Henri & Renaud Lifchitz's PRP Top records

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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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	V(1118570)	187013	Serge Batalov	07/2024
2502	2^620929-113203	186919	Enzo Doria	07/2014
2503	10^186842+168223	186843	Patrick De Geest	07/2018
2504	10^186842-8001	186842	Robert Price	03/2018
2505	V(1117640)/13411681/26823361/575709775681/989889277441	186814	Serge Batalov	07/2024
2506	2^620347-1777	186744	Lelio R Paula	07/2013
2507	(11*10^186659+133)/9	186660	Robert Price	04/2022
2508	11^179143-4170	186559	Enzo Doria	12/2012
2509	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
2510	2*10^186517+33	186518	Robert Price	11/2021
2511	2^619297-2792353	186427	Enzo Doria	02/2016
2512	(49*10^186409+383)/9	186410	Robert Price	04/2019
2513	2^618940-460139	186320	Enzo Doria	06/2015
2514	2^618046+74179	186051	Enzo Doria	04/2016
2515	3*10^186019+11	186020	Robert Price	07/2018
2516	(16*10^185978-19)/3	185979	Robert Price	02/2019
2517	(22*10^185950-7)/3	185951	Robert Price	12/2022
2518	2*10^185930-3	185931	Robert Price	07/2015
2519	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
2520	4*10^185905+91	185906	Robert Price	08/2018
2521	(34*10^185902-601)/9	185903	Robert Price	07/2022
2522	(19*10^185873+131)/3	185874	Robert Price	06/2020
2523	(37*10^185811+377)/9	185812	Robert Price	11/2018
2524	2^617250+9385	185811	Lelio R Paula	07/2013
2525	2^617130+9	185775	Stefano Morozzi	05/2021
2526	39^116749+2	185756	Robert Price	04/2015
2527	2^616924-39719	185713	Enzo Doria	09/2015
2528	2^616712+1867621	185649	Enzo Doria	04/2016
2529	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
2530	8*10^185529-67	185530	Robert Price	08/2019
2531	(5*10^185520-11)/3	185521	Tyler Busby	02/2023
2532	5*2^616124+3	185473	Jon Grantham	07/2023
2533	2^615916+26791	185410	Enzo Doria	12/2023
2534	4*10^185355+9	185356	Robert Price	05/2015
2535	(16*10^185347+89)/3	185348	Robert Price	03/2021
2536	40247^40247-56^56	185327	Henri Lifchitz	08/2024
2537	2^615622+76639	185321	Enzo Doria	05/2016
2538	2^615591+1879223	185312	Enzo Doria	08/2016
2539	2^615587+217013	185311	Enzo Doria	12/2023
2540	2^615503+1876643	185285	Enzo Doria	07/2016
2541	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
2542	(4*10^185221-91)/3	185222	Robert Price	03/2018
2543	(7*10^185221+131)/3	185222	Robert Price	06/2020
2544	(62*10^185216-413)/9	185217	Robert Price	09/2021
2545	(232*10^185180+17)/3	185182	Robert Price	04/2021
2546	56*10^185139-3	185141	Robert Price	03/2020
2547	(28*10^185105+47)/3	185106	Robert Price	02/2021
2548	2^614783-2790097	185069	Enzo Doria	12/2015
2549	2^614745-29323	185057	Enzo Doria	07/2015
2550	(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840	185052	Serge Batalov	07/2013
2551	(49*10^184993-67)/9	184994	Robert Price	03/2019
2552	(5*10^184954-191)/3	184955	Robert Price	05/2021
2553	(14*10^184950+211)/9	184951	Robert Price	04/2018
2554	2^614360+215221	184941	Enzo Doria	11/2023
2555	2^614315+81353	184928	Enzo Doria	08/2016
2556	2^614294-1849961	184921	Enzo Doria	08/2015
2557	2^614266+1877809	184913	Enzo Doria	08/2016
2558	(185*10^184878-11)/3	184880	Robert Price	10/2020
2559	91*10^184867-9	184869	Robert Price	06/2021
2560	39803^40170-40170^39803	184779	Norbert Schneider	05/2024
2561	(14789^44521-1)/(14789^211-1)	184770	Ryan Propper	11/2023
2562	(85*10^184768+77)/9	184769	Robert Price	07/2022
2563	2^613715-1860727	184747	Enzo Doria	11/2015
2564	(4*10^184730+89)/3	184731	Robert Price	08/2021
2565	2*10^184723+41	184724	Robert Price	05/2018
2566	(49*10^184703+293)/9	184704	Robert Price	03/2021
2567	2^613487-349987	184678	Enzo Doria	07/2015
2568	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
2569	14^161089-161089^14	184629	Serge Batalov	05/2016
2570	40008^40109-40109^40008	184588	Norbert Schneider	05/2024
2571	2^613033-114621	184542	Enzo Doria	05/2015
2572	3*2^612759+5	184460	Jon Grantham	07/2023
2573	2^612587+213413	184408	Enzo Doria	09/2023
2574	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
2575	2^612424+212341	184358	Enzo Doria	08/2023
2576	2^612341-1604809	184334	Enzo Doria	05/2015
2577	(11*10^184308-161)/3	184309	Robert Price	11/2021
2578	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
2579	(14*10^184150+37)/3	184151	Robert Price	12/2018
2580	2^611731-4837	184150	Yves Minet	08/2018
2581	3*10^184124-7	184125	Robert Price	08/2015
2582	2^611644+29371	184124	Enzo Doria	02/2024
2583	9*10^184122-11	184123	Mischa Rodermond	04/2023
2584	2^611628-24537	184119	Enzo Doria	08/2013
2585	3*10^184110+13	184111	Robert Price	07/2018
2586	(14280^44521-1)/(14280^211-1)	184097	Ryan Propper	11/2023
2587	(194*10^184093+1)/3	184095	Robert Price	01/2022
2588	2^611460+71881	184068	Enzo Doria	04/2016
2589	4*10^184004-63	184005	Robert Price	10/2018
2590	2^611111+84083	183963	Boyan Hu	05/2024
2591	2^610982-1867301	183924	Enzo Doria	03/2016
2592	(10^183917+1)/11/9952852373	183906	Alfred Reich	02/2024
2593	3*10^183872-49	183873	Robert Price	07/2018
2594	2^610597+1178897	183809	Enzo Doria	05/2016
2595	(8*10^183773-269)/9	183773	Robert Price	09/2021
2596	(65*10^183768-29)/9	183769	Robert Price	01/2021
2597	(17*10^183764+31)/3	183765	Robert Price	01/2019
2598	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
2599	2^610401+1277	183750	Lelio R Paula	07/2013
2600	2^610356-1849019	183736	Enzo Doria	08/2015
2601	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
2602	23*10^183710-7	183712	Robert Price	02/2020
2603	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
2604	(4*10^183659+149)/9	183659	Robert Price	04/2018
2605	(4*10^183657+41)/9	183657	Serge Batalov	11/2022
2606	7*10^183596+39	183597	Robert Price	01/2023
2607	2^609846-1834251	183582	Enzo Doria	07/2015
2608	10^183546+1547323	183547	Patrick De Geest	02/2021
2610	10^183546-800000001	183546	Robert Price	09/2020
2609	10^183546-584297	183546	Patrick De Geest	02/2021
2611	7*10^183511+39	183512	Robert Price	01/2023
2612	(23*10^183477-71)/3	183478	Robert Price	07/2020
2613	11^176176-240	183469	Enzo Doria	11/2012
2614	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
2615	6*10^183429+53	183430	Robert Price	05/2020
2616	(28*10^183403+191)/3	183404	Robert Price	02/2020
2617	U(1096855)	183383	Serge Batalov	07/2024
2618	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
2619	2^608965-113989	183317	Enzo Doria	10/2014
2620	A005165(43592)	183312	Serge Batalov	07/2017
2621	(61*10^183294+119)/9	183295	Robert Price	05/2019
2622	2^608814-461261	183272	Enzo Doria	06/2015
2623	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
2624	2^608541-608541^2	183190	Henri Lifchitz	02/2018
2625	2^608293+143807	183115	Enzo Doria	10/2016
2626	2^608164-462419	183076	Enzo Doria	08/2015
2627	2^607950-1862303	183012	Enzo Doria	12/2015
2628	5*3^383376+2^383376	182918	Jon Grantham	08/2023
2629	(46*10^182896+683)/9	182897	Robert Price	03/2019
2630	(2*10^182787+73)/3	182787	Robert Price	09/2020
2631	2^607101+1871987	182756	Enzo Doria	05/2016
2632	2^606869-69175	182686	Enzo Doria	11/2015
2633	8*10^182671+71	182672	Robert Price	05/2022
2634	(23*10^182666-71)/3	182667	Robert Price	07/2020
2635	3*10^182614-11	182615	Robert Price	07/2018
2636	2^606560-357	182593	Enzo Doria	05/2014
2637	66*10^182420+7	182422	Robert Price	07/2020
2638	2^605687+1866983	182330	Enzo Doria	03/2016
2639	2^605655-114445	182321	Enzo Doria	02/2015
2640	94*10^182291-3	182293	Robert Price	05/2020
2641	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
2642	(14*10^182177-221)/9	182178	Robert Price	04/2018
2643	2^605174-112751	182176	Enzo Doria	06/2014
2644	(905^61609-1)/904	182154	Anonymous	05/2024
2645	2^604761+1874507	182052	Enzo Doria	06/2016
2646	2^604705+1871957	182035	Enzo Doria	05/2016
2647	(14*10^182000+229)/9	182001	Robert Price	03/2018
2648	(10^181996+41)/3	181996	Robert Price	12/2017
2649	(17*10^181979+91)/9	181980	Robert Price	02/2022
2650	(10^181960+3)/7	181960	Jinyuan Wang	11/2024
2651	(5*10^181950-101)/3	181951	Robert Price	04/2018
2652	2^603915+75233	181797	Enzo Doria	04/2016
2653	39470^39537+39537^39470	181723	Norbert Schneider	12/2022
2654	(10^181710+7)/563747/2019847	181698	Alfred Reich	08/2021
2655	7*10^181594-57	181595	Robert Price	06/2020
2656	8*10^181580+29	181581	Robert Price	11/2021
2657	(83*10^181544+61)/9	181545	Serge Batalov	01/2023
2658	(2*10^181457+7)/9	181457	Rytis Slatkevicius	01/2023
2659	3*10^181445+23	181446	Robert Price	03/2022
2660	(194*10^181369-11)/3	181371	Robert Price	09/2020
2661	11^174145-360	181354	Enzo Doria	10/2012
2662	2^602351-396765	181326	Enzo Doria	08/2013
2663	6*10^181306+17	181307	Robert Price	04/2019
2664	(353^71143-1)/352	181254	Anonymous	04/2024
2665	(286*10^181220-1)/3	181222	Robert Price	11/2020
2666	2^601957-113833	181208	Enzo Doria	09/2014
2667	66^99581-65^99581	181193	Robert Price	09/2013
2668	10^181182+383973	181183	Patrick De Geest	04/2016
2669	10^181182-21	181182	Serge Batalov	12/2014
2670	(797*10^181171-41)/9	181173	Robert Price	04/2022
2671	2^601722+74209	181137	Enzo Doria	08/2023
2672	(5*10^181127-29)/3	181128	Robert Price	03/2018
2673	2^601521-29143	181076	Enzo Doria	07/2015
2674	2^601442-2797811	181053	Enzo Doria	04/2016
2675	44*10^181029+3	181031	Robert Price	04/2020
2676	5*10^180992-9	180993	Robert Price	05/2015
2677	10^180979+79477	180980	Patrick De Geest	04/2016
2678	10^180979+107739	180980	Patrick De Geest	04/2016
2679	10^180979-11	180979	Serge Batalov	12/2014
2680	2^601023-113851	180926	Enzo Doria	10/2014
2681	(23*10^180862-143)/3	180863	Robert Price	12/2019
2682	3*10^180852+29	180853	Robert Price	05/2018
2683	(277*10^180782-7)/9	180784	Robert Price	02/2022
2684	2^600412+29851	180743	Enzo Doria	03/2024
2685	(8*10^180725-629)/9	180725	Robert Price	01/2022
2686	(79*10^180710-1)/3	180712	Robert Price	02/2020
2687	2^600300-1852559	180709	Enzo Doria	08/2015
2688	(2*10^180706-77)/3	180706	Robert Price	02/2021
2689	(156^82393-1)/155	180696	Anonymous	06/2024
2690	(10^180689+71)/9	180689	Serge Batalov	07/2015
2691	2^600209+76487	180681	Enzo Doria	05/2016
2692	2^599999+378461	180618	Norman Luhn	09/2023
2693	(8*10^180536-269)/9	180536	Robert Price	09/2021
2694	2^599702-369885	180529	Enzo Doria	11/2013
2695	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
2696	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
2697	(29*10^180432-17)/3	180433	Robert Price	09/2019
2698	4*10^180360+93	180361	Robert Price	08/2018
2699	2^599035+219323	180328	Enzo Doria	03/2024
2700	2^598942+80779	180300	Enzo Doria	07/2016
2701	(38*10^180296+403)/9	180297	Robert Price	10/2018
2702	(85*10^180241+77)/9	180242	Robert Price	07/2022
2703	2^598591-1844797	180194	Enzo Doria	06/2015
2704	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
2705	2^598301+28517	180107	Enzo Doria	01/2024
2706	(29*10^180072+691)/9	180073	Robert Price	08/2021
2707	(59*10^180038+157)/9	180039	Robert Price	12/2021
2708	95*10^180019-9	180021	Robert Price	01/2022
2709	6*10^179970+91	179971	Robert Price	05/2019
2710	(4*10^179963-79)/3	179964	Robert Price	02/2018
2711	(403*10^179944-43)/9	179946	Robert Price	06/2021
2712	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
2713	2^597424-1859729	179843	Enzo Doria	11/2015
2714	Phi(180683,10)	179760	Maksym Voznyy	09/2015
2715	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
2716	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
2717	(29*10^179697+223)/9	179698	Robert Price	09/2018
2718	U(1289697)	179687	Serge Batalov	07/2024
2720	2^596884+73	179680	Stefano Morozzi	04/2021
2719	(11*10^179679+13)/3	179680	Robert Price	03/2022
2721	(68*10^179656+7)/3	179658	Robert Price	01/2020
2722	(10^179643+173)/3	179643	Robert Price	05/2021
2723	2^596690-461261	179622	Enzo Doria	07/2015
2724	2^596684-113939	179620	Enzo Doria	10/2014
2725	2^596642+39	179608	Jon Grantham	08/2023
2726	2*10^179602+63	179603	Robert Price	05/2018
2727	32262^39815-39815^32262	179514	Frank Doornink	02/2024
2728	(25*10^179488-403)/9	179489	Robert Price	01/2021
2729	7*10^179460+99	179461	Robert Price	05/2021
2730	2^596127+74333	179453	Enzo Doria	07/2023
2731	3^375887-112696	179344	Enzo Doria	07/2014
2732	4*10^179265-71	179266	Robert Price	12/2018
2733	2*10^179193+83	179194	Robert Price	12/2021
2734	2^595144-1850429	179157	Enzo Doria	08/2015
2735	2^595122-5	179150	Stefano Morozzi	07/2022
2736	3*10^179138+89	179139	Robert Price	10/2018
2737	(52*10^179062-133)/9	179063	Robert Price	09/2021
2738	2^594531+82253	178972	Enzo Doria	09/2016
2739	(664*10^178939-61)/9	178941	Robert Price	09/2021
2740	2^594260-2787899	178891	Enzo Doria	11/2015
2741	(14*10^178822+67)/9	178823	Robert Price	05/2022
2742	(29*10^178732-119)/9	178733	Robert Price	12/2021
2743	2^593631+101381	178701	Jorge Menendez	04/2018
2744	10^178695+136719	178696	Patrick De Geest	05/2016
2745	10^178695-71	178695	Serge Batalov	12/2014
2746	(2*10^178649-161)/3	178649	Robert Price	12/2020
2747	(691^62903-1)/690	178609	Michael Stocker	05/2020
2748	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
2749	2^593242+28309	178584	Enzo Doria	01/2024
2750	2^593222-14145	178578	Jorge Menendez	10/2017

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Probable Primes Top 10000

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