbert Schneider 12/2022 2661 2^575614+9 173278 Stefano Morozzi 04/2021 2662 2^575606-219533 173275 Enzo Doria 03/2024 2663 (16*10^173251+107)/3 173252 Robert Price 03/2019 2664 26618^39149-39149^26618 173242 Frank Doornink 03/2024 2665 2^575196-114053 173152 Enzo Doria 11/2014 2666 7*10^173135-53 173136 Robert Price 06/2020 2667 (301*10^173047+23)/9 173049 Robert Price 06/2021 2668 2^574591-115387 172970 Enzo Doria 07/2015 2669 25210^39297-39297^25210 172969 Frank Doornink 12/2023 2670 (202*10^172940-13)/9 172942 Robert Price 01/2020 2671 45^104608+104608^45 172940 Norbert Schneider 06/2021 2672 2^574328+81121 172890 Enzo Doria 07/2016 2673 (115*10^172862-1)/3 172864 Serge Batalov 12/2014 2674 3*10^172812+13 172813 Robert Price 07/2018 2675 4*5^247217-9 172798 Lelio R Paula 10/2015 2676 6*10^172772-31 172773 Robert Price 07/2020 2677 69061#+(467617#)/(69061#) 172766 Makoto Morimoto 10/2017 2678 (34*10^172693-547)/9 172694 Robert Price 03/2021 2679 5*10^172692+57 172693 Robert Price 12/2018 2680 2^573668-2782319 172692 Enzo Doria 09/2015 2681 2^573444-1855109 172624 Enzo Doria 09/2015 2682 25500^39173-39173^25500 172618 Frank Doornink 02/2024 2683 27180^38917-38917^27180 172568 Frank Doornink 01/2024 2684 (14*10^172532-29)/3 172533 Robert Price 09/2021 2685 3^361608+2 172531 Robert Price 08/2014 2686 (54^99563+1)/55 172481 Paul Bourdelais 11/2017 2687 2^572592-114893 172368 Enzo Doria 05/2015 2688 4*10^172354-39 172355 Robert Price 09/2020 2689 37535^37674+37674^37535 172338 Norbert Schneider 05/2022 2690 (11*10^172322-119)/9 172323 Robert Price 11/2021 2691 5^246497-4^246497 172295 Jean-Louis Charton 11/2008 2692 (38^109037-1)/37 172254 Paul Bourdelais 10/2017 2693 (4*10^172241+89)/3 172242 Robert Price 08/2021 2694 3*10^172219+73 172220 Robert Price 08/2018 2695 2^571810+28549 172132 Enzo Doria 01/2024 2696 A352736(15) 172032 Kellen Shenton 05/2022 2697 32298^38149-38149^32298 172021 Frank Doornink 02/2024 2698 2^571300+25861 171979 Enzo Doria 11/2023 2699 (36^110503+1)/37 171975 Lelio R Paula 04/2017 2700 8*10^171934+71 171935 Robert Price 05/2022 2701 (11*10^171933+601)/9 171934 Robert Price 02/2022 2702 (22*10^171929-73)/3 171930 Robert Price 04/2019 2703 (49*10^171892-319)/9 171893 Robert Price 10/2021 2704 4*10^171891-63 171892 Robert Price 10/2018 2705 67*10^171882-9 171884 Robert Price 03/2021 2706 2^570980-2782289 171883 Enzo Doria 09/2015 2707 (25*10^171849-37)/3 171850 Robert Price 10/2019 2708 10^171832+387909 171833 Patrick De Geest 08/2021 2709 10^171832-10001 171832 Robert Price 02/2021 2711 (2^(12*47563+13)-9)/7 171818 Kevin Acres 11/2013 2710 (2^570769-9)/7 171818 Stefano Morozzi 08/2022 2712 (74*10^171651-29)/9 171652 Robert Price 06/2022 2713 (536*10^171601-23)/9 171603 Robert Price 02/2020 2714 7*10^171535-99 171536 Robert Price 06/2019 2715 (28*10^171534+101)/3 171535 Robert Price 09/2020 2716 2^569563-1854607 171456 Enzo Doria 09/2015 2717 32133^38042-38042^32133 171454 Frank Doornink 02/2024 2718 3*10^171391+59 171392 Robert Price 08/2018 2719 (13*10^171306-37)/3 171307 Robert Price 01/2019 2720 8*10^171296+87 171297 Robert Price 10/2019 2721 (55^98419-1)/54 171284 Paul Bourdelais 12/2017 2722 (29*10^171275+67)/3 171276 Robert Price 12/2019 2723 (457*10^171248-7)/9 171250 Robert Price 09/2022 2724 (194*10^171193+1)/3 171195 Robert Price 01/2022 2725 2^568642+1876129 171179 Enzo Doria 07/2016 2726 4*10^171146-47 171147 Robert Price 10/2021 2727 (19*10^170970+131)/3 170971 Robert Price 06/2020 2728 (46*10^170932+143)/9 170933 Robert Price 01/2019 2729 (79*10^170901-1)/3 170903 Robert Price 02/2020 2730 (58*10^170842+221)/9 170843 Robert Price 02/2017 2731 (29*10^170830+583)/9 170831 Robert Price 06/2021 2732 3*10^170800+73 170801 Robert Price 08/2018 2733 (29*10^170799-119)/9 170800 Robert Price 12/2021 2734 11^164009-270 170798 Enzo Doria 10/2012 2735 2*10^170767+41 170768 Robert Price 05/2018 2736 3^357706-112358 170670 Enzo Doria 07/2014 2737 TheodorusPrime(170657) 170657 Eric W. Weisstein 08/2013 2738 2^566871+1876163 170646 Enzo Doria 07/2016 2739 (10657#+(404267#)/(10657#))/(1675379) 170624 Makoto Morimoto 10/2017 2740 2^566496+7 170533 Donovan Johnson 07/2006 2741 (7^201653+1)/8 170416 Paul Bourdelais 02/2010 2742 32150^37807-37807^32150 170403 Frank Doornink 02/2024 2743 7*10^170348+33 170349 Robert Price 06/2020 2744 2^565799+216011 170323 Enzo Doria 12/2023 2745 2^565183-352021 170138 Enzo Doria 07/2015 2746 2^565143-114457 170125 Enzo Doria 02/2015 2747 3*2^565024-5 170090 Jon Grantham 07/2023 2748 2^564976-49869 170075 Enzo Doria 10/2015 2749 (7*10^169944+23)/3 169945 Robert Price 06/2020 2750 (37*10^169943+251)/9 169944 Robert Price 09/2021

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 22 2024 13:34 (Time in France)

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