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) !!!
Submit your PRPs
See the Top discoverers
See the Latest PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 2501 | 31093^39018-39018^31093 | 175295 | Frank Doornink | 01/2024 |
| 2502 | (11*10^175250-149)/3 | 175251 | Robert Price | 09/2018 |
| 2503 | (29*10^175236+31)/3 | 175237 | Robert Price | 04/2021 |
| 2504 | 2^582072-1848599 | 175222 | Enzo Doria | 08/2015 |
| 2505 | (404267#+465)/(3^4*5^2*31) | 175208 | Makoto Morimoto | 06/2019 |
| 2506 | Phi(262767,10)/259613797 | 175168 | Makoto Kamada | 12/2022 |
| 2507 | (2^581871-15)/7 | 175160 | Stefano Morozzi | 08/2022 |
| 2508 | (5*10^175117-311)/9 | 175117 | Robert Price | 12/2021 |
| 2509 | 31193^38966-38966^31193 | 175116 | Frank Doornink | 01/2024 |
| 2510 | 10^175093-89 | 175093 | Riley Fisher | 10/2023 |
| 2511 | (220221^32768+1)/2 | 175075 | Serge Batalov | 03/2018 |
| 2512 | 2^581560+1874911 | 175068 | Enzo Doria | 06/2016 |
| 2513 | (25*10^174987-97)/9 | 174988 | Robert Price | 01/2022 |
| 2514 | (75^93307-1)/74 | 174955 | Paul Bourdelais | 09/2017 |
| 2515 | 26446^39555-39555^26446 | 174927 | Frank Doornink | 03/2024 |
| 2516 | 31522^38883-38883^31522 | 174920 | Frank Doornink | 01/2024 |
| 2517 | (27398^39601-1)/(27398^199-1) | 174855 | Ryan Propper | 11/2023 |
| 2518 | (861^59557-1)/860 | 174798 | Jinyuan Wang | 11/2023 |
| 2519 | 31492^38859-38859^31492 | 174796 | Frank Doornink | 01/2024 |
| 2520 | (47*10^174790+493)/9 | 174791 | Robert Price | 03/2019 |
| 2521 | 2^580528-114035 | 174757 | Enzo Doria | 11/2014 |
| 2522 | (19*10^174754+737)/9 | 174755 | Robert Price | 07/2018 |
| 2523 | (35*10^174704-377)/9 | 174705 | Robert Price | 07/2018 |
| 2524 | (49*10^174681+293)/9 | 174682 | Robert Price | 03/2021 |
| 2525 | 6*10^174681+11 | 174682 | Robert Price | 07/2022 |
| 2526 | 3*10^174665-97 | 174666 | Robert Price | 07/2018 |
| 2527 | 2^580046-459161 | 174612 | Enzo Doria | 05/2015 |
| 2528 | 2^579992-39779 | 174595 | Enzo Doria | 09/2015 |
| 2529 | 25613^39582-39582^25613 | 174496 | Frank Doornink | 02/2024 |
| 2530 | (29*10^174481-149)/3 | 174482 | Robert Price | 08/2022 |
| 2531 | (4*10^174423+101)/3 | 174424 | Robert Price | 11/2021 |
| 2532 | (2^579371-17)/3 | 174408 | Stefano Morozzi | 08/2022 |
| 2533 | (2*10^174301-71)/3 | 174301 | Robert Price | 12/2017 |
| 2534 | 14^152048+3 | 174267 | Paul Bourdelais | 12/2020 |
| 2535 | (2^578696+1)/257 | 174203 | Lelio R Paula | 09/2015 |
| 2536 | 2^578656-1851809 | 174193 | Enzo Doria | 08/2015 |
| 2537 | 2^578583-113917 | 174171 | Enzo Doria | 10/2014 |
| 2538 | 2^578434-83 | 174126 | Yves Minet | 07/2017 |
| 2539 | 15^148048-2 | 174118 | Robert Price | 06/2015 |
| 2540 | 5*10^174101+81 | 174102 | Robert Price | 03/2019 |
| 2541 | 2^578346+2794249 | 174100 | Enzo Doria | 03/2016 |
| 2542 | 10^173947+1372429 | 173948 | Patrick De Geest | 08/2021 |
| 2544 | 10^173947-500000001 | 173947 | Robert Price | 12/2020 |
| 2543 | 10^173947-286391 | 173947 | Patrick De Geest | 08/2021 |
| 2545 | 5*10^173904-13 | 173905 | Robert Price | 01/2019 |
| 2546 | (8*10^173862-59)/3 | 173863 | Robert Price | 08/2021 |
| 2547 | (71*10^173854-287)/9 | 173855 | Robert Price | 09/2019 |
| 2548 | (43*10^173826+101)/9 | 173827 | Robert Price | 11/2018 |
| 2549 | 2*10^173809-87 | 173810 | Robert Price | 04/2018 |
| 2550 | (2^577372-23)/7 | 173806 | Stefano Morozzi | 08/2022 |
| 2551 | (L!41532)/2 | 173772 | Serge Batalov | 07/2017 |
| 2552 | 2^577146-49877 | 173739 | Enzo Doria | 10/2015 |
| 2553 | 2^576889+49727 | 173661 | Enzo Doria | 09/2016 |
| 2554 | (167*10^173571-17)/3 | 173573 | Robert Price | 03/2020 |
| 2555 | 37803^37916+37916^37803 | 173562 | Norbert Schneider | 06/2022 |
| 2556 | 5*10^173534+29 | 173535 | Robert Price | 12/2020 |
| 2557 | (2^576551-1)/4612409/64758208321/242584327930759 | 173528 | Dario Alpern | 06/2014 |
| 2558 | 4*10^173509+99 | 173510 | Robert Price | 12/2020 |
| 2559 | (13*10^173467-37)/3 | 173468 | Robert Price | 01/2019 |
| 2560 | 2^576016-113919 | 173399 | Enzo Doria | 11/2014 |
| 2561 | 2^575911-1849387 | 173367 | Enzo Doria | 08/2015 |
| 2562 | 2^575879+215843 | 173357 | Enzo Doria | 11/2023 |
| 2563 | 2^575871+28733 | 173355 | Enzo Doria | 01/2024 |
| 2564 | 515^63898+63898^515 | 173280 | Norbert Schneider | 12/2022 |
| 2565 | 2^575614+9 | 173278 | Stefano Morozzi | 04/2021 |
| 2566 | 2^575606-219533 | 173275 | Enzo Doria | 03/2024 |
| 2567 | (16*10^173251+107)/3 | 173252 | Robert Price | 03/2019 |
| 2568 | 26618^39149-39149^26618 | 173242 | Frank Doornink | 03/2024 |
| 2569 | 2^575196-114053 | 173152 | Enzo Doria | 11/2014 |
| 2570 | 7*10^173135-53 | 173136 | Robert Price | 06/2020 |
| 2571 | (301*10^173047+23)/9 | 173049 | Robert Price | 06/2021 |
| 2572 | 2^574591-115387 | 172970 | Enzo Doria | 07/2015 |
| 2573 | 25210^39297-39297^25210 | 172969 | Frank Doornink | 12/2023 |
| 2574 | (202*10^172940-13)/9 | 172942 | Robert Price | 01/2020 |
| 2575 | 45^104608+104608^45 | 172940 | Norbert Schneider | 06/2021 |
| 2576 | 2^574328+81121 | 172890 | Enzo Doria | 07/2016 |
| 2577 | (115*10^172862-1)/3 | 172864 | Serge Batalov | 12/2014 |
| 2578 | 3*10^172812+13 | 172813 | Robert Price | 07/2018 |
| 2579 | 4*5^247217-9 | 172798 | Lelio R Paula | 10/2015 |
| 2580 | 6*10^172772-31 | 172773 | Robert Price | 07/2020 |
| 2581 | 69061#+(467617#)/(69061#) | 172766 | Makoto Morimoto | 10/2017 |
| 2582 | (34*10^172693-547)/9 | 172694 | Robert Price | 03/2021 |
| 2583 | 5*10^172692+57 | 172693 | Robert Price | 12/2018 |
| 2584 | 2^573668-2782319 | 172692 | Enzo Doria | 09/2015 |
| 2585 | 2^573444-1855109 | 172624 | Enzo Doria | 09/2015 |
| 2586 | 25500^39173-39173^25500 | 172618 | Frank Doornink | 02/2024 |
| 2587 | 27180^38917-38917^27180 | 172568 | Frank Doornink | 01/2024 |
| 2588 | (14*10^172532-29)/3 | 172533 | Robert Price | 09/2021 |
| 2589 | 3^361608+2 | 172531 | Robert Price | 08/2014 |
| 2590 | (54^99563+1)/55 | 172481 | Paul Bourdelais | 11/2017 |
| 2591 | 2^572592-114893 | 172368 | Enzo Doria | 05/2015 |
| 2592 | 4*10^172354-39 | 172355 | Robert Price | 09/2020 |
| 2593 | 37535^37674+37674^37535 | 172338 | Norbert Schneider | 05/2022 |
| 2594 | (11*10^172322-119)/9 | 172323 | Robert Price | 11/2021 |
| 2595 | 5^246497-4^246497 | 172295 | Jean-Louis Charton | 11/2008 |
| 2596 | (38^109037-1)/37 | 172254 | Paul Bourdelais | 10/2017 |
| 2597 | (4*10^172241+89)/3 | 172242 | Robert Price | 08/2021 |
| 2598 | 3*10^172219+73 | 172220 | Robert Price | 08/2018 |
| 2599 | 2^571810+28549 | 172132 | Enzo Doria | 01/2024 |
| 2600 | A352736(15) | 172032 | Kellen Shenton | 05/2022 |
| 2601 | 32298^38149-38149^32298 | 172021 | Frank Doornink | 02/2024 |
| 2602 | 2^571300+25861 | 171979 | Enzo Doria | 11/2023 |
| 2603 | (36^110503+1)/37 | 171975 | Lelio R Paula | 04/2017 |
| 2604 | 8*10^171934+71 | 171935 | Robert Price | 05/2022 |
| 2605 | (11*10^171933+601)/9 | 171934 | Robert Price | 02/2022 |
| 2606 | (22*10^171929-73)/3 | 171930 | Robert Price | 04/2019 |
| 2607 | (49*10^171892-319)/9 | 171893 | Robert Price | 10/2021 |
| 2608 | 4*10^171891-63 | 171892 | Robert Price | 10/2018 |
| 2609 | 67*10^171882-9 | 171884 | Robert Price | 03/2021 |
| 2610 | 2^570980-2782289 | 171883 | Enzo Doria | 09/2015 |
| 2611 | (25*10^171849-37)/3 | 171850 | Robert Price | 10/2019 |
| 2612 | 10^171832+387909 | 171833 | Patrick De Geest | 08/2021 |
| 2613 | 10^171832-10001 | 171832 | Robert Price | 02/2021 |
| 2615 | (2^(12*47563+13)-9)/7 | 171818 | Kevin Acres | 11/2013 |
| 2614 | (2^570769-9)/7 | 171818 | Stefano Morozzi | 08/2022 |
| 2616 | (74*10^171651-29)/9 | 171652 | Robert Price | 06/2022 |
| 2617 | (536*10^171601-23)/9 | 171603 | Robert Price | 02/2020 |
| 2618 | 7*10^171535-99 | 171536 | Robert Price | 06/2019 |
| 2619 | (28*10^171534+101)/3 | 171535 | Robert Price | 09/2020 |
| 2620 | 2^569563-1854607 | 171456 | Enzo Doria | 09/2015 |
| 2621 | 32133^38042-38042^32133 | 171454 | Frank Doornink | 02/2024 |
| 2622 | 3*10^171391+59 | 171392 | Robert Price | 08/2018 |
| 2623 | (13*10^171306-37)/3 | 171307 | Robert Price | 01/2019 |
| 2624 | 8*10^171296+87 | 171297 | Robert Price | 10/2019 |
| 2625 | (55^98419-1)/54 | 171284 | Paul Bourdelais | 12/2017 |
| 2626 | (29*10^171275+67)/3 | 171276 | Robert Price | 12/2019 |
| 2627 | (457*10^171248-7)/9 | 171250 | Robert Price | 09/2022 |
| 2628 | (194*10^171193+1)/3 | 171195 | Robert Price | 01/2022 |
| 2629 | 2^568642+1876129 | 171179 | Enzo Doria | 07/2016 |
| 2630 | 4*10^171146-47 | 171147 | Robert Price | 10/2021 |
| 2631 | (19*10^170970+131)/3 | 170971 | Robert Price | 06/2020 |
| 2632 | (46*10^170932+143)/9 | 170933 | Robert Price | 01/2019 |
| 2633 | (79*10^170901-1)/3 | 170903 | Robert Price | 02/2020 |
| 2634 | (58*10^170842+221)/9 | 170843 | Robert Price | 02/2017 |
| 2635 | (29*10^170830+583)/9 | 170831 | Robert Price | 06/2021 |
| 2636 | 3*10^170800+73 | 170801 | Robert Price | 08/2018 |
| 2637 | (29*10^170799-119)/9 | 170800 | Robert Price | 12/2021 |
| 2638 | 11^164009-270 | 170798 | Enzo Doria | 10/2012 |
| 2639 | 2*10^170767+41 | 170768 | Robert Price | 05/2018 |
| 2640 | 3^357706-112358 | 170670 | Enzo Doria | 07/2014 |
| 2641 | TheodorusPrime(170657) | 170657 | Eric W. Weisstein | 08/2013 |
| 2642 | 2^566871+1876163 | 170646 | Enzo Doria | 07/2016 |
| 2643 | (10657#+(404267#)/(10657#))/(1675379) | 170624 | Makoto Morimoto | 10/2017 |
| 2644 | 2^566496+7 | 170533 | Donovan Johnson | 07/2006 |
| 2645 | (7^201653+1)/8 | 170416 | Paul Bourdelais | 02/2010 |
| 2646 | 32150^37807-37807^32150 | 170403 | Frank Doornink | 02/2024 |
| 2647 | 7*10^170348+33 | 170349 | Robert Price | 06/2020 |
| 2648 | 2^565799+216011 | 170323 | Enzo Doria | 12/2023 |
| 2649 | 2^565183-352021 | 170138 | Enzo Doria | 07/2015 |
| 2650 | 2^565143-114457 | 170125 | Enzo Doria | 02/2015 |
| 2651 | 3*2^565024-5 | 170090 | Jon Grantham | 07/2023 |
| 2652 | 2^564976-49869 | 170075 | Enzo Doria | 10/2015 |
| 2653 | (7*10^169944+23)/3 | 169945 | Robert Price | 06/2020 |
| 2654 | (37*10^169943+251)/9 | 169944 | Robert Price | 09/2021 |
| 2655 | 2^564526-351401 | 169940 | Enzo Doria | 07/2015 |
| 2656 | 4*10^169759+19 | 169760 | Robert Price | 10/2018 |
| 2657 | (2^563903-13)/5 | 169752 | Stefano Morozzi | 08/2022 |
| 2658 | 21^128327-20^128327 | 169677 | Jean-Louis Charton | 11/2014 |
| 2659 | 2^563583+89 | 169656 | Stefano Morozzi | 04/2021 |
| 2660 | 2^563311+215813 | 169574 | Enzo Doria | 11/2023 |
| 2661 | (4*10^169559+83)/3 | 169560 | Robert Price | 02/2018 |
| 2662 | (194*10^169461-17)/3 | 169463 | Robert Price | 09/2020 |
| 2663 | 2^562749+2793047 | 169405 | Enzo Doria | 02/2016 |
| 2664 | (154*10^169337-1)/9 | 169339 | Serge Batalov | 12/2014 |
| 2665 | (109*10^169337+11)/3 | 169339 | Robert Price | 06/2022 |
| 2666 | (56*10^169311+691)/9 | 169312 | Robert Price | 05/2019 |
| 2667 | 2^562369-29503 | 169290 | Enzo Doria | 08/2015 |
| 2668 | (17*10^169283+19)/9 | 169284 | Robert Price | 03/2021 |
| 2669 | 10^169074-5000000001 | 169074 | Robert Price | 09/2022 |
| 2670 | 8*10^169071+59 | 169072 | Robert Price | 11/2021 |
| 2671 | (10^169044+173)/3 | 169044 | Robert Price | 05/2021 |
| 2672 | (22*10^169019+383)/9 | 169020 | Robert Price | 05/2018 |
| 2673 | (64*10^168935+143)/9 | 168936 | Robert Price | 05/2021 |
| 2674 | (22*10^168906+47)/3 | 168907 | Robert Price | 06/2021 |
| 2675 | 5*10^168807+87 | 168808 | Robert Price | 02/2019 |
| 2676 | (77*10^168803-149)/9 | 168804 | Robert Price | 03/2022 |
| 2677 | 4*10^168788-47 | 168789 | Robert Price | 10/2021 |
| 2678 | (154*10^168781+17)/9 | 168783 | Robert Price | 06/2022 |
| 2679 | (418*10^168751-31)/9 | 168753 | Robert Price | 05/2022 |
| 2680 | (29*10^168711+691)/9 | 168712 | Robert Price | 08/2021 |
| 2681 | 2^560405-39943 | 168699 | Enzo Doria | 09/2015 |
| 2682 | (397*10^168634+17)/9 | 168636 | Robert Price | 03/2022 |
| 2683 | 89*10^168614-7 | 168616 | Robert Price | 04/2020 |
| 2684 | (23*10^168608-83)/3 | 168609 | Robert Price | 08/2019 |
| 2685 | (94*10^168541+11)/3 | 168543 | Robert Price | 04/2020 |
| 2686 | 2^559686-350471 | 168483 | Enzo Doria | 06/2015 |
| 2687 | 2^559672-1855889 | 168479 | Enzo Doria | 09/2015 |
| 2688 | (5*10^168379-473)/9 | 168379 | Robert Price | 01/2018 |
| 2689 | 2024^50920+3 | 168353 | Martin Hopf | 01/2024 |
| 2690 | 2^559000-59939 | 168276 | Enzo Doria | 11/2015 |
| 2691 | 2^558830+25009 | 168225 | Enzo Doria | 11/2023 |
| 2692 | (16*10^168181+41)/3 | 168182 | Robert Price | 03/2019 |
| 2693 | (19*10^168173+77)/3 | 168174 | Robert Price | 05/2019 |
| 2694 | (74*10^168170+529)/9 | 168171 | Robert Price | 02/2022 |
| 2695 | 2^558640-114149 | 168168 | Enzo Doria | 12/2014 |
| 2696 | 2^558498-1849277 | 168125 | Enzo Doria | 08/2015 |
| 2697 | 2^558476-1850249 | 168119 | Enzo Doria | 08/2015 |
| 2698 | (7*10^168067+71)/3 | 168068 | Robert Price | 05/2018 |
| 2699 | 2^558150-1852211 | 168020 | Enzo Doria | 08/2015 |
| 2700 | 2^558125-113661 | 168013 | Enzo Doria | 09/2014 |
| 2701 | 393^64747-392^64747 | 167980 | Jean-Louis Charton | 08/2012 |
| 2702 | (8*10^167965-11)/3 | 167966 | Robert Price | 07/2023 |
| 2703 | 2^557916+216151 | 167950 | Enzo Doria | 12/2023 |
| 2704 | (13*10^167911+179)/3 | 167912 | Robert Price | 11/2018 |
| 2705 | (26*10^167861-167)/3 | 167862 | Robert Price | 10/2019 |
| 2706 | 36^107827-107827 | 167812 | Kellen Shenton | 06/2023 |
| 2707 | 32027^37242-37242^32027 | 167795 | Frank Doornink | 01/2024 |
| 2708 | 39^105456+2 | 167788 | Robert Price | 04/2015 |
| 2709 | 2^557322+217519 | 167771 | Enzo Doria | 01/2024 |
| 2710 | (28^115877-1)/27 | 167691 | Paul Bourdelais | 12/2017 |
| 2711 | 6*10^167662-13 | 167663 | Robert Price | 07/2022 |
| 2712 | 10^167639+121911 | 167640 | Patrick De Geest | 07/2018 |
| 2713 | 10^167639-8001 | 167639 | Robert Price | 03/2018 |
| 2714 | 2^556504-462059 | 167525 | Enzo Doria | 07/2015 |
| 2715 | (88*10^167522-637)/9 | 167523 | Robert Price | 11/2020 |
| 2716 | 5*10^167510+9 | 167511 | Robert Price | 08/2015 |
| 2717 | 7*10^167437-93 | 167438 | Robert Price | 08/2020 |
| 2718 | 25455^37978-37978^25455 | 167323 | Frank Doornink | 01/2024 |
| 2719 | 11^160663+6 | 167314 | Paul Bourdelais | 02/2021 |
| 2720 | (7*10^167308-493)/9 | 167308 | Robert Price | 04/2021 |
| 2721 | 2^555759+74333 | 167301 | Enzo Doria | 07/2023 |
| 2722 | 26084^37871-37871^26084 | 167253 | Frank Doornink | 03/2024 |
| 2723 | 2^555343+1874333 | 167175 | Enzo Doria | 06/2016 |
| 2724 | 2^555210-461261 | 167135 | Enzo Doria | 07/2015 |
| 2725 | 9*10^166996+59 | 166997 | Robert Price | 01/2020 |
| 2726 | (68*10^166976-329)/9 | 166977 | Robert Price | 03/2021 |
| 2727 | (64*10^166901+683)/9 | 166902 | Robert Price | 06/2022 |
| 2728 | 2^554372+1880527 | 166883 | Enzo Doria | 11/2016 |
| 2729 | 2^554299+72173 | 166861 | Enzo Doria | 04/2016 |
| 2730 | (185*10^166837+7)/3 | 166839 | Robert Price | 03/2020 |
| 2731 | (14*10^166813+139)/9 | 166814 | Robert Price | 11/2021 |
| 2732 | 26084^37767-37767^26084 | 166794 | Frank Doornink | 03/2024 |
| 2733 | 2^554037-2797063 | 166782 | Enzo Doria | 03/2016 |
| 2734 | 31861^37028-37028^31861 | 166747 | Frank Doornink | 01/2024 |
| 2735 | (49*10^166721-139)/9 | 166722 | Robert Price | 03/2019 |
| 2736 | 2*10^166646+69 | 166647 | Robert Price | 06/2020 |
| 2737 | 2^553484-29819 | 166616 | Enzo Doria | 08/2015 |
| 2738 | (188*10^166611+7)/3 | 166613 | Robert Price | 03/2020 |
| 2739 | 2^553383-2784217 | 166585 | Enzo Doria | 10/2015 |
| 2740 | 2^553069+76427 | 166491 | Enzo Doria | 05/2016 |
| 2741 | 25218^37819-37819^25218 | 166469 | Frank Doornink | 12/2023 |
| 2742 | 2*10^166458+51 | 166459 | Robert Price | 05/2018 |
| 2743 | 589^60089-588^60089 | 166454 | Jean-Louis Charton | 09/2012 |
| 2744 | 25214^37799-37799^25214 | 166378 | Frank Doornink | 11/2023 |
| 2745 | 11^159756-2424 | 166369 | Mike Oakes | 06/2010 |
| 2746 | 2^552649-361275 | 166364 | Enzo Doria | 05/2014 |
| 2747 | 2^552628-113669 | 166358 | Enzo Doria | 09/2014 |
| 2748 | (19*10^166325+137)/3 | 166326 | Robert Price | 03/2022 |
| 2749 | 10^166324+550603 | 166325 | Patrick De Geest | 07/2018 |
| 2750 | 10^166324-801 | 166324 | Robert Price | 02/2018 |
