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 (> 30000)	Who ?	When ?
2501	2*5^154948-7	108305	Lelio R Paula	11/2014
2502	10^108303+13	108304	Lelio R Paula	02/2017
2503	10^108303-207959	108303	Patrick De Geest	03/2017
2504	2^359730+753	108290	Lelio R Paula	12/2011
2505	2^359650-19797	108266	Enzo Doria	06/2013
2506	91^55259-90^55259	108255	Robert Price	07/2015
2507	3^226845+68	108233	Lelio R Paula	03/2017
2508	5^154822-12866	108216	Enzo Doria	05/2014
2509	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
2510	2^359454-177	108207	Lelio R Paula	12/2011
2511	6^139022-59	108181	Lelio R Paula	02/2017
2512	2^359352-179	108176	Lelio R Paula	12/2011
2513	2^359338-1858781	108172	Enzo Doria	04/2016
2514	12^100230-97	108167	Lelio R Paula	03/2017
2515	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
2516	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
2517	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
2518	6^138956-59	108129	Lelio R Paula	02/2017
2519	2^359184+30285	108126	Lelio R Paula	04/2017
2520	13^97059+10	108119	Lelio R Paula	03/2017
2521	2^359137-81	108112	Lelio R Paula	12/2011
2523	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
2522	2^359110-11655	108103	Lelio R Paula	04/2017
2524	8*6^138875+5	108067	Lelio R Paula	11/2014
2525	2^358987-216919	108066	Enzo Doria	05/2014
2526	39^67918-67918^39	108062	Norbert Schneider	02/2017
2527	2^358785-16933	108006	Enzo Doria	05/2013
2528	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
2529	6^138770-77	107985	Lelio R Paula	02/2017
2530	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
2531	10^107976+19	107977	Lelio R Paula	02/2017
2532	10^107976-202103	107976	Patrick De Geest	03/2017
2533	2^358684+75781	107975	Enzo Doria	04/2016
2534	99^54094+2	107952	Lelio R Paula	06/2013
2535	(2^358583-9)/391	107942	Lelio R Paula	12/2013
2536	2^358538+55	107931	Lelio R Paula	12/2011
2537	2^358517-109009	107925	Enzo Doria	03/2014
2538	3^226159+104	107906	Lelio R Paula	03/2017
2539	2^358310-11655	107863	Lelio R Paula	03/2017
2540	2^358275-112987	107852	Enzo Doria	07/2014
2541	2^358233-20005	107839	Enzo Doria	06/2013
2542	2^358194+175	107828	Lelio R Paula	12/2011
2543	107^53125-106	107812	Norbert Schneider	12/2016
2544	3^225922-2	107793	Lelio R Paula	10/2013
2545	12^99874-95	107783	Lelio R Paula	03/2017
2546	2^358030-171	107778	Lelio R Paula	12/2011
2547	11^103488-4170	107772	Enzo Doria	12/2012
2548	2^357911-20089	107742	Enzo Doria	06/2013
2549	2^357885+12857	107735	Yves Minet	07/2010
2550	7^127473+40	107728	Lelio R Paula	03/2017
2551	5*2^357850+9	107725	Lelio R Paula	09/2014
2552	2^357786-291191	107705	Enzo Doria	06/2015
2553	18^85798-23	107700	Lelio R Paula	04/2017
2554	2^357688-1854269	107675	Enzo Doria	09/2015
2555	2^357671-112225	107670	Enzo Doria	06/2014
2556	2^357618-21005	107654	Enzo Doria	06/2013
2557	2^357615-17505	107653	Enzo Doria	05/2013
2558	(30^72871-1)/29	107638	Robert Price	12/2011
2559	2^357521+1870217	107625	Enzo Doria	05/2016
2560	2^357477-1203	107612	Lelio R Paula	03/2017
2561	5^153894-18	107568	Lelio R Paula	02/2017
2562	2^357324-69059	107566	Enzo Doria	11/2015
2563	2^357283-869688105	107553	Lelio R Paula	01/2017
2564	2^357280-16805	107552	Enzo Doria	05/2013
2565	10^107547+481719	107548	Patrick De Geest	03/2017
2566	10^107547-47	107547	Lelio R Paula	02/2017
2567	17^87396-32	107537	Lelio R Paula	04/2017
2568	2^357081+107	107493	Lelio R Paula	12/2011
2569	2^357058-3911	107486	Yves Minet	04/2017
2570	3^225274+64	107484	Lelio R Paula	03/2017
2571	18^85619-95	107476	Lelio R Paula	04/2017
2572	3^225248-130	107471	Lelio R Paula	03/2017
2573	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
2574	2^356935-18085	107449	Enzo Doria	05/2013
2575	10^107409+37	107410	Lelio R Paula	02/2017
2576	10^107409-329633	107409	Patrick De Geest	03/2017
2577	2^356787-109027	107404	Enzo Doria	04/2014
2578	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
2579	5^153622-42	107378	Lelio R Paula	02/2017
2580	2^356699-97305	107378	Lelio R Paula	03/2017
2581	2^356654+85	107364	Lelio R Paula	11/2011
2582	2^356641-19921	107360	Enzo Doria	06/2013
2583	2^356623-465	107355	Lelio R Paula	03/2017
2584	19^83945-92	107345	Lelio R Paula	02/2017
2585	10^107334+28149	107335	Patrick De Geest	03/2017
2586	10^107334-83	107334	Lelio R Paula	02/2017
2587	2^356518+885	107323	Lelio R Paula	03/2017
2588	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
2589	2^356442-114713	107300	Enzo Doria	04/2015
2590	2^356425+72257	107295	Enzo Doria	04/2016
2591	2^356351-112237	107273	Enzo Doria	06/2014
2592	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
2593	2^356322+74539	107264	Enzo Doria	04/2016
2594	2^356274+1874479	107250	Enzo Doria	06/2016
2595	20^82422-93	107234	Lelio R Paula	02/2017
2596	2^356157-20365	107214	Enzo Doria	06/2013
2597	2^356129-18949	107206	Enzo Doria	05/2013
2598	2^356100-109587	107197	Enzo Doria	04/2014
2599	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
2600	2^355968-64875	107158	Lelio R Paula	01/2017
2601	2^355952+1870321	107153	Enzo Doria	05/2016
2602	2^355915-117	107142	Lelio R Paula	11/2011
2603	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
2604	3^224495-8	107112	Lelio R Paula	12/2013
2605	7^126691-44	107067	Lelio R Paula	03/2017
2606	4^177830-8243	107065	Mike Oakes	02/2011
2607	2^355524-21237	107024	Enzo Doria	06/2013
2608	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
2609	2^355494-19901	107015	Enzo Doria	06/2013
2610	2^355454-869688105	107003	Lelio R Paula	01/2017
2611	2^355366+54615	106976	Lelio R Paula	01/2017
2612	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
2613	2^355275-19861	106949	Enzo Doria	06/2013
2614	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
2615	4*10^106892-3	106893	Robert Price	10/2015
2616	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
2617	2^354946-3	106850	M. Frind & P. Underwood	08/2002
2618	2^354873-18693	106828	Enzo Doria	05/2013
2619	2^354828+4257	106814	Lelio R Paula	01/2017
2620	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
2621	2^354640-354640+1	106758	Robert Price	10/2014
2622	2^354585+95	106741	Lelio R Paula	10/2011
2623	2^354553+189	106732	Lelio R Paula	10/2011
2624	2^354514-109031	106720	Enzo Doria	04/2014
2625	2^354509-109465	106718	Enzo Doria	04/2014
2626	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
2627	15^90710+28	106684	Lelio R Paula	04/2017
2628	7^126237+34	106683	Lelio R Paula	03/2017
2629	2^354385-115315	106681	Enzo Doria	06/2015
2630	2^354327-19305	106664	Enzo Doria	06/2013
2631	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
2632	10^106636+97	106637	Lelio R Paula	02/2017
2633	10^106636-22923	106636	Patrick De Geest	03/2017
2634	2^354220-57	106631	Lelio R Paula	10/2011
2635	2^354157-17041	106612	Enzo Doria	05/2013
2636	12^98778+73	106600	Lelio R Paula	02/2017
2637	2^354064+1870651	106584	Enzo Doria	05/2016
2638	2^353992-57	106563	Lelio R Paula	10/2011
2639	(7*10^106516+113)/3	106517	Robert Price	02/2018
2640	2^353832-1853849	106515	Enzo Doria	09/2015
2641	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
2642	2^353794-18453	106503	Enzo Doria	05/2013
2643	2^353728+7695	106483	Lelio R Paula	01/2017
2644	2^353672-303	106466	Yves Minet	02/2012
2645	6^136811+101	106460	Lelio R Paula	02/2017
2646	2^353641+1871981	106457	Enzo Doria	05/2016
2647	2^353553+54615	106431	Lelio R Paula	01/2017
2648	2^353544-18897	106428	Enzo Doria	05/2013
2649	6^136729-133	106396	Lelio R Paula	02/2017
2650	2^353418+1605	106390	Lelio R Paula	01/2017
2651	2^353387+65	106381	Lelio R Paula	10/2011
2652	2^353372+74311	106376	Enzo Doria	04/2016
2653	2^353344-3693	106368	Yves Minet	03/2017
2655	2^353277-20089	106347	Enzo Doria	06/2013
2654	2^353275+72173	106347	Enzo Doria	04/2016
2656	2^353268-17705	106345	Enzo Doria	05/2013
2657	2^353267-19857	106344	Enzo Doria	06/2013
2658	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
2659	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
2660	2^353025+72257	106272	Enzo Doria	04/2016
2661	2^352932-20345	106244	Enzo Doria	06/2013
2662	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
2663	2^352883-187	106229	Lelio R Paula	10/2011
2664	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
2665	2^352814-131	106208	Lelio R Paula	10/2011
2666	2^352752+73951	106189	Enzo Doria	04/2016
2667	6^136434+5	106167	Lelio R Paula	11/2014
2668	7*5^151872-8	106155	Lelio R Paula	11/2014
2669	105^52520-2	106153	Lelio R Paula	10/2017
2670	2^352601-1604809	106144	Enzo Doria	05/2015
2671	12^98353-43	106141	Lelio R Paula	02/2017
2672	2^352585-18901	106139	Enzo Doria	05/2013
2673	(2^352554-3)/193	106128	Lelio R Paula	12/2013
2674	2^352540+15015	106126	Lelio R Paula	01/2017
2675	2^352524-3149	106121	Yves Minet	10/2014
2676	2^352486-1858781	106109	Enzo Doria	04/2016
2677	2^352444+12705	106097	Lelio R Paula	01/2017
2678	2^352228-18953	106032	Enzo Doria	05/2013
2679	2^352107+1872533	105995	Enzo Doria	05/2016
2680	2^352066-2591	105983	Yves Minet	07/2014
2681	2^352030+715	105972	Lelio R Paula	10/2011
2682	9*6^136176-5	105967	Lelio R Paula	11/2014
2683	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
2684	155^48377+2	105962	Lelio R Paula	08/2013
2685	2^351865+1869707	105922	Enzo Doria	05/2016
2686	2^351831+23	105912	Lelio R Paula	10/2011
2687	9*2^351784-5	105899	Lelio R Paula	09/2014
2688	2^351671-112387	105864	Enzo Doria	06/2014
2689	2^351669-109501	105863	Enzo Doria	04/2014
2690	2^351644+74731	105856	Enzo Doria	04/2016
2691	13^95025-42	105853	Lelio R Paula	12/2016
2692	2^351599+15015	105842	Lelio R Paula	01/2017
2693	19^82763+90	105834	Lelio R Paula	01/2017
2694	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
2695	20^81329-51	105812	Lelio R Paula	01/2017
2696	(5*10^105811+211)/9	105811	Robert Price	02/2018
2697	2^351483+28425	105807	Lelio R Paula	01/2017
2698	15^89960+86	105802	Lelio R Paula	02/2017
2699	2^351460-17289	105801	Enzo Doria	05/2013
2700	19^82735+22	105798	Lelio R Paula	01/2017
2701	2^351435-109077	105793	Enzo Doria	04/2014
2702	2^351393+1089	105780	Lelio R Paula	01/2017
2703	2^351364+72631	105772	Enzo Doria	04/2016
2704	2^351305+1872467	105754	Enzo Doria	05/2016
2705	3^221649+16	105754	Lelio R Paula	11/2016
2706	8*3^221637-5	105749	Lelio R Paula	09/2014
2707	2^351279-2780449	105746	Enzo Doria	03/2016
2708	15^89903-26	105735	Lelio R Paula	02/2017
2709	2^351213-73	105726	Lelio R Paula	10/2011
2710	2^351192-4589	105720	Yves Minet	07/2011
2711	20^81250-33	105709	Lelio R Paula	12/2016
2712	2^351076-113159	105685	Enzo Doria	07/2014
2713	93^53688-2	105684	Lelio R Paula	09/2013
2714	2^351060-4559	105680	Yves Minet	07/2011
2715	11^101473-750	105674	Enzo Doria	11/2012
2716	3*5^151181-8	105672	Lelio R Paula	11/2014
2717	15^89831-34	105650	Lelio R Paula	02/2017
2719	11^101448-360	105648	Enzo Doria	08/2012
2718	3*7^125011+4	105648	Lelio R Paula	11/2014
2720	2^350943-113269	105645	Enzo Doria	07/2014
2721	2^350868-19725	105622	Enzo Doria	06/2013
2722	2^350858-59291	105619	Enzo Doria	10/2015
2723	2^350851+135	105617	Lelio R Paula	10/2011
2724	2^350841-741	105614	Lelio R Paula	01/2017
2725	8*10^105571+3	105572	Robert Price	08/2015
2726	2^350674-78557	105564	Jorge Menendez	03/2018
2727	2*5^151026-3	105563	Lelio R Paula	11/2014
2728	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
2729	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
2730	3^221211+236	105545	Lelio R Paula	11/2016
2731	10^105515+33	105516	Lelio R Paula	11/2016
2732	10^105515-41033	105515	Patrick De Geest	12/2016
2733	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
2734	17^85732-72	105489	Lelio R Paula	01/2017
2735	2^350307-110329	105453	Enzo Doria	05/2014
2736	2^350253-20365	105437	Enzo Doria	06/2013
2737	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
2738	2^350139-109009	105403	Enzo Doria	04/2014
2739	3*5^150763+4	105380	Lelio R Paula	11/2014
2740	12^97643+91	105375	Lelio R Paula	02/2017
2741	6*5^150744-7	105367	Lelio R Paula	11/2014
2742	2^349996-112169	105360	Enzo Doria	06/2014
2743	11^101142-1080	105329	Enzo Doria	12/2012
2744	(68*10^105320-41)/9	105321	Robert Price	10/2013
2745	3^220712-9934	105307	Enzo Doria	05/2014
2746	7*10^105296+9	105297	Robert Price	09/2015
2747	2^349739+1873373	105282	Enzo Doria	06/2016
2748	7^124574+24	105278	Lelio R Paula	11/2016
2749	2^349708-20957	105273	Enzo Doria	06/2013
2750	2^349649-20469	105255	Enzo Doria	06/2013

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PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)