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	2^372638-1859441	112176	Enzo Doria	03/2016
2502	3^235074-113056	112159	Enzo Doria	07/2014
2503	(91*10^112098-1)/9	112100	Robert Price	04/2015
2504	2^372310-85061	112077	Paul Bourdelais	02/2012
2505	(10^112067+53)/9	112067	Serge Batalov	07/2015
2506	75^59760+2	112054	Lelio R Paula	08/2013
2507	2^372108+74221	112016	Enzo Doria	04/2016
2508	215^48018+48018^215	112000	Norbert Schneider	10/2018
2509	2^371970-459491	111975	Enzo Doria	05/2015
2510	41^69427-40^69427	111971	Robert Price	07/2012
2511	(10^111902+71)/9	111902	Serge Batalov	07/2015
2512	2^371440-112865	111815	Enzo Doria	06/2014
2513	2^371426-459161	111811	Enzo Doria	05/2015
2514	2^371276-461267	111766	Enzo Doria	07/2015
2515	2^371098-113261	111712	Enzo Doria	07/2014
2516	(7*10^111706-61)/9	111706	Erik Branger	01/2011
2517	2^371044+1869391	111696	Enzo Doria	05/2016
2518	88^57416+87	111645	Norbert Schneider	11/2015
2519	2^370829-109693	111631	Enzo Doria	04/2014
2520	15^94906-2	111619	Lelio R Paula	11/2013
2522	2^370643-37	111575	Yves Minet	01/2012
2521	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
2523	2^370610-3911	111565	Yves Minet	04/2017
2524	286^45405+45405^286	111532	Norbert Schneider	04/2015
2525	4*5^159563-9	111531	Lelio R Paula	11/2014
2526	(4^185225+23)/3	111517	Robert Price	10/2018
2527	2^370393-2797093	111500	Enzo Doria	03/2016
2528	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
2529	2^370292-2791979	111469	Enzo Doria	03/2016
2530	2^370177-461551	111435	Enzo Doria	07/2015
2531	109^54683-108	111413	Norbert Schneider	02/2017
2532	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
2533	2^369974+733	111374	Lelio R Paula	05/2013
2534	121^53470+120	111367	Norbert Schneider	10/2018
2535	2^369915-286267	111356	Enzo Doria	07/2015
2536	2^369855-1615	111338	Lelio R Paula	05/2017
2537	7*10^111325+3	111326	Robert Price	08/2015
2538	51^65176+2	111293	Lelio R Paula	08/2013
2539	2^369643-1865767	111274	Enzo Doria	03/2016
2540	2^369603+885	111262	Lelio R Paula	05/2017
2541	L(532277)	111240	Renaud Lifchitz	03/2004
2543	105^55033-2	111233	Lelio R Paula	10/2017
2542	(35*10^111232-737)/9	111233	Robert Price	07/2018
2544	2^369392+29835	111199	Lelio R Paula	05/2017
2545	2^369354-3413	111187	Yves Minet	12/2016
2546	2^369296-27	111170	Lelio R Paula	02/2013
2547	2^369239-109837	111153	Enzo Doria	05/2014
2548	2^369224-291839	111148	Enzo Doria	07/2015
2549	2^369216+2798881	111146	Enzo Doria	04/2016
2550	10^111111+163849	111112	Patrick De Geest	03/2017
2551	10^111111-312911	111111	Patrick De Geest	03/2017
2552	2^369092-216923	111108	Enzo Doria	05/2014
2553	2^369081-55	111105	Lelio R Paula	02/2013
2554	88^57124-87	111077	Norbert Schneider	11/2015
2555	2^368980+753	111075	Lelio R Paula	05/2013
2556	2^368946-3623	111064	Yves Minet	03/2017
2557	2^368929+29835	111059	Lelio R Paula	05/2017
2558	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
2559	111^54298+110	111057	Norbert Schneider	04/2017
2560	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
2561	2^368641-460303	110972	Enzo Doria	06/2015
2562	2^368619-109087	110966	Enzo Doria	04/2014
2563	3*2^368489+7	110927	Lelio R Paula	09/2014
2564	(14*10^110922+61)/3	110923	Robert Price	12/2018
2565	97411!4-2	110913	Robert Price	07/2017
2566	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
2567	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
2568	2^368050-64875	110795	Lelio R Paula	05/2017
2569	2^368048+25	110794	Lelio R Paula	02/2013
2570	69^60239-2	110771	Lelio R Paula	10/2013
2571	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
2572	2^367924-69	110757	Lelio R Paula	02/2013
2573	2^367709-109723	110692	Enzo Doria	04/2014
2574	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
2575	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
2576	2^367215+1879223	110543	Enzo Doria	09/2016
2577	2^367141+41	110521	Lelio R Paula	02/2013
2578	2^367126+29835	110516	Lelio R Paula	05/2017
2579	(11*10^110496+49)/3	110497	Robert Price	07/2018
2580	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
2581	2^366853+5711	110434	Lelio R Paula	05/2017
2582	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
2583	2^366816+315	110423	Lelio R Paula	05/2017
2584	2^366775-2787037	110411	Enzo Doria	03/2016
2585	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
2586	2^366751+2797553	110404	Enzo Doria	03/2016
2587	2^366748+255	110403	Lelio R Paula	05/2017
2588	2^366738-2985	110400	Yves Minet	09/2014
2589	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
2590	2^366716+1871791	110393	Enzo Doria	05/2016
2591	2^366649+1871687	110373	Enzo Doria	05/2016
2592	2^366629-351205	110367	Enzo Doria	06/2015
2593	2^366558+1874479	110345	Enzo Doria	06/2016
2594	18^87853-4409	110280	Enzo Doria	03/2013
2595	2^366218-23	110243	Lelio R Paula	02/2013
2596	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
2597	2^366178-343991	110231	Enzo Doria	07/2015
2598	2^365944+1871341	110161	Enzo Doria	05/2016
2599	2^365838-461267	110129	Enzo Doria	07/2015
2600	2^365763-6555	110106	Lelio R Paula	04/2017
2601	(2^365689+2^182845+1)/5	110083		11/2006
2602	2^365666-459161	110077	Enzo Doria	05/2015
2603	3*10^110076-7	110077	Robert Price	08/2015
2604	13^98785-72	110041	Lelio R Paula	03/2017
2605	(25^78707+1)/26	110027	Robert Price	06/2013
2606	(7*10^110006-151)/9	110006	Robert Price	02/2018
2607	6^141361-7	110001	Lelio R Paula	11/2014
2608	20^84536+81	109984	Lelio R Paula	03/2017
2609	5*2^365347-9	109982	Lelio R Paula	09/2014
2610	9*6^141303+7	109957	Lelio R Paula	11/2014
2611	78^58099+77	109929	Norbert Schneider	02/2015
2612	2*10^109928-7	109929	Robert Price	10/2015
2613	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
2614	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
2615	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
2616	18^87533-11	109878	Lelio R Paula	04/2017
2617	2^364982-5	109871	Henri Lifchitz	04/2006
2618	3*10^109861+59	109862	Robert Price	08/2018
2619	2^364936-1867979	109857	Enzo Doria	04/2016
2620	2^364867-112087	109836	Enzo Doria	06/2014
2621	4^182415-85061	109825	Mike Oakes	06/2011
2622	(17^89227+16^89227)/33	109788	Robert Price	08/2013
2623	2^364687-187	109782	Lelio R Paula	01/2012
2624	2^364644+67	109769	Lelio R Paula	01/2012
2625	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
2626	(2^364616+5)/9	109760	Lelio R Paula	01/2014
2627	12^101694+73	109747	Lelio R Paula	03/2017
2628	13^98518-66	109744	Lelio R Paula	03/2017
2629	2^364478-113261	109719	Enzo Doria	07/2014
2630	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
2631	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
2632	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
2633	3^229824+340	109654	Lelio R Paula	03/2017
2634	(2*10^109645-71)/3	109645	Robert Price	12/2017
2635	2^364169-112813	109626	Enzo Doria	06/2014
2636	10^109615+21	109616	Lelio R Paula	03/2017
2637	10^109615-456267	109615	Patrick De Geest	03/2017
2638	2^364094-113	109604	Lelio R Paula	01/2012
2639	(4^182026+11)/3	109591	Robert Price	02/2017
2640	2^364041-6883	109588	Lelio R Paula	09/2011
2641	12^101545+11	109586	Lelio R Paula	03/2017
2642	2^363842-2787101	109528	Enzo Doria	03/2016
2643	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
2644	2^363769+5711	109506	Lelio R Paula	04/2017
2645	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
2646	p(22245)#/2-8	109462	Robert Price	01/2017
2647	2^363556+55	109442	Lelio R Paula	01/2012
2648	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
2649	2^363406+1871569	109397	Enzo Doria	05/2016
2650	(2^363349+7)/9	109378	Lelio R Paula	01/2014
2651	3^229236+100	109374	Lelio R Paula	03/2017
2652	2^363268-58695	109355	Lelio R Paula	04/2017
2653	2^363191-112321	109332	Enzo Doria	06/2014
2654	4*10^109316-63	109317	Robert Price	10/2018
2655	2^363120+3	109311	Donovan Johnson	04/2006
2656	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
2657	2^363042-114641	109287	Enzo Doria	04/2015
2658	2^363020-112793	109280	Enzo Doria	06/2014
2659	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
2660	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
2661	5^156181+38	109166	Lelio R Paula	02/2017
2662	4*10^109142+91	109143	Robert Price	08/2018
2663	3^228750+68	109142	Lelio R Paula	03/2017
2664	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
2665	65^60167-64^60167	109078	Robert Price	08/2013
2666	7*3^228589-2	109066	Lelio R Paula	09/2014
2667	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
2668	2*7^129008+9	109025	Lelio R Paula	11/2014
2669	(5*10^108960+91)/3	108961	Robert Price	04/2018
2670	2^361957+76367	108960	Enzo Doria	05/2016
2671	2^361873-1411	108935	Yves Minet	01/2013
2672	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
2673	115^52842-114	108892	Norbert Schneider	07/2018
2674	13^97745-24	108883	Lelio R Paula	03/2017
2675	17^88475+8	108864	Lelio R Paula	04/2017
2676	2^361567+51	108843	Lelio R Paula	01/2012
2677	2^361563-109501	108842	Enzo Doria	04/2014
2678	12^100852+83	108838	Lelio R Paula	03/2017
2679	2^361497+767	108822	Lelio R Paula	01/2012
2680	2^361280-112349	108757	Enzo Doria	06/2014
2681	2^361271-5955	108754	Lelio R Paula	04/2017
2682	12^100757+19	108736	Lelio R Paula	03/2017
2683	14^94849-61	108710	Lelio R Paula	05/2017
2684	(19^85009-5^85009)/14	108705	Robert Price	07/2013
2685	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
2686	2^360973+1299	108664	Lelio R Paula	04/2017
2687	2^360959-109101	108660	Enzo Doria	04/2014
2688	6*5^155454+7	108659	Lelio R Paula	11/2014
2689	10^108656+79	108657	Lelio R Paula	02/2017
2690	10^108656-50001	108656	Patrick De Geest	03/2017
2691	2^360918-35	108648	Lelio R Paula	01/2012
2692	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
2693	3*10^108624-49	108625	Robert Price	07/2018
2694	2^360706-458903	108584	Enzo Doria	04/2015
2695	2^360641-113185	108564	Enzo Doria	07/2014
2696	2^360618+75019	108557	Enzo Doria	04/2016
2697	(14*10^108545-221)/9	108546	Robert Price	04/2018
2698	3*5^155286+2	108541	Lelio R Paula	11/2014
2699	7^128422+4	108530	Lelio R Paula	11/2014
2700	7^128421-80	108529	Lelio R Paula	03/2017
2701	2^360497+53807	108521	Yves Minet	07/2010
2702	2^360366+1459	108481	Lelio R Paula	09/2011
2703	2^360364-1499	108481	Yves Minet	05/2013
2704	14^94642-23	108472	Lelio R Paula	05/2017
2705	4*10^108412+9	108413	Robert Price	05/2015
2706	2^360093-351103	108399	Enzo Doria	06/2015
2707	2^360042+723	108384	Lelio R Paula	01/2012
2708	85^56164-2	108364	Lelio R Paula	10/2013
2709	2^359937-29323	108352	Enzo Doria	07/2015
2710	2^359898-19997	108341	Enzo Doria	06/2013
2711	2*5^154948-7	108305	Lelio R Paula	11/2014
2712	10^108303+13	108304	Lelio R Paula	02/2017
2713	10^108303-207959	108303	Patrick De Geest	03/2017
2714	2^359730+753	108290	Lelio R Paula	12/2011
2715	(8*10^108273+13)/3	108274	Robert Price	06/2018
2716	2^359650-19797	108266	Enzo Doria	06/2013
2717	91^55259-90^55259	108255	Robert Price	07/2015
2718	3^226845+68	108233	Lelio R Paula	03/2017
2719	5^154822-12866	108216	Enzo Doria	05/2014
2720	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
2721	2^359454-177	108207	Lelio R Paula	12/2011
2722	6^139022-59	108181	Lelio R Paula	02/2017
2723	2^359352-179	108176	Lelio R Paula	12/2011
2724	2^359338-1858781	108172	Enzo Doria	04/2016
2725	12^100230-97	108167	Lelio R Paula	03/2017
2726	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
2727	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
2728	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
2729	6^138956-59	108129	Lelio R Paula	02/2017
2730	2^359184+30285	108126	Lelio R Paula	04/2017
2731	13^97059+10	108119	Lelio R Paula	03/2017
2732	2^359137-81	108112	Lelio R Paula	12/2011
2734	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
2733	2^359110-11655	108103	Lelio R Paula	04/2017
2735	8*6^138875+5	108067	Lelio R Paula	11/2014
2736	2^358987-216919	108066	Enzo Doria	05/2014
2737	39^67918-67918^39	108062	Norbert Schneider	02/2017
2738	2^358785-16933	108006	Enzo Doria	05/2013
2739	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
2740	6^138770-77	107985	Lelio R Paula	02/2017
2741	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
2742	10^107976+19	107977	Lelio R Paula	02/2017
2743	10^107976-202103	107976	Patrick De Geest	03/2017
2744	2^358684+75781	107975	Enzo Doria	04/2016
2745	99^54094+2	107952	Lelio R Paula	06/2013
2746	(2^358583-9)/391	107942	Lelio R Paula	12/2013
2747	2^358538+55	107931	Lelio R Paula	12/2011
2748	2^358517-109009	107925	Enzo Doria	03/2014
2749	3^226159+104	107906	Lelio R Paula	03/2017
2750	2^358310-11655	107863	Lelio R Paula	03/2017

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PRP Records

Probable Primes Top 10000

(247113 PRPs in the top)