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
Search by form
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 2501 | 2^695841+225 | 209470 | Henri Lifchitz | 01/2025 |
| 2502 | (35^135623+1)/36 | 209410 | Paul Bourdelais | 07/2018 |
| 2503 | 7*10^209161+39 | 209162 | Robert Price | 01/2023 |
| 2504 | 2^694633+1887257 | 209106 | Enzo Doria | 05/2017 |
| 2505 | fibonacci(999790)-4 | 208944 | Jon Grantham | 08/2023 |
| 2506 | 2^693959+180923 | 208903 | Enzo Doria | 07/2016 |
| 2507 | (2^693747-11)/3 | 208839 | Stefano Morozzi | 08/2022 |
| 2508 | 2^693462-1847561 | 208753 | Enzo Doria | 07/2015 |
| 2509 | 3^436268+436268 | 208153 | Anonymous | 08/2026 |
| 2510 | 2^690890-59981 | 207979 | Enzo Doria | 11/2015 |
| 2511 | (38^131591+1)/39 | 207884 | Paul Bourdelais | 07/2018 |
| 2512 | 3*2^690484+5 | 207857 | Jon Grantham | 07/2023 |
| 2513 | 2^690163+1877063 | 207760 | Enzo Doria | 07/2016 |
| 2514 | Phi(64773,-64773) | 207680 | Henri Lifchitz | 06/2025 |
| 2515 | 7^245608-2 | 207563 | Paul Bourdelais | 01/2021 |
| 2516 | (67*10^207556+23)/9 | 207557 | Serge Batalov | 01/2023 |
| 2517 | 2^689286-29381 | 207496 | Enzo Doria | 08/2015 |
| 2518 | 11^199202+10 | 207448 | Alfred Reich | 06/2026 |
| 2519 | 2^689122-114521 | 207447 | Enzo Doria | 04/2015 |
| 2520 | 9*10^207254-89 | 207255 | Robert Price | 02/2023 |
| 2521 | 2^688373+6077 | 207221 | Enzo Doria | 02/2016 |
| 2522 | 2^688201+1875527 | 207170 | Enzo Doria | 07/2016 |
| 2523 | (42^127609+1)/43 | 207140 | Paul Bourdelais | 07/2018 |
| 2524 | 2^687938+213589 | 207090 | Enzo Doria | 10/2023 |
| 2525 | 2^687619+81563 | 206994 | Enzo Doria | 08/2016 |
| 2526 | 3*10^206927+37 | 206928 | Robert Price | 08/2023 |
| 2527 | 2^687383+21803 | 206923 | Enzo Doria | 09/2023 |
| 2528 | (11*10^206688+19)/3 | 206689 | Robert Price | 07/2024 |
| 2529 | 2^686572-1845299 | 206679 | Enzo Doria | 07/2015 |
| 2530 | (21^156217-1)/20 | 206552 | Paul Bourdelais | 04/2010 |
| 2531 | 2^685970+39415 | 206498 | Enzo Doria | 11/2024 |
| 2532 | 4^342873-342873 | 206431 | Anonymous | 08/2026 |
| 2533 | (2^685739+1)/(3*87774593) | 206420 | Gord Palameta | 08/2018 |
| 2534 | 2^685578+3 | 206380 | Paul Bourdelais | 04/2012 |
| 2535 | 2^685078+218599 | 206230 | Enzo Doria | 01/2024 |
| 2536 | 2^684836-49349 | 206157 | Enzo Doria | 10/2015 |
| 2537 | (73^110603-1)/72 | 206088 | Paul Bourdelais | 06/2018 |
| 2538 | 2^684163-2790967 | 205954 | Enzo Doria | 12/2015 |
| 2539 | 326^81943-325^81943 | 205941 | Jean-Louis Charton | 07/2012 |
| 2540 | (2^684127-1)/23765203727 | 205933 | Jens K. Andersen | 04/2009 |
| 2541 | (68*10^205510+13)/9 | 205511 | Serge Batalov | 01/2023 |
| 2542 | 3^430622+430622 | 205459 | Anonymous | 08/2026 |
| 2543 | 4^341233-3^341233 | 205443 | Jean-Louis Charton | 01/2006 |
| 2544 | 2^682414+215029 | 205428 | Enzo Doria | 11/2023 |
| 2545 | (963^68821-1)/962 | 205334 | Jinyuan Wang | 01/2024 |
| 2546 | (43*10^205183-421)/9 | 205184 | Robert Price | 10/2023 |
| 2547 | 2^681545+467 | 205166 | Lelio R Paula | 11/2013 |
| 2548 | 2^681306+81049 | 205094 | Enzo Doria | 07/2016 |
| 2549 | Sm(43213)/581 | 204956 | Youcef Lemsafer | 06/2026 |
| 2550 | 2^680697+1877057 | 204911 | Enzo Doria | 07/2016 |
| 2551 | 2^680415+71783 | 204826 | Enzo Doria | 04/2016 |
| 2552 | 10^204764-8001 | 204764 | Robert Price | 03/2023 |
| 2553 | (26*10^204730-77)/3 | 204731 | Robert Price | 03/2023 |
| 2554 | 2^679860-459995 | 204659 | Enzo Doria | 06/2015 |
| 2555 | 2^679593+1879547 | 204578 | Enzo Doria | 09/2016 |
| 2556 | 2^678899+220073 | 204369 | Enzo Doria | 03/2024 |
| 2557 | 2^678753+21677 | 204326 | Enzo Doria | 08/2023 |
| 2558 | 2^678651+1875023 | 204295 | Enzo Doria | 07/2016 |
| 2559 | 2^678561+678561 | 204268 | Henri Lifchitz | 05/2006 |
| 2560 | 2^678408+590295810358705651711 | 204222 | Alfred Reich | 05/2026 |
| 2561 | 5*3^427884+2^427884 | 204154 | Jon Grantham | 08/2023 |
| 2562 | 2^678101-114043 | 204129 | Enzo Doria | 11/2014 |
| 2563 | 2^678028+1875631 | 204107 | Enzo Doria | 06/2016 |
| 2564 | 2^677721+28607 | 204015 | Enzo Doria | 01/2024 |
| 2565 | (19*10^203798-7)/3 | 203799 | Robert Price | 12/2023 |
| 2566 | 2^676992-59783 | 203795 | Enzo Doria | 10/2015 |
| 2567 | 2^676972+1866871 | 203789 | Enzo Doria | 03/2016 |
| 2568 | 2^676815+22583 | 203742 | Enzo Doria | 09/2023 |
| 2569 | 2^676761-9 | 203726 | Robert Price | 01/2017 |
| 2570 | 2^676592-23 | 203675 | Stefano Morozzi | 07/2022 |
| 2571 | 2^676563-2792407 | 203666 | Enzo Doria | 02/2016 |
| 2572 | 2^676306-114713 | 203589 | Enzo Doria | 04/2015 |
| 2573 | (2^675977-1)/(1686378749257*7171117283326998925471) | 203456 | Dario Alpern | 07/2015 |
| 2574 | 6*10^203365+53 | 203366 | Robert Price | 09/2023 |
| 2575 | 2^675433-118231 | 203326 | Stefano Morozzi | 09/2025 |
| 2576 | 2^675433-138811 | 203326 | Stefano Morozzi | 09/2025 |
| 2577 | 2^675430-133685 | 203325 | Stefano Morozzi | 09/2025 |
| 2578 | 2^675430-29937 | 203325 | Stefano Morozzi | 09/2025 |
| 2579 | 2^675430-57281 | 203325 | Stefano Morozzi | 09/2025 |
| 2580 | 2^675422-99827 | 203323 | Stefano Morozzi | 09/2025 |
| 2581 | 2^675424-130715 | 203323 | Stefano Morozzi | 09/2025 |
| 2582 | 2^675420-36699 | 203322 | Stefano Morozzi | 09/2025 |
| 2583 | 2^675421-65269 | 203322 | Stefano Morozzi | 09/2025 |
| 2584 | 2^675417-43003 | 203321 | Stefano Morozzi | 09/2025 |
| 2585 | 2^675412-151665 | 203320 | Stefano Morozzi | 09/2025 |
| 2586 | 2^675413-124789 | 203320 | Stefano Morozzi | 09/2025 |
| 2587 | 2^675413-186285 | 203320 | Stefano Morozzi | 09/2025 |
| 2588 | 2^675409-163929 | 203319 | Stefano Morozzi | 09/2025 |
| 2589 | 2^675409-5841 | 203319 | Stefano Morozzi | 09/2025 |
| 2590 | 2^675411-100471 | 203319 | Stefano Morozzi | 09/2025 |
| 2591 | 2^675411-13075 | 203319 | Stefano Morozzi | 09/2025 |
| 2592 | 2^675406-8877 | 203318 | Stefano Morozzi | 09/2025 |
| 2593 | 2^675407-176385 | 203318 | Stefano Morozzi | 09/2025 |
| 2594 | 2^675402-188523 | 203317 | Stefano Morozzi | 09/2025 |
| 2595 | 2^675398-150683 | 203316 | Stefano Morozzi | 08/2025 |
| 2596 | 2^675399-132069 | 203316 | Stefano Morozzi | 08/2025 |
| 2597 | 2^675401-130593 | 203316 | Stefano Morozzi | 08/2025 |
| 2598 | 2^675397-134749 | 203315 | Stefano Morozzi | 08/2025 |
| 2599 | 2^675385-169051 | 203312 | Stefano Morozzi | 08/2025 |
| 2600 | 2^675383-97737 | 203311 | Stefano Morozzi | 08/2025 |
| 2601 | 2^675380-94305 | 203310 | Stefano Morozzi | 08/2025 |
| 2602 | 2^675381-78495 | 203310 | Stefano Morozzi | 08/2025 |
| 2603 | 2^675373-1039 | 203308 | Stefano Morozzi | 08/2025 |
| 2604 | 2^675374-190163 | 203308 | Stefano Morozzi | 08/2025 |
| 2605 | 2^675374-9177 | 203308 | Stefano Morozzi | 08/2025 |
| 2606 | 2^675368-144215 | 203307 | Stefano Morozzi | 08/2025 |
| 2607 | 2^675369-44433 | 203307 | Stefano Morozzi | 08/2025 |
| 2608 | 2^675370-118025 | 203307 | Stefano Morozzi | 08/2025 |
| 2609 | 2^675370-190293 | 203307 | Stefano Morozzi | 08/2025 |
| 2610 | 2^675366-150243 | 203306 | Stefano Morozzi | 08/2025 |
| 2611 | 2^675362-131235 | 203305 | Stefano Morozzi | 08/2025 |
| 2612 | 2^675362-161171 | 203305 | Stefano Morozzi | 08/2025 |
| 2613 | 2^675363-189607 | 203305 | Stefano Morozzi | 08/2025 |
| 2614 | 2^675364-20763 | 203305 | Stefano Morozzi | 08/2025 |
| 2615 | 2^675357-45801 | 203303 | Stefano Morozzi | 07/2025 |
| 2616 | 2^675354-109623 | 203302 | Stefano Morozzi | 07/2025 |
| 2617 | 2^675350-124911 | 203301 | Stefano Morozzi | 07/2025 |
| 2618 | 2^675345-83365 | 203300 | Stefano Morozzi | 07/2025 |
| 2619 | 2^675347-160357 | 203300 | Stefano Morozzi | 07/2025 |
| 2620 | 2^675339-178989 | 203298 | Stefano Morozzi | 07/2025 |
| 2621 | 2^675337-135031 | 203297 | Stefano Morozzi | 07/2025 |
| 2622 | 2^675337-21693 | 203297 | Stefano Morozzi | 07/2025 |
| 2623 | 2^675334-194937 | 203296 | Stefano Morozzi | 07/2025 |
| 2624 | 2^675334-34313 | 203296 | Stefano Morozzi | 07/2025 |
| 2625 | 2^675330-167061 | 203295 | Stefano Morozzi | 07/2025 |
| 2626 | 2^675331-148659 | 203295 | Stefano Morozzi | 07/2025 |
| 2627 | 2^675326-178983 | 203294 | Stefano Morozzi | 07/2025 |
| 2628 | 2^675327-107469 | 203294 | Stefano Morozzi | 07/2025 |
| 2629 | 2^675327-55159 | 203294 | Stefano Morozzi | 07/2025 |
| 2630 | 2^675328-92097 | 203294 | Stefano Morozzi | 07/2025 |
| 2631 | 2^675323-197989 | 203293 | Stefano Morozzi | 07/2025 |
| 2632 | 2^675315-104421 | 203291 | Stefano Morozzi | 07/2025 |
| 2633 | 2^675316-155007 | 203291 | Stefano Morozzi | 07/2025 |
| 2634 | 2^675317-30613 | 203291 | Stefano Morozzi | 07/2025 |
| 2635 | 2^675318-116925 | 203291 | Stefano Morozzi | 07/2025 |
| 2636 | 2^675312-135209 | 203290 | Stefano Morozzi | 06/2025 |
| 2637 | 2^675313-131635 | 203290 | Stefano Morozzi | 06/2025 |
| 2638 | 2^675314-187365 | 203290 | Stefano Morozzi | 07/2025 |
| 2639 | 2^675305-75049 | 203288 | Stefano Morozzi | 06/2025 |
| 2640 | 2^675308-198257 | 203288 | Stefano Morozzi | 06/2025 |
| 2641 | 2^675308-80475 | 203288 | Stefano Morozzi | 06/2025 |
| 2642 | 2^675302-68271 | 203287 | Stefano Morozzi | 06/2025 |
| 2643 | 2^675304-74217 | 203287 | Stefano Morozzi | 06/2025 |
| 2644 | 2^675299-103321 | 203286 | Stefano Morozzi | 06/2025 |
| 2645 | 2^675292-125489 | 203284 | Stefano Morozzi | 06/2025 |
| 2646 | 2^675289-140833 | 203283 | Stefano Morozzi | 06/2025 |
| 2647 | 2^675291-141087 | 203283 | Stefano Morozzi | 06/2025 |
| 2648 | 2^675285-177525 | 203282 | Stefano Morozzi | 06/2025 |
| 2649 | 2^675288-133227 | 203282 | Stefano Morozzi | 06/2025 |
| 2650 | 2^675282-24717 | 203281 | Stefano Morozzi | 06/2025 |
| 2651 | 2^675279-113179 | 203280 | Stefano Morozzi | 06/2025 |
| 2652 | 2^675266-25557 | 203276 | Stefano Morozzi | 06/2025 |
| 2653 | 2^675267-112125 | 203276 | Stefano Morozzi | 06/2025 |
| 2654 | 2^675263-164881 | 203275 | Stefano Morozzi | 06/2025 |
| 2655 | 2^675261-4885 | 203274 | Stefano Morozzi | 06/2025 |
| 2656 | 2^675261-9489 | 203274 | Stefano Morozzi | 06/2025 |
| 2657 | 2^675255-100321 | 203273 | Stefano Morozzi | 06/2025 |
| 2658 | 2^675256-41439 | 203273 | Stefano Morozzi | 06/2025 |
| 2659 | 2^675257-34623 | 203273 | Stefano Morozzi | 06/2025 |
| 2660 | 2^675254-132177 | 203272 | Stefano Morozzi | 06/2025 |
| 2661 | 2^675254-58053 | 203272 | Stefano Morozzi | 06/2025 |
| 2662 | 2^675242-117707 | 203269 | Stefano Morozzi | 06/2025 |
| 2663 | 2^675243-156531 | 203269 | Stefano Morozzi | 06/2025 |
| 2664 | 2^675243-56595 | 203269 | Stefano Morozzi | 06/2025 |
| 2665 | 2^675239-90471 | 203268 | Stefano Morozzi | 06/2025 |
| 2666 | 2^675240-34863 | 203268 | Stefano Morozzi | 06/2025 |
| 2667 | 2^675234-71207 | 203266 | Stefano Morozzi | 06/2025 |
| 2668 | 2^675235-195175 | 203266 | Stefano Morozzi | 06/2025 |
| 2669 | 2^675235-199855 | 203266 | Stefano Morozzi | 06/2025 |
| 2670 | 2^675229-71601 | 203265 | Stefano Morozzi | 06/2025 |
| 2671 | 2^675219-66709 | 203262 | Stefano Morozzi | 06/2025 |
| 2672 | 2^675220-98999 | 203262 | Stefano Morozzi | 06/2025 |
| 2673 | 2^675221-149589 | 203262 | Stefano Morozzi | 06/2025 |
| 2674 | 2^675211-198405 | 203259 | Stefano Morozzi | 04/2025 |
| 2675 | 2^675209+1791 | 203259 | Stefano Morozzi | 09/2025 |
| 2676 | 2^675208-131505 | 203258 | Stefano Morozzi | 04/2025 |
| 2677 | 2^675206+131877 | 203258 | Stefano Morozzi | 09/2025 |
| 2678 | 2^675208+97257 | 203258 | Stefano Morozzi | 09/2025 |
| 2679 | 2^675202-14823 | 203257 | Stefano Morozzi | 04/2025 |
| 2680 | 2^675202-35967 | 203257 | Stefano Morozzi | 04/2025 |
| 2681 | 2^675202-54681 | 203257 | Stefano Morozzi | 04/2025 |
| 2682 | 2^675205-107845 | 203257 | Stefano Morozzi | 04/2025 |
| 2683 | 2^675199-131397 | 203256 | Stefano Morozzi | 04/2025 |
| 2684 | 2^675199-34219 | 203256 | Stefano Morozzi | 04/2025 |
| 2685 | 2^675199-56175 | 203256 | Stefano Morozzi | 04/2025 |
| 2686 | 2^675200+100045 | 203256 | Stefano Morozzi | 09/2025 |
| 2687 | 2^675198-106925 | 203255 | Stefano Morozzi | 04/2025 |
| 2688 | 2^675196+191491 | 203255 | Stefano Morozzi | 09/2025 |
| 2689 | 2^675198+5289 | 203255 | Stefano Morozzi | 09/2025 |
| 2690 | 2^675192-192243 | 203254 | Stefano Morozzi | 04/2025 |
| 2691 | 2^675192+36871 | 203254 | Stefano Morozzi | 09/2025 |
| 2692 | 2^675195+174711 | 203254 | Stefano Morozzi | 09/2025 |
| 2693 | 2^675189-37383 | 203253 | Stefano Morozzi | 04/2025 |
| 2694 | 2^675190-68711 | 203253 | Stefano Morozzi | 04/2025 |
| 2695 | 2^675191-114549 | 203253 | Stefano Morozzi | 04/2025 |
| 2696 | 2^675191-29445 | 203253 | Stefano Morozzi | 04/2025 |
| 2697 | 2^675189+16221 | 203253 | Stefano Morozzi | 08/2025 |
| 2698 | 2^675190+43477 | 203253 | Stefano Morozzi | 08/2025 |
| 2699 | 2^675186-24563 | 203252 | Stefano Morozzi | 04/2025 |
| 2700 | 2^675187-185041 | 203252 | Stefano Morozzi | 04/2025 |
| 2701 | 2^675188-121613 | 203252 | Stefano Morozzi | 04/2025 |
| 2702 | 2^675188+103585 | 203252 | Stefano Morozzi | 08/2025 |
| 2703 | 2^675183-43587 | 203251 | Stefano Morozzi | 04/2025 |
| 2704 | 2^675184-60563 | 203251 | Stefano Morozzi | 04/2025 |
| 2705 | 2^675182+128499 | 203251 | Stefano Morozzi | 08/2025 |
| 2706 | 2^675185+11 | 203251 | Stefano Morozzi | 08/2025 |
| 2707 | 10247^50678-50678^10247 | 203250 | Norbert Schneider | 03/2022 |
| 2708 | 2^675179+85311 | 203250 | Stefano Morozzi | 08/2025 |
| 2709 | 2^675177-30495 | 203249 | Stefano Morozzi | 04/2025 |
| 2710 | 2^675176+161467 | 203249 | Stefano Morozzi | 08/2025 |
| 2711 | 2^675178+15745 | 203249 | Stefano Morozzi | 08/2025 |
| 2712 | 2^675172+24927 | 203248 | Stefano Morozzi | 08/2025 |
| 2713 | 2^675170-170651 | 203247 | Stefano Morozzi | 04/2025 |
| 2714 | 2^675171-21231 | 203247 | Stefano Morozzi | 04/2025 |
| 2715 | 2^675169+107577 | 203247 | Stefano Morozzi | 08/2025 |
| 2716 | 2^675171+159551 | 203247 | Stefano Morozzi | 08/2025 |
| 2717 | 2^675166-116351 | 203246 | Stefano Morozzi | 04/2025 |
| 2718 | 2^675166-63465 | 203246 | Stefano Morozzi | 04/2025 |
| 2719 | 2^675167-11047 | 203246 | Stefano Morozzi | 04/2025 |
| 2720 | 2^675168-197307 | 203246 | Stefano Morozzi | 04/2025 |
| 2721 | 2^675168-89379 | 203246 | Stefano Morozzi | 04/2025 |
| 2722 | 2^675166+23097 | 203246 | Stefano Morozzi | 07/2025 |
| 2723 | 2^675167+7725 | 203246 | Stefano Morozzi | 07/2025 |
| 2724 | 2^675167+35999 | 203246 | Stefano Morozzi | 07/2025 |
| 2725 | 2^675162-24471 | 203245 | Stefano Morozzi | 04/2025 |
| 2726 | 2^675163-4971 | 203245 | Stefano Morozzi | 04/2025 |
| 2727 | 2^675163-69489 | 203245 | Stefano Morozzi | 04/2025 |
| 2728 | 2^675165-153541 | 203245 | Stefano Morozzi | 04/2025 |
| 2729 | 2^675159-107809 | 203244 | Stefano Morozzi | 04/2025 |
| 2730 | 2^675160+107463 | 203244 | Stefano Morozzi | 07/2025 |
| 2731 | 2^675160+174355 | 203244 | Stefano Morozzi | 07/2025 |
| 2732 | 2^675156-156785 | 203243 | Stefano Morozzi | 04/2025 |
| 2733 | 2^675157-177433 | 203243 | Stefano Morozzi | 04/2025 |
| 2734 | 2^675154-66563 | 203242 | Stefano Morozzi | 04/2025 |
| 2735 | 2^675153+21477 | 203242 | Stefano Morozzi | 07/2025 |
| 2736 | 2^675153+88607 | 203242 | Stefano Morozzi | 07/2025 |
| 2737 | 2^675154+7609 | 203242 | Stefano Morozzi | 07/2025 |
| 2738 | 2^675155+128255 | 203242 | Stefano Morozzi | 07/2025 |
| 2739 | 2^675148-71007 | 203240 | Stefano Morozzi | 04/2025 |
| 2740 | 2^675148-94815 | 203240 | Stefano Morozzi | 04/2025 |
| 2741 | 2^675146+28957 | 203240 | Stefano Morozzi | 06/2025 |
| 2742 | 2^675143+55865 | 203239 | Stefano Morozzi | 06/2025 |
| 2743 | 2^675143+100619 | 203239 | Stefano Morozzi | 06/2025 |
| 2744 | 2^675143+191895 | 203239 | Stefano Morozzi | 06/2025 |
| 2745 | 2^675144+34207 | 203239 | Stefano Morozzi | 06/2025 |
| 2746 | 2^675142+160903 | 203238 | Stefano Morozzi | 06/2025 |
| 2747 | 2^675138-52371 | 203237 | Stefano Morozzi | 04/2025 |
| 2748 | 2^675138+114979 | 203237 | Stefano Morozzi | 06/2025 |
| 2749 | 2^675133-7273 | 203236 | Stefano Morozzi | 04/2025 |
| 2750 | 2^675134-73473 | 203236 | Stefano Morozzi | 04/2025 |
