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
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
2501 | 2^498623+1866983 | 150101 | Enzo Doria | 03/2016 |
2502 | (25*10^150050-403)/9 | 150051 | Robert Price | 12/2020 |
2503 | numbpart(18140942830) | 150033 | Serge Batalov | 04/2017 |
2504 | 10^150029+4381 | 150030 | Patrick De Geest | 05/2016 |
2505 | 10^150029-41 | 150029 | Serge Batalov | 12/2014 |
2506 | 10^150000+1158603 | 150001 | Patrick De Geest | 09/2018 |
2507 | 10^150000-245703 | 150000 | Patrick De Geest | 09/2018 |
2508 | (38*10^149999+691)/9 | 150000 | Robert Price | 10/2018 |
2509 | 2043563126843649194^8192+2043563126843649185^8192 | 150000 | Youcef Lemsafer | 01/2023 |
2510 | (2043563126843649232^8192+2043563126843649201^8192)/147457 | 149994 | Youcef Lemsafer | 01/2023 |
2511 | 2^498238-53 | 149985 | Lelio R Paula | 12/2017 |
2512 | 45728^1905+1905^45728 | 149984 | Hans Havermann | 10/2020 |
2513 | 5*10^149907+23 | 149908 | Robert Price | 03/2019 |
2514 | 39347^6442+6442^39347 | 149874 | Hans Havermann | 09/2020 |
2515 | 2^497850+81049 | 149868 | Enzo Doria | 07/2016 |
2516 | 37228^10575+10575^37228 | 149816 | Hans Havermann | 10/2020 |
2517 | (5*2^497673+1)/2743 | 149812 | Lelio R Paula | 10/2015 |
2518 | (5*2^497671+1)/373703 | 149810 | Lelio R Paula | 10/2015 |
2519 | (2*10^149803-143)/3 | 149803 | Robert Price | 03/2018 |
2520 | 33845^26604+26604^33845 | 149763 | Hans Havermann | 09/2020 |
2521 | 2^497434-2784191 | 149743 | Enzo Doria | 10/2015 |
2522 | (865*10^149737-1)/9 | 149739 | Robert Price | 04/2020 |
2523 | 10^149695-7000001 | 149695 | Robert Price | 06/2021 |
2524 | 38237^8214+8214^38237 | 149681 | Hans Havermann | 09/2020 |
2525 | (23*10^149655+19)/3 | 149656 | Robert Price | 07/2019 |
2526 | 2^497068-113579 | 149633 | Enzo Doria | 08/2014 |
2527 | 2^497037+73727 | 149624 | Enzo Doria | 04/2016 |
2528 | 11*10^149618+3 | 149620 | Robert Price | 07/2021 |
2529 | 34942^19067+19067^34942 | 149562 | Hans Havermann | 09/2020 |
2530 | 33696^27449+27449^33696 | 149561 | Hans Havermann | 09/2020 |
2531 | 2^496773+77747 | 149544 | Enzo Doria | 05/2016 |
2532 | (7*10^149483-493)/9 | 149483 | Robert Price | 04/2021 |
2533 | (206*10^149459+7)/3 | 149461 | Robert Price | 07/2020 |
2534 | 34589^20940+20940^34589 | 149459 | Hans Havermann | 09/2020 |
2535 | 2^496477-113485 | 149455 | Enzo Doria | 08/2014 |
2536 | ((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9 | 149410 | Hans Havermann | 09/2019 |
2537 | 2^496270-49451 | 149393 | Enzo Doria | 10/2015 |
2538 | 2^496238-1865081 | 149383 | Enzo Doria | 01/2016 |
2539 | 33831^26030+26030^33831 | 149380 | Hans Havermann | 09/2020 |
2540 | 34131^23780+23780^34131 | 149365 | Hans Havermann | 09/2020 |
2541 | (5*10^149335-53)/3 | 149336 | Robert Price | 09/2020 |
2542 | 2^495968-1853699 | 149302 | Enzo Doria | 09/2015 |
2543 | 2^495935-4117 | 149292 | Yves Minet | 02/2018 |
2544 | 35816^14709+14709^35816 | 149267 | Hans Havermann | 09/2020 |
2545 | (10^149264+7)/191/2683/80557 | 149254 | Alfred Reich | 07/2021 |
2546 | 10^149240-40000001 | 149240 | Robert Price | 07/2022 |
2547 | 2^495712-396765 | 149225 | Enzo Doria | 07/2013 |
2548 | (21*2^495676-1)/4835 | 149211 | Lelio R Paula | 10/2015 |
2549 | 2^495420+1880701 | 149137 | Enzo Doria | 10/2016 |
2550 | 2^495337-1847293 | 149112 | Enzo Doria | 07/2015 |
2551 | (2^495193-7)/5 | 149068 | Lelio R Paula | 10/2015 |
2552 | 2^495163+111546435 | 149059 | Paul Bourdelais | 10/2021 |
2553 | 33282^30097+30097^33282 | 149055 | Hans Havermann | 09/2020 |
2554 | 37384^9705+9705^37384 | 149050 | Hans Havermann | 09/2020 |
2555 | 34808^19143+19143^34808 | 149049 | Hans Havermann | 09/2020 |
2556 | 413^56963-412^56963 | 149013 | Jean-Louis Charton | 08/2012 |
2557 | 47^89113-46^89113 | 149006 | Robert Price | 10/2012 |
2558 | 2^494916+87855 | 148985 | Lelio R Paula | 01/2016 |
2559 | 6*10^148982+73 | 148983 | Robert Price | 04/2019 |
2560 | 10^148934+1530019 | 148935 | Patrick De Geest | 02/2021 |
2561 | 10^148934-1000000001 | 148934 | Robert Price | 11/2020 |
2562 | 10^148934-512057 | 148934 | Patrick De Geest | 02/2021 |
2563 | 39000^6571+6571^39000 | 148888 | Hans Havermann | 10/2020 |
2564 | 2^494586-2791991 | 148886 | Enzo Doria | 02/2016 |
2565 | 8*10^148860-3 | 148861 | Ray Chandler | 04/2011 |
2566 | 38262^7769+7769^38262 | 148854 | Hans Havermann | 10/2020 |
2567 | 10^148816-500001 | 148816 | Robert Price | 03/2022 |
2568 | (53*10^148811-287)/9 | 148812 | Robert Price | 02/2022 |
2569 | 2^494333-286183 | 148810 | Enzo Doria | 06/2015 |
2570 | 2^494144-264119 | 148753 | Enzo Doria | 05/2014 |
2571 | 6*10^148734+47 | 148735 | Robert Price | 06/2022 |
2572 | 36502^11823+11823^36502 | 148663 | Hans Havermann | 11/2020 |
2573 | (5*2^493838-1)/3721 | 148658 | Lelio R Paula | 10/2015 |
2574 | 64239^206+206^64239 | 148641 | Hans Havermann | 10/2020 |
2575 | (23*2^493761-1)/555 | 148636 | Lelio R Paula | 10/2015 |
2576 | (23*10^148627-137)/3 | 148628 | Robert Price | 08/2021 |
2577 | (151*10^148601-1)/3 | 148603 | Robert Price | 03/2020 |
2578 | 2^493636+82081 | 148600 | Enzo Doria | 09/2016 |
2579 | ((((((((((((((34251^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2 | 148593 | Serge Batalov | 07/2016 |
2580 | 177487#+(519643#)/(177487#) | 148558 | Makoto Morimoto | 11/2017 |
2581 | (2*10^148460-23)/3 | 148460 | Robert Price | 04/2018 |
2582 | (28*10^148445+101)/3 | 148446 | Robert Price | 09/2020 |
2583 | 36203^12556+12556^36203 | 148391 | Hans Havermann | 10/2020 |
2584 | 33912^23749+23749^33912 | 148387 | Hans Havermann | 10/2020 |
2585 | (8*10^148328+1)/9 | 148328 | Serge Batalov | 05/2010 |
2586 | 34294^21117+21117^34294 | 148309 | Hans Havermann | 10/2020 |
2587 | (71*10^148306-539)/9 | 148307 | Robert Price | 07/2019 |
2588 | 38042^7875+7875^38042 | 148222 | Hans Havermann | 10/2020 |
2589 | 5^211959-12874 | 148153 | Enzo Doria | 05/2014 |
2590 | 34142^21831+21831^34142 | 148145 | Hans Havermann | 10/2020 |
2591 | 10^148112+34059 | 148113 | Patrick De Geest | 05/2021 |
2592 | 10^148112-70000001 | 148112 | Robert Price | 03/2021 |
2593 | 10^148112-106593 | 148112 | Patrick De Geest | 05/2021 |
2594 | 36303^12016+12016^36303 | 148108 | Hans Havermann | 10/2020 |
2595 | (77*10^148089-149)/9 | 148090 | Robert Price | 03/2022 |
2596 | (16*10^148071+41)/3 | 148072 | Robert Price | 03/2019 |
2597 | 187^65175-2 | 148068 | Lelio R Paula | 11/2017 |
2598 | 2^491851+1871453 | 148062 | Enzo Doria | 05/2016 |
2599 | (68*10^148060-257)/9 | 148061 | Robert Price | 07/2019 |
2600 | (151*10^148020-1)/3 | 148022 | Robert Price | 03/2020 |
2601 | 39153^6032+6032^39153 | 148017 | Hans Havermann | 10/2020 |
2602 | 36798^10507+10507^36798 | 147983 | Hans Havermann | 12/2020 |
2603 | (26*10^147973-23)/3 | 147974 | Robert Price | 12/2019 |
2604 | 2^491521-1865323 | 147963 | Enzo Doria | 02/2016 |
2605 | (2^491476+7)/71 | 147948 | Lelio R Paula | 10/2015 |
2606 | 2*10^147928+47 | 147929 | Robert Price | 12/2021 |
2607 | 2^491391-7807 | 147924 | Lelio R Paula | 01/2013 |
2608 | 39736^5279+5279^39736 | 147920 | Hans Havermann | 11/2020 |
2609 | 2^491370-113297 | 147918 | Enzo Doria | 07/2014 |
2610 | (32760^32760+32759^32759)/95546586737133567708319 | 147900 | Robert Price | 07/2016 |
2611 | 44368^2155+2155^44368 | 147899 | Hans Havermann | 12/2020 |
2612 | (17*10^147890+79)/3 | 147891 | Robert Price | 04/2019 |
2613 | 94*10^147871-3 | 147873 | Robert Price | 05/2020 |
2614 | 10^147843+620967 | 147844 | Patrick De Geest | 05/2021 |
2615 | 10^147843-50000000001 | 147843 | Robert Price | 12/2020 |
2616 | 10^147843-182891 | 147843 | Patrick De Geest | 05/2021 |
2617 | 35805^13346+13346^35805 | 147709 | Hans Havermann | 11/2020 |
2618 | 2^490672+255255 | 147707 | Paul Bourdelais | 10/2021 |
2619 | 2^490660-17 | 147704 | Lelio R Paula | 12/2017 |
2620 | (229*10^147699-1)/3 | 147701 | Robert Price | 07/2020 |
2621 | 40656^4289+4289^40656 | 147678 | Hans Havermann | 11/2020 |
2622 | 2^490550+1179439 | 147671 | Enzo Doria | 06/2016 |
2623 | (23*10^147649-59)/9 | 147650 | Robert Price | 05/2018 |
2624 | 2^490303+2793653 | 147596 | Enzo Doria | 03/2016 |
2625 | 2^490266+255255 | 147585 | Paul Bourdelais | 10/2021 |
2626 | 199^64181-2 | 147543 | Lelio R Paula | 11/2017 |
2627 | 32849^30958+30958^32849 | 147518 | Hans Havermann | 11/2020 |
2628 | 2^489871-286987 | 147466 | Enzo Doria | 07/2015 |
2629 | 2^489864-351899 | 147464 | Enzo Doria | 07/2015 |
2630 | 175^65724-2 | 147422 | Lelio R Paula | 11/2017 |
2631 | 2^489712+1874851 | 147419 | Enzo Doria | 06/2016 |
2632 | 34473^18830+18830^34473 | 147367 | Hans Havermann | 11/2020 |
2633 | 63^81896-2 | 147359 | Lelio R Paula | 10/2017 |
2634 | 34580^18237+18237^34580 | 147344 | Hans Havermann | 11/2020 |
2635 | (11*10^147313-107)/3 | 147314 | Robert Price | 09/2018 |
2636 | (397*10^147310+17)/9 | 147312 | Robert Price | 03/2022 |
2637 | 2^489305-59815 | 147296 | Enzo Doria | 10/2015 |
2638 | (2^489280-7)/6381 | 147285 | Lelio R Paula | 09/2015 |
2639 | 2*10^147264-61 | 147265 | Robert Price | 10/2021 |
2640 | 2*10^147260+29 | 147261 | Robert Price | 02/2021 |
2641 | 33556^24457+24457^33556 | 147258 | Hans Havermann | 11/2020 |
2642 | 2^489125+80357 | 147242 | Enzo Doria | 06/2016 |
2643 | 10^147240-40000001 | 147240 | Robert Price | 07/2022 |
2644 | 32835^30452+30452^32835 | 147220 | Hans Havermann | 12/2020 |
2645 | (19*10^147213-97)/3 | 147214 | Robert Price | 10/2021 |
2646 | (148*10^147139-1)/3 | 147141 | Robert Price | 03/2020 |
2647 | 34338^19255+19255^34338 | 147123 | Hans Havermann | 11/2020 |
2648 | 2^488648-112799 | 147098 | Enzo Doria | 07/2014 |
2649 | 2^488627-350317 | 147092 | Enzo Doria | 06/2015 |
2650 | 33432^25075+25075^33432 | 147076 | Hans Havermann | 12/2020 |
2651 | (2^488441-1)/(61543567*30051203516986199) | 147012 | Dario Alpern | 12/2014 |
2652 | 2^488280-2165 | 146987 | Yves Minet | 07/2014 |
2653 | 2^488278+45 | 146987 | Lelio R Paula | 12/2017 |
2654 | 2^487927-39 | 146881 | Lelio R Paula | 12/2017 |
2655 | (7*10^146860-13)/3 | 146861 | Robert Price | 07/2018 |
2656 | (26*10^146856-77)/3 | 146857 | Robert Price | 11/2019 |
2657 | 32948^28611+28611^32948 | 146834 | Hans Havermann | 11/2020 |
2658 | 42596^2799+2799^42596 | 146829 | Hans Havermann | 12/2020 |
2659 | 2^487726-1863341 | 146821 | Enzo Doria | 12/2015 |
2660 | 43838^2229+2229^43838 | 146775 | Hans Havermann | 11/2020 |
2661 | 35005^15594+15594^35005 | 146775 | Hans Havermann | 11/2020 |
2662 | (167*10^146764+7)/3 | 146766 | Robert Price | 04/2021 |
2663 | 53^85114+85114 | 146761 | Kellen Shenton | 05/2022 |
2664 | (59*10^146738+157)/9 | 146739 | Robert Price | 12/2021 |
2665 | ((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9 | 146728 | Hans Havermann | 09/2019 |
2666 | 32963^28234+28234^32963 | 146711 | Hans Havermann | 12/2020 |
2667 | (22*10^146661-19)/3 | 146662 | Robert Price | 04/2019 |
2668 | 33958^20825+20825^33958 | 146651 | Hans Havermann | 12/2020 |
2669 | 2^487121-39523 | 146639 | Enzo Doria | 09/2015 |
2670 | 61063^252+252^61063 | 146637 | Hans Havermann | 12/2020 |
2671 | (7*2^486967+1)/39 | 146591 | Lelio R Paula | 09/2015 |
2672 | 34099^19900+19900^34099 | 146587 | Hans Havermann | 11/2020 |
2673 | 2^486893-79 | 146570 | Yves Minet | 09/2017 |
2674 | 36818^9567+9567^36818 | 146565 | Hans Havermann | 12/2020 |
2675 | 2^486840+1879141 | 146554 | Enzo Doria | 08/2016 |
2676 | 2^486774-87 | 146534 | Lelio R Paula | 12/2017 |
2677 | 38655^6176+6176^38655 | 146530 | Hans Havermann | 11/2020 |
2678 | 8*10^146522-81 | 146523 | Robert Price | 02/2021 |
2679 | 32820^29059+29059^32820 | 146485 | Hans Havermann | 12/2020 |
2680 | 37261^8530+8530^37261 | 146472 | Hans Havermann | 12/2020 |
2681 | 66953^154+154^66953 | 146462 | Hans Havermann | 12/2020 |
2682 | 96^73877-95^73877 | 146445 | Robert Price | 10/2015 |
2683 | 8*10^146421+81 | 146422 | Robert Price | 08/2019 |
2684 | 33153^26090+26090^33153 | 146420 | Hans Havermann | 11/2020 |
2685 | (52^85259+1)/53 | 146304 | Paul Bourdelais | 09/2017 |
2686 | 179^64935+2 | 146290 | Lelio R Paula | 10/2017 |
2687 | 32595^30758+30758^32595 | 146285 | Hans Havermann | 11/2020 |
2688 | 34972^15157+15157^34972 | 146205 | Hans Havermann | 12/2020 |
2689 | (16*10^146200+131)/3 | 146201 | Robert Price | 03/2022 |
2690 | (19*10^146181-49)/3 | 146182 | Robert Price | 05/2019 |
2691 | 2^485531-114621 | 146160 | Enzo Doria | 05/2015 |
2692 | 2^485473-933075 | 146142 | Paul Bourdelais | 06/2021 |
2693 | (2^485461-9)/4249 | 146135 | Lelio R Paula | 09/2015 |
2694 | (22*10^146130-193)/9 | 146131 | Robert Price | 07/2022 |
2695 | 2^485389+81887 | 146117 | Enzo Doria | 08/2016 |
2696 | 32554^30773+30773^32554 | 146108 | Hans Havermann | 11/2020 |
2697 | (10^146063+71)/9 | 146063 | Serge Batalov | 07/2015 |
2698 | 2*10^146051-63 | 146052 | Robert Price | 01/2022 |
2699 | (2^485119+7)/2745 | 146032 | Lelio R Paula | 09/2015 |
2700 | (22*10^146029+257)/9 | 146030 | Robert Price | 06/2018 |
2701 | 7*10^145982-53 | 145983 | Robert Price | 06/2020 |
2702 | 2^484743+1872923 | 145923 | Enzo Doria | 05/2016 |
2703 | 33140^25287+25287^33140 | 145913 | Hans Havermann | 01/2021 |
2704 | 37875^7112+7112^37875 | 145895 | Hans Havermann | 01/2021 |
2705 | 32862^27473+27473^32862 | 145872 | Hans Havermann | 01/2021 |
2706 | 32836^27587+27587^32836 | 145815 | Hans Havermann | 01/2021 |
2707 | 2^484341+1879157 | 145802 | Enzo Doria | 08/2016 |
2708 | 2*10^145784-91 | 145785 | Robert Price | 04/2020 |
2709 | 2^484271-51 | 145781 | Lelio R Paula | 11/2017 |
2710 | (188*10^145750-11)/3 | 145752 | Robert Price | 02/2022 |
2711 | 70^78989-69^78989 | 145743 | Robert Price | 01/2014 |
2712 | 51^85334+2 | 145714 | Robert Price | 07/2015 |
2713 | 2^483886-1857101 | 145665 | Enzo Doria | 10/2015 |
2714 | 33350^23307+23307^33350 | 145656 | Hans Havermann | 01/2021 |
2715 | (19*10^145585+131)/3 | 145586 | Robert Price | 06/2020 |
2716 | 2^483563-1863457 | 145567 | Enzo Doria | 12/2015 |
2717 | 4*10^145563-69 | 145564 | Robert Price | 01/2022 |
2718 | 2^483516-1861409 | 145553 | Enzo Doria | 11/2015 |
2719 | 2^483384-115019 | 145514 | Enzo Doria | 06/2015 |
2720 | (259*10^145501-1)/3 | 145503 | Robert Price | 12/2020 |
2721 | (19*10^145499-61)/3 | 145500 | Robert Price | 05/2019 |
2722 | 2^483302-3221 | 145489 | Lelio R Paula | 12/2012 |
2723 | (23*10^145463+61)/3 | 145464 | Robert Price | 01/2022 |
2724 | 35523^12434+12434^35523 | 145453 | Hans Havermann | 01/2021 |
2725 | 2^483046+1874029 | 145412 | Enzo Doria | 06/2016 |
2726 | 2^482991-2789317 | 145395 | Enzo Doria | 12/2015 |
2727 | 2^482978-2789711 | 145391 | Enzo Doria | 12/2015 |
2728 | 2^482966-2789711 | 145388 | Enzo Doria | 12/2015 |
2729 | 2^482817-1858843 | 145343 | Enzo Doria | 10/2015 |
2730 | 2^482751-113635 | 145323 | Enzo Doria | 08/2014 |
2731 | 2^482705-459763 | 145309 | Enzo Doria | 05/2015 |
2732 | (4^241306+11)/3 | 145281 | Robert Price | 03/2017 |
2733 | (238*10^145276-1)/3 | 145278 | Robert Price | 04/2020 |
2734 | (19*2^482534+1)/7 | 145258 | Lelio R Paula | 09/2015 |
2735 | 53^84239-52^84239 | 145252 | Robert Price | 01/2013 |
2736 | 47952^1067+1067^47952 | 145207 | Hans Havermann | 01/2021 |
2737 | (2^482333+5)/9287 | 145193 | Lelio R Paula | 09/2015 |
2738 | 2^482087+72623 | 145123 | Enzo Doria | 04/2016 |
2739 | 2^482016-286565 | 145102 | Enzo Doria | 07/2015 |
2740 | (19*10^145093+101)/3 | 145094 | Robert Price | 09/2019 |
2741 | 2^481956+121 | 145084 | Stefano Morozzi | 04/2021 |
2742 | 2^481840+15 | 145049 | Robert Price | 09/2015 |
2743 | 2^481801-481801 | 145037 | Henri Lifchitz | 03/2005 |
2744 | 2^481775+1869083 | 145029 | Enzo Doria | 05/2016 |
2745 | 29^99167+2 | 145022 | Ray Chandler | 08/2011 |
2746 | 2^481663+1875653 | 144996 | Enzo Doria | 07/2016 |
2747 | 8*10^144977+27 | 144978 | Robert Price | 09/2021 |
2748 | 36486^9379+9379^36486 | 144929 | Hans Havermann | 12/2020 |
2749 | 35111^13378+13378^35111 | 144882 | Hans Havermann | 01/2021 |
2750 | 2^481149-459073 | 144841 | Enzo Doria | 05/2015 |