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	2*10^193981-43	193982	Robert Price	04/2018
2502	2^644382+75169	193979	Enzo Doria	04/2016
2503	2^644304-1861409	193955	Enzo Doria	11/2015
2504	(29*10^193950-23)/3	193951	Robert Price	03/2022
2505	5*10^193907-9	193908	Robert Price	05/2015
2506	2^644043+1876703	193877	Enzo Doria	07/2016
2507	2*10^193841-63	193842	Robert Price	01/2022
2508	2^643735+1879733	193784	Enzo Doria	09/2016
2509	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
2510	9*10^193712+71	193713	Robert Price	08/2020
2511	2^643216-286565	193628	Enzo Doria	07/2015
2512	2^643204+215011	193624	Enzo Doria	11/2023
2513	10^193566+1126339	193567	Patrick De Geest	09/2022
2515	10^193566-10000000001	193566	Robert Price	04/2021
2514	10^193566-454041	193566	Patrick De Geest	08/2021
2517	2^642888-24965	193529	Enzo Doria	09/2013
2516	2^642889+25367	193529	Enzo Doria	11/2023
2518	2^642448-114825	193397	Enzo Doria	05/2015
2519	2^642437-1856623	193393	Enzo Doria	10/2015
2520	2^642039-59797	193273	Enzo Doria	11/2015
2521	2^641987+39	193258	Jon Grantham	08/2023
2522	10^193230+513861	193231	Patrick De Geest	07/2018
2523	10^193230-8001	193230	Robert Price	03/2018
2524	(62*10^193225-233)/9	193226	Robert Price	02/2022
2525	2^641692-286349	193169	Enzo Doria	07/2015
2526	2^641690-24737	193168	Enzo Doria	09/2013
2527	22268^44421+44421^22268	193129	Norbert Schneider	06/2023
2528	2^641514+1876549	193115	Enzo Doria	07/2016
2529	2^640888-2785619	192927	Enzo Doria	10/2015
2530	2^640874-2783741	192923	Enzo Doria	09/2015
2531	10^192922+192207	192923	Patrick De Geest	08/2021
2532	10^192922-7001	192922	Robert Price	04/2021
2533	2^640854+25	192917	Stefano Morozzi	05/2021
2534	34*10^192868-9	192870	Robert Price	06/2020
2535	(46*10^192841+683)/9	192842	Robert Price	03/2019
2536	2^640181+467	192714	Lelio R Paula	08/2013
2537	2^640072+27541	192681	Enzo Doria	01/2024
2538	2^639536-1850249	192520	Enzo Doria	08/2015
2539	40714<>40712<>...<>1086421357911<>...<>40711<>40713	192464	Hans Havermann	12/2019
2540	5*10^192422-43	192423	Robert Price	01/2019
2541	2^639110-2792441	192392	Enzo Doria	02/2016
2542	(241^80761-1)/240	192372	Anonymous	04/2024
2543	2^638955-29827	192345	Enzo Doria	08/2015
2544	15^163539+14	192337	Alfred Reich	10/2023
2545	2^638713-2784223	192272	Enzo Doria	10/2015
2546	(10^192216+7)/149	192214	Alfred Reich	07/2021
2547	2^638490-113507	192205	Enzo Doria	08/2014
2548	2^638189-39943	192115	Enzo Doria	09/2015
2549	2^638110+1877119	192091	Enzo Doria	07/2016
2550	MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)+82440	192083	Sergey Batalov	05/2024
2551	MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)	192083	Sergey Batalov	05/2024
2552	2^638066-2785211	192078	Enzo Doria	10/2015
2553	(35*10^191973-341)/9	191974	Robert Price	08/2021
2554	(112*10^191900+17)/3	191902	Robert Price	03/2020
2555	2^637475-115309	191900	Enzo Doria	07/2015
2556	(68*10^191754-113)/9	191755	Robert Price	03/2021
2557	2^636930-11	191736	Stefano Morozzi	07/2022
2558	(47*10^191732+259)/9	191733	Robert Price	03/2022
2559	41459^41522-41522^41459	191733	Norbert Schneider	04/2025
2560	2^636661+1876577	191655	Enzo Doria	07/2016
2561	(9^200807-2^200807)/7	191618	Jon Grantham	07/2023
2562	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
2563	fibonacci(916540)-2	191546	Jon Grantham	08/2023
2564	2^636177-1855123	191509	Enzo Doria	09/2015
2565	2^636158-113627	191503	Enzo Doria	08/2014
2566	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
2567	2^636035+79823	191466	Enzo Doria	06/2016
2568	2^636011-1860847	191459	Enzo Doria	11/2015
2569	2^635926-1860611	191433	Enzo Doria	11/2015
2570	3*2^635755+5	191382	Jon Grantham	07/2023
2571	3*10^191152-7	191153	Robert Price	08/2015
2572	2^634883-1865677	191119	Enzo Doria	02/2016
2573	2^634801+1871957	191095	Enzo Doria	05/2016
2574	(77*10^191080+157)/9	191081	Robert Price	05/2022
2575	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
2576	9*10^191018-41	191019	Robert Price	08/2020
2577	2^634470-59861	190995	Enzo Doria	11/2015
2578	2^634368-29519	190964	Enzo Doria	08/2015
2579	(19*10^190935+11)/3	190936	Robert Price	07/2023
2580	2^634188-350609	190910	Enzo Doria	06/2015
2581	(65*10^190899+493)/9	190900	Robert Price	08/2021
2582	(62*10^190795-413)/9	190796	Robert Price	09/2021
2583	(26*10^190789-131)/3	190790	Robert Price	10/2019
2584	(13*10^190732-61)/3	190733	Robert Price	11/2018
2585	3*2^633524+5	190711	Jon Grantham	07/2023
2586	(7*10^190683+143)/3	190684	Robert Price	03/2018
2587	2^633088-113879	190579	Enzo Doria	10/2014
2588	2^633064+1874911	190572	Enzo Doria	06/2016
2589	5*3^399402+2^399402	190564	Jon Grantham	08/2023
2590	(43*10^190547+83)/9	190548	Robert Price	11/2018
2591	99*10^190543+7	190545	Robert Price	05/2021
2592	(299*10^190533+1)/3	190535	Robert Price	04/2020
2593	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
2594	2^632815-15	190497	Stefano Morozzi	07/2022
2595	2^632795-351205	190491	Enzo Doria	06/2015
2596	41171^41272+41272^41171	190454	Norbert Schneider	05/2023
2597	(16*10^190420-19)/3	190421	Robert Price	02/2019
2598	(43*10^190351+101)/9	190352	Robert Price	11/2018
2599	2^632156+78391	190298	Enzo Doria	06/2016
2600	97*10^190295-3	190297	Robert Price	05/2020
2601	2^632082-1851971	190276	Enzo Doria	08/2015
2602	2^632020+1880311	190257	Enzo Doria	09/2016
2603	(5*10^190242-77)/9	190242	Robert Price	04/2021
2604	7*10^190210+13	190211	Robert Price	03/2021
2605	2^631637-462373	190142	Enzo Doria	08/2015
2606	2*10^190126-21	190127	Robert Price	09/2020
2607	(28*10^190105+191)/3	190106	Robert Price	02/2020
2608	2*10^190093+33	190094	Robert Price	11/2021
2609	(68*10^190053-113)/9	190054	Robert Price	03/2021
2610	2^631183+213413	190006	Enzo Doria	09/2023
2611	2^631122-39251	189987	Enzo Doria	08/2015
2612	(26*10^189928-89)/9	189929	Robert Price	06/2018
2613	2^630839-97	189902	Yves Minet	07/2017
2614	99*10^189876-7	189878	Robert Price	07/2020
2615	41147^41147+30^30	189867	Henri Lifchitz	09/2024
2616	2^630359+1788953	189757	Enzo Doria	05/2016
2617	2^630228+1871971	189718	Enzo Doria	05/2016
2618	2^630108+781	189682	Lelio R Paula	08/2013
2619	2^629870-1867811	189610	Enzo Doria	04/2016
2620	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
2621	2^629326+2792929	189447	Enzo Doria	02/2016
2622	4*10^189401+13	189402	Robert Price	02/2021
2623	(10^189385-61)/3	189385	Serge Batalov	12/2014
2624	2^629036+1874011	189359	Enzo Doria	06/2016
2625	2^628930+80779	189327	Enzo Doria	07/2016
2626	(134*10^189309-11)/3	189311	Robert Price	01/2022
2627	9*10^189306-11	189307	Mischa Rodermond	04/2023
2628	3^396740-396740^3	189294	Henri Lifchitz	07/2024
2629	2^628582+1179439	189223	Enzo Doria	06/2016
2630	(44*10^188999-503)/9	189000	Robert Price	12/2018
2631	(16*10^188823+167)/3	188824	Robert Price	06/2019
2632	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
2633	2^627037-2785843	188757	Enzo Doria	10/2015
2634	(10^188566+7)/311640753181661	188552	Alfred Reich	04/2022
2635	(16*10^188457+161)/3	188458	Robert Price	02/2019
2636	L(901657)	188436	Renaud Lifchitz	11/2008
2637	(19*10^188375+137)/3	188376	Robert Price	03/2022
2638	2^625651+74213	188340	Enzo Doria	04/2016
2639	2^625584-460919	188320	Enzo Doria	06/2015
2640	(8*10^188308-71)/9	188308	Serge Batalov	11/2022
2641	5^269399-3^269399-1	188302	Jon Grantham	08/2023
2642	(14*10^188218+139)/9	188219	Robert Price	11/2021
2643	40760^40821-40821^40760	188195	Norbert Schneider	07/2024
2644	(10^188164+359)/9	188164	Serge Batalov	12/2014
2645	2^624481-113611	187988	Enzo Doria	08/2014
2646	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
2647	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
2648	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
2649	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
2650	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
2651	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
2653	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
2652	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
2654	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
2655	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
2656	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
2657	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
2658	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
2660	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
2659	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
2661	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
2662	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
2663	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
2664	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
2665	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
2666	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
2667	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
2669	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
2668	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
2670	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
2671	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
2672	2^624077-112723	187866	Enzo Doria	07/2014
2673	2^624008+1874941	187846	Enzo Doria	06/2016
2674	2^623870+78679	187804	Enzo Doria	05/2016
2675	2^623714-114035	187757	Enzo Doria	11/2014
2676	2^623651-1834251	187738	Enzo Doria	07/2015
2677	(7*10^187645+53)/3	187646	Robert Price	05/2018
2678	21650^43269+43269^21650	187591	Norbert Schneider	02/2023
2679	2^623146+1879609	187586	Enzo Doria	09/2016
2680	(401*10^187512+13)/9	187514	Robert Price	09/2021
2681	(5*10^187471+91)/3	187472	Robert Price	04/2018
2682	2^622500+81931	187392	Enzo Doria	08/2016
2683	(13*10^187382-157)/9	187383	Robert Price	05/2021
2684	2^622300-1861739	187331	Enzo Doria	12/2015
2685	(22*10^187317-91)/3	187318	Robert Price	02/2022
2686	(38*10^187281+349)/9	187282	Robert Price	10/2018
2687	2^622052+76771	187257	Enzo Doria	05/2016
2688	2^622005-24091	187243	Enzo Doria	08/2013
2689	7*10^187205-57	187206	Robert Price	06/2020
2690	2^621879-351787	187205	Enzo Doria	07/2015
2691	(5*10^187168-53)/3	187169	Robert Price	09/2020
2692	(23*10^187164-143)/3	187165	Robert Price	12/2019
2693	2^621700+79411	187151	Enzo Doria	06/2016
2694	2^621597+39	187120	Jon Grantham	08/2023
2695	(7*10^187101+131)/3	187102	Robert Price	06/2020
2696	(2*10^187062-71)/3	187062	Robert Price	12/2017
2697	V(1118570)	187013	Serge Batalov	07/2024
2698	2^620929-113203	186919	Enzo Doria	07/2014
2699	10^186842+168223	186843	Patrick De Geest	07/2018
2700	10^186842-8001	186842	Robert Price	03/2018
2701	V(1117640)/13411681/26823361/575709775681/989889277441	186814	Serge Batalov	07/2024
2702	2^620347-1777	186744	Lelio R Paula	07/2013
2703	(11*10^186659+133)/9	186660	Robert Price	04/2022
2704	11^179143-4170	186559	Enzo Doria	12/2012
2705	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
2706	2*10^186517+33	186518	Robert Price	11/2021
2707	2^619297-2792353	186427	Enzo Doria	02/2016
2708	(49*10^186409+383)/9	186410	Robert Price	04/2019
2709	2^618940-460139	186320	Enzo Doria	06/2015
2710	2^618046+74179	186051	Enzo Doria	04/2016
2711	3*10^186019+11	186020	Robert Price	07/2018
2712	(16*10^185978-19)/3	185979	Robert Price	02/2019
2713	(22*10^185950-7)/3	185951	Robert Price	12/2022
2714	2*10^185930-3	185931	Robert Price	07/2015
2715	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
2716	4*10^185905+91	185906	Robert Price	08/2018
2717	(34*10^185902-601)/9	185903	Robert Price	07/2022
2718	(19*10^185873+131)/3	185874	Robert Price	06/2020
2719	(37*10^185811+377)/9	185812	Robert Price	11/2018
2720	2^617250+9385	185811	Lelio R Paula	07/2013
2721	2^617130+9	185775	Stefano Morozzi	05/2021
2722	39^116749+2	185756	Robert Price	04/2015
2723	2^616924-39719	185713	Enzo Doria	09/2015
2724	2^616712+1867621	185649	Enzo Doria	04/2016
2725	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
2726	8*10^185529-67	185530	Robert Price	08/2019
2727	(5*10^185520-11)/3	185521	Tyler Busby	02/2023
2728	5*2^616124+3	185473	Jon Grantham	07/2023
2729	2^615916+26791	185410	Enzo Doria	12/2023
2730	4*10^185355+9	185356	Robert Price	05/2015
2731	(16*10^185347+89)/3	185348	Robert Price	03/2021
2732	40247^40247-56^56	185327	Henri Lifchitz	08/2024
2733	2^615622+76639	185321	Enzo Doria	05/2016
2734	2^615591+1879223	185312	Enzo Doria	08/2016
2735	2^615587+217013	185311	Enzo Doria	12/2023
2736	2^615503+1876643	185285	Enzo Doria	07/2016
2737	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
2738	(4*10^185221-91)/3	185222	Robert Price	03/2018
2739	(7*10^185221+131)/3	185222	Robert Price	06/2020
2740	(62*10^185216-413)/9	185217	Robert Price	09/2021
2741	(232*10^185180+17)/3	185182	Robert Price	04/2021
2742	56*10^185139-3	185141	Robert Price	03/2020
2743	(28*10^185105+47)/3	185106	Robert Price	02/2021
2744	2^614783-2790097	185069	Enzo Doria	12/2015
2745	2^614745-29323	185057	Enzo Doria	07/2015
2746	(((((((((((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
2747	(49*10^184993-67)/9	184994	Robert Price	03/2019
2748	(5*10^184954-191)/3	184955	Robert Price	05/2021
2749	(14*10^184950+211)/9	184951	Robert Price	04/2018
2750	2^614360+215221	184941	Enzo Doria	11/2023

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