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	33193^11370+11370^33193	134623	Hans Havermann	12/2020
2502	30736^23979+23979^30736	134619	Hans Havermann	11/2020
2503	2^447094-113193	134589	Enzo Doria	07/2014
2504	3^282041-9934	134568	Enzo Doria	05/2014
2505	2^447019-109039	134567	Enzo Doria	04/2014
2506	31376^19437+19437^31376	134561	Hans Havermann	12/2020
2507	2^446990-22041	134558	Enzo Doria	07/2013
2508	123^64370+122	134528	Karsten Bonath	04/2018
2509	30100^29461+29461^30100	134525	Hans Havermann	11/2020
2510	31251^20158+20158^31251	134519	Hans Havermann	11/2020
2511	2^446782-39701	134495	Enzo Doria	09/2015
2512	31817^16858+16858^31817	134485	Hans Havermann	12/2020
2513	32448^13937+13937^32448	134471	Hans Havermann	12/2020
2514	2^446494-16485	134409	Enzo Doria	04/2013
2515	30042^29785+29785^30042	134408	Hans Havermann	12/2020
2516	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
2517	2^446441+65	134393	Lelio R Paula	08/2017
2518	(10^134385+719)/9	134385	Serge Batalov	12/2014
2519	30043^29688+29688^30043	134370	Hans Havermann	12/2020
2520	(2*10^134364+529)/9	134364	Robert Price	01/2018
2521	34657^7512+7512^34657	134323	Hans Havermann	11/2020
2522	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
2523	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
2524	42035^1564+1564^42035	134270	Hans Havermann	12/2020
2526	(2^446022-7)/339	134264	Lelio R Paula	07/2015
2525	30621^24248+24248^30621	134264	Hans Havermann	12/2020
2527	30341^26562+26562^30341	134237	Hans Havermann	11/2020
2528	10^134209-80000001	134209	Robert Price	04/2021
2529	29976^29953+29953^29976	134186	Hans Havermann	12/2020
2530	35038^6755+6755^35038	134183	Hans Havermann	12/2020
2531	63^74568+2	134174	Lelio R Paula	06/2017
2532	2^445671-22071	134161	Enzo Doria	07/2013
2533	532^49205+49205^532	134129	Norbert Schneider	02/2019
2534	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
2535	2^445515-113859	134114	Enzo Doria	10/2014
2536	(22*10^134111-37)/3	134112	Robert Price	04/2019
2537	31622^17379+17379^31622	134079	Hans Havermann	04/2021
2538	2^445328-216917	134058	Enzo Doria	05/2014
2539	2^445202+1874899	134020	Enzo Doria	06/2016
2540	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
2541	(35*10^133979-593)/9	133980	Robert Price	07/2018
2542	2*10^133955+51	133956	Robert Price	05/2018
2543	2^444964-113639	133948	Enzo Doria	08/2014
2545	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
2544	10^133902-100001	133902	Robert Price	07/2020
2546	2^444784-113859	133894	Enzo Doria	10/2014
2547	34942^6721+6721^34942	133739	Hans Havermann	04/2021
2548	34792^6935+6935^34792	133638	Hans Havermann	04/2021
2549	(266*10^133603+1)/3	133605	Robert Price	04/2020
2550	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
2551	62^74521-61^74521	133571	Robert Price	05/2013
2552	(182*10^133543+1)/3	133545	Robert Price	02/2020
2553	(103*10^133535+11)/3	133537	Robert Price	01/2021
2554	32589^12520+12520^32589	133537	Hans Havermann	03/2021
2555	30135^26882+26882^30135	133482	Hans Havermann	04/2021
2556	2^443198-1867301	133416	Enzo Doria	03/2016
2557	(19*10^133390+101)/3	133391	Robert Price	09/2019
2558	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
2559	2^442799+1874633	133296	Enzo Doria	06/2016
2560	L(637751)	133283	Henri Lifchitz	09/2008
2561	109^65410-2	133269	Lelio R Paula	10/2017
2562	2^442688-113489	133263	Enzo Doria	08/2014
2563	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
2564	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
2565	2^442437-1849993	133187	Enzo Doria	08/2015
2566	2^442430-2791721	133185	Enzo Doria	03/2016
2567	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
2568	29959^27870+27870^29959	133172	Hans Havermann	03/2021
2569	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
2570	34240^7737+7737^34240	133145	Hans Havermann	03/2021
2571	452^50145+50145^452	133142	Norbert Schneider	09/2020
2572	30659^21796+21796^30659	133011	Hans Havermann	04/2021
2573	33276^9935+9935^33276	133010	Hans Havermann	04/2021
2574	30111^26122+26122^30111	133001	Hans Havermann	04/2021
2575	30790^20869+20869^30790	132998	Hans Havermann	04/2021
2576	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
2577	2^441781-2787883	132990	Enzo Doria	03/2016
2578	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
2579	2^441618+37	132941	Lelio R Paula	08/2017
2580	35571^5452+5452^35571	132914	Hans Havermann	04/2021
2581	2^441521-113575	132912	Enzo Doria	08/2014
2582	7*10^132884-99	132885	Robert Price	06/2019
2583	(103*10^132879+17)/3	132881	Robert Price	08/2020
2584	2^441396-65	132874	Lelio R Paula	08/2017
2585	2^441330+1871959	132854	Enzo Doria	05/2016
2586	2^441063+383	132774	Lelio R Paula	06/2012
2587	(22*10^132746+53)/3	132747	Robert Price	07/2019
2588	2^440846+1870909	132708	Enzo Doria	05/2016
2589	2^440656-113489	132651	Enzo Doria	08/2014
2590	numbpart(14180123587)	132646	Serge Batalov	04/2017
2591	32950^10591+10591^32950	132622	Hans Havermann	04/2021
2592	33302^9597+9597^33302	132614	Hans Havermann	04/2021
2593	(19*10^132550+191)/3	132551	Robert Price	05/2019
2594	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
2595	(38^83891+1)/39	132529	Robert Price	09/2013
2596	2*10^132493-43	132494	Robert Price	04/2018
2597	(418*10^132441+23)/9	132443	Robert Price	02/2020
2598	2^439931-21	132433	Lelio R Paula	08/2017
2599	47^79201-46^79201	132432	Robert Price	10/2012
2600	2^439897-113653	132423	Enzo Doria	08/2014
2601	35505^5362+5362^35505	132410	Hans Havermann	03/2021
2602	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
2603	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
2604	2^439576-113247	132326	Enzo Doria	07/2014
2605	2^439497-29143	132302	Enzo Doria	07/2015
2606	2^439409-114193	132276	Enzo Doria	12/2014
2607	(44*10^132233-233)/9	132234	Robert Price	01/2019
2608	9*10^132148-7	132149	Robert Price	09/2015
2609	(47*10^132125-119)/9	132126	Robert Price	05/2019
2610	2^438845+1870217	132106	Enzo Doria	05/2016
2611	2^438789+87855	132089	Lelio R Paula	01/2016
2612	2^438774-2786411	132085	Enzo Doria	03/2016
2613	2^438755-1848205	132079	Enzo Doria	07/2015
2614	2^438739-112087	132074	Enzo Doria	06/2014
2615	35872^4777+4777^35872	131979	Hans Havermann	04/2021
2616	31198^16945+16945^31198	131938	Hans Havermann	03/2021
2617	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
2618	L(631181)	131910	Henri Lifchitz	09/2008
2619	(47*10^131886-119)/9	131887	Robert Price	05/2019
2620	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
2621	2^438079-1863877	131875	Enzo Doria	03/2016
2622	(2^438067+5)/329	131869	Lelio R Paula	06/2015
2623	2^437908-113855	131824	Enzo Doria	09/2014
2624	2^437884-286349	131817	Enzo Doria	07/2015
2625	(11*10^131784-17)/3	131785	Robert Price	06/2018
2626	4*10^131719-93	131720	Robert Price	07/2020
2627	3^276062-112292	131716	Enzo Doria	07/2014
2628	(7*10^131682+89)/3	131683	Robert Price	08/2020
2629	29512^28969+28969^29512	131681	Hans Havermann	03/2021
2630	2^437343+75953	131654	Enzo Doria	04/2016
2631	35^85243-34^85243	131621	Robert Price	05/2012
2632	(59*10^131575+391)/9	131576	Robert Price	03/2021
2633	39984^1945+1945^39984	131505	Hans Havermann	03/2021
2634	(203*10^131457+1)/3	131459	Robert Price	03/2020
2635	87309^32+32^87309	131414	Hans Havermann	03/2021
2636	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
2637	2^436451+1884713	131385	Enzo Doria	03/2017
2638	2^436365+35	131359	Robert Price	11/2015
2640	2^436300+1866871	131340	Enzo Doria	03/2016
2639	(7*10^131339+179)/3	131340	Robert Price	09/2018
2641	14^114592-3	131338	Paul Bourdelais	12/2020
2642	(37*10^131270+341)/9	131271	Robert Price	08/2018
2643	29863^24790+24790^29863	131227	Hans Havermann	03/2021
2644	(5*10^131223-29)/3	131224	Robert Price	03/2018
2645	29524^27825+27825^29524	131218	Hans Havermann	03/2021
2646	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
2647	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
2649	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
2648	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
2651	2^435773+1875557	131181	Enzo Doria	06/2016
2652	(16*10^131180+167)/3	131181	Robert Price	06/2019
2650	(26*10^131180-77)/3	131181	Robert Price	11/2019
2653	(25*10^131144-7)/9	131145	Robert Price	05/2018
2654	2^435612-2789939	131133	Enzo Doria	12/2015
2655	33976^7231+7231^33976	131121	Hans Havermann	03/2021
2656	33715^7746+7746^33715	131121	Hans Havermann	03/2021
2657	66^72047-65^72047	131093	Robert Price	09/2013
2658	(5*10^131090+37)/3	131091	Robert Price	03/2018
2659	2^435468+75631	131089	Enzo Doria	04/2016
2660	37^83588-2	131083	Lelio R Paula	08/2015
2661	(4^217720+11)/3	131081	Robert Price	02/2017
2662	30407^20448+20448^30407	131074	Hans Havermann	04/2021
2663	29487^27836+27836^29487	131059	Hans Havermann	04/2021
2664	29962^23615+23615^29962	131030	Hans Havermann	03/2021
2665	2^435202-113193	131009	Enzo Doria	07/2014
2666	9*10^130998-19	130999	Robert Price	07/2019
2667	36243^4108+4108^36243	130969	Hans Havermann	04/2021
2668	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
2669	2^434835-111937	130899	Enzo Doria	05/2014
2670	2^434685+72257	130854	Enzo Doria	04/2016
2671	(7*10^130825+113)/3	130826	Robert Price	02/2018
2672	2^434539-29317	130810	Enzo Doria	07/2015
2673	2^434469-114259	130789	Enzo Doria	01/2015
2674	2^434246+33	130722	Robert Price	11/2015
2675	30156^21599+21599^30156	130710	Hans Havermann	04/2021
2676	(17*10^130695-161)/9	130695	Robert Price	02/2021
2677	30513^19148+19148^30513	130661	Hans Havermann	03/2021
2678	9*10^130638+41	130639	Robert Price	08/2020
2679	2^433911-91	130621	Lelio R Paula	06/2017
2680	30786^17449+17449^30786	130588	Hans Havermann	03/2021
2681	2^433744-114419	130570	Enzo Doria	02/2015
2683	2^433708+1869451	130560	Enzo Doria	05/2016
2682	2^433710+93	130560	Lelio R Paula	06/2017
2684	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
2685	3^273521+10	130503	Tyler NeSmith	01/2021
2686	41659^1356+1356^41659	130487	Hans Havermann	03/2021
2687	4*10^130480+9	130481	Robert Price	05/2015
2688	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
2689	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
2690	33481^7848+7848^33481	130401	Hans Havermann	03/2021
2691	2^433023-113497	130353	Enzo Doria	08/2014
2692	31175^15178+15178^31175	130350	Hans Havermann	04/2021
2693	2^433002+1179379	130347	Enzo Doria	06/2016
2694	2^432974+19	130339	Robert Price	08/2015
2695	31903^12168+12168^31903	130331	Hans Havermann	04/2021
2696	29577^25370+25370^29577	130267	Hans Havermann	04/2021
2697	31738^12685+12685^31738	130231	Hans Havermann	03/2021
2698	29489^25956+25956^29489	130172	Hans Havermann	04/2021
2699	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
2700	2^432217+41	130111	Lelio R Paula	06/2017
2701	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
2702	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
2703	97^65480-2	130094	Lelio R Paula	05/2017
2704	36007^4102+4102^36007	130094	Hans Havermann	04/2021
2705	4*10^130088-89	130089	Robert Price	11/2018
2706	2^432117-113215	130081	Enzo Doria	07/2014
2707	2^431804+72511	129986	Enzo Doria	04/2016
2708	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
2709	31385^13702+13702^31385	129833	Hans Havermann	04/2021
2710	(47*10^129789-119)/9	129790	Robert Price	05/2019
2711	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
2712	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
2713	2^430807+1869563	129686	Enzo Doria	05/2016
2714	2^430721-21429	129660	Enzo Doria	07/2013
2715	2^430415-276271	129568	Enzo Doria	07/2015
2716	37095^3104+3104^37095	129533	Hans Havermann	04/2021
2717	31132^14459+14459^31132	129514	Hans Havermann	04/2021
2718	32582^9435+9435^32582	129506	Hans Havermann	03/2021
2719	30442^17953+17953^30442	129505	Hans Havermann	03/2021
2720	(199*10^129487-7)/3	129489	Robert Price	05/2020
2721	2^430142-2791721	129486	Enzo Doria	03/2016
2722	(7*10^129472-13)/3	129473	Robert Price	07/2018
2723	(8*10^129469+79)/3	129470	Robert Price	10/2020
2724	31678^12213+12213^31678	129463	Hans Havermann	04/2021
2725	31100^14439+14439^31100	129362	Hans Havermann	04/2021
2726	2^429568-21017	129313	Enzo Doria	07/2013
2727	(11*10^129239-179)/3	129240	Robert Price	09/2018
2728	28659^28988+28988^28659	129208	Norbert Schneider	02/2021
2729	29423^24616+24616^29423	129203	Hans Havermann	03/2021
2730	2^429194-112685	129201	Enzo Doria	06/2014
2731	2^429145-2780449	129186	Enzo Doria	04/2016
2732	33577^7014+7014^33577	129136	Hans Havermann	03/2021
2733	2^428892-113453	129110	Enzo Doria	07/2014
2734	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
2735	2^428727-113959	129060	Enzo Doria	10/2014
2736	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
2737	(10^129051-31)/3	129051	Serge Batalov	12/2014
2738	(134*10^129038+7)/3	129040	Robert Price	02/2020
2739	2^428564+71161	129011	Enzo Doria	04/2016
2740	28781^28930+28930^28781	129002	Norbert Schneider	02/2021
2741	29065^27424+27424^29065	128995	Hans Havermann	04/2021
2742	2^428502-113285	128992	Enzo Doria	07/2014
2743	2^428421-21373	128968	Enzo Doria	06/2013
2744	L(616787)	128901	Henri Lifchitz	09/2008
2745	20^99055-3	128874	Paul Bourdelais	12/2020
2746	91^65772-2	128851	Lelio R Paula	05/2017
2747	2^428022+43	128848	Lelio R Paula	05/2017
2748	2^427999-459397	128841	Enzo Doria	05/2015
2749	2^427993+76847	128839	Enzo Doria	05/2016
2750	31059^14060+14060^31059	128833	Hans Havermann	03/2021

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