## 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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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 (8*10^180725-629)/9 180725 Robert Price 01/2022 2502 (79*10^180710-1)/3 180712 Robert Price 02/2020 2503 2^600300-1852559 180709 Enzo Doria 08/2015 2504 (2*10^180706-77)/3 180706 Robert Price 02/2021 2505 (156^82393-1)/155 180696 Anonymous 06/2024 2506 (10^180689+71)/9 180689 Serge Batalov 07/2015 2507 2^600209+76487 180681 Enzo Doria 05/2016 2508 2^599999+378461 180618 Norman Luhn 09/2023 2509 (8*10^180536-269)/9 180536 Robert Price 09/2021 2510 2^599702-369885 180529 Enzo Doria 11/2013 2511 Tau(643^11688) 180524 Nik Lygeros / Olivier Rozier 05/2015 2512 (2951*29^123418-3)/4 180490 Curtis Bright 05/2015 2513 (29*10^180432-17)/3 180433 Robert Price 09/2019 2514 4*10^180360+93 180361 Robert Price 08/2018 2515 2^599035+219323 180328 Enzo Doria 03/2024 2516 2^598942+80779 180300 Enzo Doria 07/2016 2517 (38*10^180296+403)/9 180297 Robert Price 10/2018 2518 (85*10^180241+77)/9 180242 Robert Price 07/2022 2519 2^598591-1844797 180194 Enzo Doria 06/2015 2520 (100^90089+1)/101 180176 Paul Bourdelais 08/2017 2521 2^598301+28517 180107 Enzo Doria 01/2024 2522 (29*10^180072+691)/9 180073 Robert Price 08/2021 2523 (59*10^180038+157)/9 180039 Robert Price 12/2021 2524 95*10^180019-9 180021 Robert Price 01/2022 2525 6*10^179970+91 179971 Robert Price 05/2019 2526 (4*10^179963-79)/3 179964 Robert Price 02/2018 2527 (403*10^179944-43)/9 179946 Robert Price 06/2021 2528 Gamma-Prime(179849) 179849 Eric W. Weisstein 06/2011 2529 2^597424-1859729 179843 Enzo Doria 11/2015 2530 Phi(180683,10) 179760 Maksym Voznyy 09/2015 2531 (10^180683-1)*9/(10^643-1)/(10^281-1) 179760 Robert Price 07/2016 2532 (3^376657-2^376657)/22301107657 179701 Mike Oakes 04/2017 2533 (29*10^179697+223)/9 179698 Robert Price 09/2018 2534 U(1289697) 179687 Serge Batalov 07/2024 2536 2^596884+73 179680 Stefano Morozzi 04/2021 2535 (11*10^179679+13)/3 179680 Robert Price 03/2022 2537 (68*10^179656+7)/3 179658 Robert Price 01/2020 2538 (10^179643+173)/3 179643 Robert Price 05/2021 2539 2^596690-461261 179622 Enzo Doria 07/2015 2540 2^596684-113939 179620 Enzo Doria 10/2014 2541 2^596642+39 179608 Jon Grantham 08/2023 2542 2*10^179602+63 179603 Robert Price 05/2018 2543 32262^39815-39815^32262 179514 Frank Doornink 02/2024 2544 (25*10^179488-403)/9 179489 Robert Price 01/2021 2545 7*10^179460+99 179461 Robert Price 05/2021 2546 2^596127+74333 179453 Enzo Doria 07/2023 2547 3^375887-112696 179344 Enzo Doria 07/2014 2548 4*10^179265-71 179266 Robert Price 12/2018 2549 2*10^179193+83 179194 Robert Price 12/2021 2550 2^595144-1850429 179157 Enzo Doria 08/2015 2551 2^595122-5 179150 Stefano Morozzi 07/2022 2552 3*10^179138+89 179139 Robert Price 10/2018 2553 (52*10^179062-133)/9 179063 Robert Price 09/2021 2554 2^594531+82253 178972 Enzo Doria 09/2016 2555 (664*10^178939-61)/9 178941 Robert Price 09/2021 2556 2^594260-2787899 178891 Enzo Doria 11/2015 2557 (14*10^178822+67)/9 178823 Robert Price 05/2022 2558 (29*10^178732-119)/9 178733 Robert Price 12/2021 2559 2^593631+101381 178701 Jorge Menendez 04/2018 2560 10^178695+136719 178696 Patrick De Geest 05/2016 2561 10^178695-71 178695 Serge Batalov 12/2014 2562 (2*10^178649-161)/3 178649 Robert Price 12/2020 2563 (691^62903-1)/690 178609 Michael Stocker 05/2020 2564 (2^148330+1)^4-2 178608 Cletus Emmanuel 12/2003 2565 2^593242+28309 178584 Enzo Doria 01/2024 2566 2^593222-14145 178578 Jorge Menendez 10/2017 2567 7*10^178566+33 178567 Robert Price 06/2020 2568 2^593178+1867219 178565 Enzo Doria 03/2016 2569 2^593152+22441 178557 Enzo Doria 09/2023 2570 (38*10^178456+151)/9 178457 Robert Price 03/2022 2571 (302*10^178369+13)/9 178371 Robert Price 02/2020 2572 (26*10^178296-113)/3 178297 Robert Price 06/2020 2573 (18^142031-1)/17 178287 Paul Bourdelais 03/2010 2574 (13*10^178233+137)/3 178234 Robert Price 06/2021 2575 (5*10^178206+91)/3 178207 Robert Price 04/2018 2576 2^591872-291929 178172 Enzo Doria 07/2015 2577 2^591682-286871 178115 Enzo Doria 07/2015 2578 (7^210761-5^210761)/2 178114 Jon Grantham 08/2023 2579 4*10^178091+9 178092 Robert Price 05/2015 2580 410747#+478483 178007 Makoto Morimoto 02/2016 2581 3*10^177872+73 177873 Robert Price 08/2018 2582 2^590762-396765 177838 Enzo Doria 08/2013 2583 (136*10^177754-1)/9 177756 Serge Batalov 12/2014 2584 ReverseConsecutiveIntegerPrime(37765) 177719 Eric W. Weisstein 04/2010 2585 Smr(37765) 177719 Eric W. Weisstein 12/2021 2586 (266*10^177577-11)/3 177579 Robert Price 04/2020 2587 (11*10^177466-113)/3 177467 Robert Price 10/2018 2588 3*10^177373-97 177374 Robert Price 07/2018 2589 2^589204+1881151 177369 Enzo Doria 11/2016 2590 2^589132-69479 177347 Enzo Doria 01/2016 2591 (101*10^177302-17)/3 177304 Robert Price 02/2020 2592 2^588912-113519 177281 Enzo Doria 08/2014 2593 (682*10^177266-7)/9 177268 Robert Price 08/2021 2594 15^150706+2 177245 Robert Price 06/2015 2595 (31208^39601-1)/(31208^199-1) 177084 Ryan Propper 11/2023 2596 2^588194-1861001 177065 Enzo Doria 11/2015 2597 5*10^177016-37 177017 Robert Price 11/2021 2598 fibonacci(846926)-4 176997 Jon Grantham 08/2023 2599 (23*10^176964-47)/3 176965 Robert Price 09/2019 2600 20530^41031+41031^20530 176942 Norbert Schneider 07/2022 2601 (19*10^176932+521)/9 176933 Robert Price 05/2018 2602 (8*10^176908+43)/3 176909 Robert Price 06/2018 2603 (85*10^176900+203)/9 176901 Robert Price 09/2020 2604 2^587560-113699 176874 Enzo Doria 09/2014 2605 20596^40995+40995^20596 176844 Norbert Schneider 07/2022 2606 (101*10^176815-17)/3 176817 Robert Price 02/2020 2607 (25*10^176715-37)/3 176716 Robert Price 10/2019 2608 5^252763-12862 176674 Enzo Doria 05/2014 2609 38442^38531+38531^38442 176658 Norbert Schneider 09/2022 2610 2^586829+23961 176654 Enzo Doria 10/2023 2611 2^586804+81721 176646 Enzo Doria 08/2016 2612 (10^176584+77)/3 176584 Robert Price 01/2018 2613 2^586570+1874419 176576 Enzo Doria 06/2016 2614 (157*10^176482-1)/3 176484 Robert Price 01/2022 2615 5*2^586202+3 176466 Jon Grantham 07/2023 2616 27122^39799-39799^27122 176442 Frank Doornink 01/2024 2617 2^585994-3311 176402 Yves Minet 12/2014 2618 8*10^176383-81 176384 Robert Price 02/2021 2619 (23*10^176357+61)/3 176358 Robert Price 01/2022 2620 2^585832-112799 176354 Enzo Doria 07/2014 2621 fibonacci(843383)+4 176257 Jon Grantham 08/2023 2622 (29*10^176240+49)/3 176241 Robert Price 09/2021 2623 (2^585387-11)/3 176219 Stefano Morozzi 08/2022 2624 2^585336-461039 176204 Enzo Doria 06/2015 2625 (25*10^176164+143)/3 176165 Robert Price 08/2020 2626 2^585095-1848127 176132 Enzo Doria 08/2015 2627 (5*10^176101-311)/9 176101 Robert Price 12/2021 2628 6*10^176092+77 176093 Robert Price 06/2020 2629 2^584950-115451 176088 Enzo Doria 07/2015 2630 (646*10^176044+11)/9 176046 Robert Price 10/2021 2631 (7^208283-5^208283)/2 176020 Jon Grantham 08/2023 2632 2^584671-3697 176004 Yves Minet 03/2017 2633 (13*10^175965-37)/3 175966 Robert Price 01/2019 2634 31728^39089-39089^31728 175957 Frank Doornink 01/2024 2635 2*10^175860-87 175861 Robert Price 04/2018 2636 27009^39670-39670^27009 175798 Frank Doornink 01/2024 2637 (86*10^175774-221)/9 175775 Robert Price 09/2019 2638 2^583614+216037 175686 Enzo Doria 11/2023 2639 9*10^175654+47 175655 Robert Price 01/2022 2640 25430^39869-39869^25430 175637 Frank Doornink 01/2024 2641 10^175608+2971 175609 Mike Oakes 05/2010 2642 10^175608-55829 175608 Patrick De Geest 09/2013 2643 2^583051+1879793 175516 Enzo Doria 09/2016 2644 (76*10^175514+491)/9 175515 Robert Price 10/2021 2646 2^582860-23829 175459 Enzo Doria 08/2013 2645 (200^76253-1)/199 175459 Anonymous 06/2024 2647 (8*10^175428-53)/9 175428 Serge Batalov 11/2022 2648 (28*10^175417-67)/3 175418 Robert Price 10/2020 2649 2^582670-23913 175402 Enzo Doria 08/2013 2650 2^582573-29563 175372 Enzo Doria 08/2015 2651 2^582435-1862767 175331 Enzo Doria 12/2015 2652 10^175295-40000001 175295 Robert Price 07/2022 2653 31093^39018-39018^31093 175295 Frank Doornink 01/2024 2654 (11*10^175250-149)/3 175251 Robert Price 09/2018 2655 (29*10^175236+31)/3 175237 Robert Price 04/2021 2656 2^582072-1848599 175222 Enzo Doria 08/2015 2657 (404267#+465)/(3^4*5^2*31) 175208 Makoto Morimoto 06/2019 2658 Phi(262767,10)/259613797 175168 Makoto Kamada 12/2022 2659 (2^581871-15)/7 175160 Stefano Morozzi 08/2022 2660 (5*10^175117-311)/9 175117 Robert Price 12/2021 2661 31193^38966-38966^31193 175116 Frank Doornink 01/2024 2662 2^581695+225893 175108 Enzo Doria 08/2024 2663 10^175093-89 175093 Riley Fisher 10/2023 2664 (220221^32768+1)/2 175075 Serge Batalov 03/2018 2665 2^581560+1874911 175068 Enzo Doria 06/2016 2666 (25*10^174987-97)/9 174988 Robert Price 01/2022 2667 (75^93307-1)/74 174955 Paul Bourdelais 09/2017 2668 26446^39555-39555^26446 174927 Frank Doornink 03/2024 2669 31522^38883-38883^31522 174920 Frank Doornink 01/2024 2670 (27398^39601-1)/(27398^199-1) 174855 Ryan Propper 11/2023 2671 (861^59557-1)/860 174798 Jinyuan Wang 11/2023 2672 31492^38859-38859^31492 174796 Frank Doornink 01/2024 2673 (47*10^174790+493)/9 174791 Robert Price 03/2019 2674 2^580528-114035 174757 Enzo Doria 11/2014 2675 (19*10^174754+737)/9 174755 Robert Price 07/2018 2676 V(1045270)/4181081/12543241/81333115129561 174730 Serge Batalov 07/2024 2677 (35*10^174704-377)/9 174705 Robert Price 07/2018 2679 (49*10^174681+293)/9 174682 Robert Price 03/2021 2678 6*10^174681+11 174682 Robert Price 07/2022 2680 3*10^174665-97 174666 Robert Price 07/2018 2681 2^580046-459161 174612 Enzo Doria 05/2015 2682 2^579992-39779 174595 Enzo Doria 09/2015 2683 25613^39582-39582^25613 174496 Frank Doornink 02/2024 2684 (29*10^174481-149)/3 174482 Robert Price 08/2022 2685 (4*10^174423+101)/3 174424 Robert Price 11/2021 2686 (2^579371-17)/3 174408 Stefano Morozzi 08/2022 2687 (2*10^174301-71)/3 174301 Robert Price 12/2017 2688 14^152048+3 174267 Paul Bourdelais 12/2020 2689 (2^578696+1)/257 174203 Lelio R Paula 09/2015 2690 2^578656-1851809 174193 Enzo Doria 08/2015 2691 2^578583-113917 174171 Enzo Doria 10/2014 2692 2^578434-83 174126 Yves Minet 07/2017 2693 15^148048-2 174118 Robert Price 06/2015 2694 5*10^174101+81 174102 Robert Price 03/2019 2695 2^578346+2794249 174100 Enzo Doria 03/2016 2696 10^173947+1372429 173948 Patrick De Geest 08/2021 2698 10^173947-500000001 173947 Robert Price 12/2020 2697 10^173947-286391 173947 Patrick De Geest 08/2021 2699 5*10^173904-13 173905 Robert Price 01/2019 2700 (8*10^173862-59)/3 173863 Robert Price 08/2021 2701 (71*10^173854-287)/9 173855 Robert Price 09/2019 2702 (43*10^173826+101)/9 173827 Robert Price 11/2018 2703 2*10^173809-87 173810 Robert Price 04/2018 2704 (2^577372-23)/7 173806 Stefano Morozzi 08/2022 2705 (L!41532)/2 173772 Serge Batalov 07/2017 2706 2^577146-49877 173739 Enzo Doria 10/2015 2707 2^576889+49727 173661 Enzo Doria 09/2016 2708 (167*10^173571-17)/3 173573 Robert Price 03/2020 2709 37803^37916+37916^37803 173562 Norbert Schneider 06/2022 2710 5*10^173534+29 173535 Robert Price 12/2020 2711 (2^576551-1)/4612409/64758208321/242584327930759 173528 Dario Alpern 06/2014 2712 4*10^173509+99 173510 Robert Price 12/2020 2713 (13*10^173467-37)/3 173468 Robert Price 01/2019 2714 2^576016-113919 173399 Enzo Doria 11/2014 2715 2^575911-1849387 173367 Enzo Doria 08/2015 2716 2^575879+215843 173357 Enzo Doria 11/2023 2717 2^575871+28733 173355 Enzo Doria 01/2024 2718 515^63898+63898^515 173280 Norbert Schneider 12/2022 2719 2^575614+9 173278 Stefano Morozzi 04/2021 2720 2^575606-219533 173275 Enzo Doria 03/2024 2721 (16*10^173251+107)/3 173252 Robert Price 03/2019 2722 26618^39149-39149^26618 173242 Frank Doornink 03/2024 2723 2^575196-114053 173152 Enzo Doria 11/2014 2724 7*10^173135-53 173136 Robert Price 06/2020 2725 (301*10^173047+23)/9 173049 Robert Price 06/2021 2726 2^574591-115387 172970 Enzo Doria 07/2015 2727 25210^39297-39297^25210 172969 Frank Doornink 12/2023 2728 (202*10^172940-13)/9 172942 Robert Price 01/2020 2729 45^104608+104608^45 172940 Norbert Schneider 06/2021 2730 2^574328+81121 172890 Enzo Doria 07/2016 2731 (115*10^172862-1)/3 172864 Serge Batalov 12/2014 2732 3*10^172812+13 172813 Robert Price 07/2018 2733 4*5^247217-9 172798 Lelio R Paula 10/2015 2734 6*10^172772-31 172773 Robert Price 07/2020 2735 69061#+(467617#)/(69061#) 172766 Makoto Morimoto 10/2017 2736 (34*10^172693-547)/9 172694 Robert Price 03/2021 2737 5*10^172692+57 172693 Robert Price 12/2018 2738 2^573668-2782319 172692 Enzo Doria 09/2015 2739 2^573444-1855109 172624 Enzo Doria 09/2015 2740 25500^39173-39173^25500 172618 Frank Doornink 02/2024 2741 27180^38917-38917^27180 172568 Frank Doornink 01/2024 2742 (14*10^172532-29)/3 172533 Robert Price 09/2021 2743 3^361608+2 172531 Robert Price 08/2014 2744 (54^99563+1)/55 172481 Paul Bourdelais 11/2017 2745 2^572592-114893 172368 Enzo Doria 05/2015 2746 4*10^172354-39 172355 Robert Price 09/2020 2747 37535^37674+37674^37535 172338 Norbert Schneider 05/2022 2748 (11*10^172322-119)/9 172323 Robert Price 11/2021 2749 5^246497-4^246497 172295 Jean-Louis Charton 11/2008 2750 (38^109037-1)/37 172254 Paul Bourdelais 10/2017

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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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