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	2^378128-262977	113828	Enzo Doria	05/2014
2502	2^378123-113215	113827	Enzo Doria	07/2014
2503	6^146274-18893	113824	Enzo Doria	03/2013
2504	2^378078+75	113813	Lelio R Paula	03/2013
2505	2^377940+63	113772	Lelio R Paula	03/2013
2506	2^377941-2785843	113772	Enzo Doria	04/2016
2507	2^377810+1875109	113733	Enzo Doria	09/2016
2508	2^377803-1838635	113731	Enzo Doria	05/2015
2509	2^377799+52223	113729	Yves Minet	08/2010
2510	11^109190-270	113710	Enzo Doria	12/2012
2511	7*10^113693+9	113694	Robert Price	09/2015
2512	4*10^113658+49	113659	Robert Price	01/2019
2513	(2*10^113631+529)/9	113631	Robert Price	01/2018
2514	2^377408-2798279	113612	Enzo Doria	04/2016
2515	5*10^113586+57	113587	Robert Price	12/2018
2516	2^377222+93679	113556	Yves Minet	02/2011
2517	262147#+316847	113552	Makoto Morimoto	02/2016
2518	2^377026-458903	113497	Enzo Doria	04/2015
2519	35^73477-34^73477	113454	Robert Price	05/2012
2520	2^376790+27	113426	Lelio R Paula	03/2013
2521	2^376786-112701	113424	Enzo Doria	06/2014
2522	2^376731+21	113408	Lelio R Paula	03/2013
2524	2^376634+1871245	113379	Enzo Doria	05/2016
2523	(4^188318+17)/3	113379	Robert Price	02/2017
2525	2^376576-344369	113361	Enzo Doria	07/2015
2526	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
2527	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
2528	2^376128-21237	113226	Enzo Doria	06/2013
2529	5*10^113224-81	113225	Robert Price	01/2019
2530	2^375638-1787171	113079	Enzo Doria	03/2016
2531	2^375537+4847	113048	Yves Minet	02/2011
2532	(17^91837+16^91837)/33	113000	Robert Price	08/2013
2533	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
2534	2^375350-3221	112992	Yves Minet	07/2011
2535	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
2536	2^375305+76757	112979	Enzo Doria	05/2016
2537	2^375258+1874989	112964	Enzo Doria	07/2016
2538	(29^77237-1)/28	112950	Robert Price	04/2012
2539	2^375154+74959	112933	Enzo Doria	04/2016
2540	2^374993-2787163	112885	Enzo Doria	11/2015
2541	123^53970+2	112793	Lelio R Paula	06/2013
2542	p(22852)#/2+512	112745	Robert Price	05/2017
2543	(11*10^112742-131)/3	112743	Robert Price	09/2018
2544	2^374441-21049	112718	Enzo Doria	06/2013
2545	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
2546	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
2547	3^236011-8828	112606	Enzo Doria	05/2014
2548	39^70666+2	112435	Lelio R Paula	11/2013
2549	(2^373350-7)/3	112390	Lelio R Paula	03/2014
2550	2^373306-1840931	112377	Enzo Doria	06/2015
2551	2^373117+1872107	112320	Enzo Doria	05/2016
2552	2^373040+2792761	112297	Enzo Doria	03/2016
2553	EPrime(112280)	112280	Eric W. Weisstein	10/2010
2554	2^372950+7	112270	Lelio R Paula	03/2013
2555	2^372945+1872167	112268	Enzo Doria	05/2016
2556	2^372695+72113	112193	Enzo Doria	04/2016
2557	2^372689-2563	112191	Yves Minet	07/2014
2558	2^372638-1859441	112176	Enzo Doria	03/2016
2559	3^235074-113056	112159	Enzo Doria	07/2014
2560	(91*10^112098-1)/9	112100	Robert Price	04/2015
2561	2^372310-85061	112077	Paul Bourdelais	02/2012
2562	(10^112067+53)/9	112067	Serge Batalov	07/2015
2563	75^59760+2	112054	Lelio R Paula	08/2013
2564	2^372108+74221	112016	Enzo Doria	04/2016
2565	215^48018+48018^215	112000	Norbert Schneider	10/2018
2566	2^371970-459491	111975	Enzo Doria	05/2015
2567	41^69427-40^69427	111971	Robert Price	07/2012
2568	(10^111902+71)/9	111902	Serge Batalov	07/2015
2569	2^371440-112865	111815	Enzo Doria	06/2014
2570	2^371426-459161	111811	Enzo Doria	05/2015
2571	2^371276-461267	111766	Enzo Doria	07/2015
2572	2^371098-113261	111712	Enzo Doria	07/2014
2573	(7*10^111706-61)/9	111706	Erik Branger	01/2011
2574	2^371044+1869391	111696	Enzo Doria	05/2016
2575	88^57416+87	111645	Norbert Schneider	11/2015
2576	2^370829-109693	111631	Enzo Doria	04/2014
2577	15^94906-2	111619	Lelio R Paula	11/2013
2579	2^370643-37	111575	Yves Minet	01/2012
2578	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
2580	2^370610-3911	111565	Yves Minet	04/2017
2581	286^45405+45405^286	111532	Norbert Schneider	04/2015
2582	4*5^159563-9	111531	Lelio R Paula	11/2014
2583	(4^185225+23)/3	111517	Robert Price	10/2018
2584	2^370393-2797093	111500	Enzo Doria	03/2016
2585	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
2586	2^370292-2791979	111469	Enzo Doria	03/2016
2587	2^370177-461551	111435	Enzo Doria	07/2015
2588	109^54683-108	111413	Norbert Schneider	02/2017
2589	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
2590	2^369974+733	111374	Lelio R Paula	05/2013
2591	121^53470+120	111367	Norbert Schneider	10/2018
2592	2^369915-286267	111356	Enzo Doria	07/2015
2593	2^369855-1615	111338	Lelio R Paula	05/2017
2594	7*10^111325+3	111326	Robert Price	08/2015
2595	51^65176+2	111293	Lelio R Paula	08/2013
2596	2^369643-1865767	111274	Enzo Doria	03/2016
2597	2^369603+885	111262	Lelio R Paula	05/2017
2598	L(532277)	111240	Renaud Lifchitz	03/2004
2599	105^55033-2	111233	Lelio R Paula	10/2017
2600	(35*10^111232-737)/9	111233	Robert Price	07/2018
2601	2^369392+29835	111199	Lelio R Paula	05/2017
2602	2^369354-3413	111187	Yves Minet	12/2016
2603	2^369296-27	111170	Lelio R Paula	02/2013
2604	2^369239-109837	111153	Enzo Doria	05/2014
2605	2^369224-291839	111148	Enzo Doria	07/2015
2606	2^369216+2798881	111146	Enzo Doria	04/2016
2607	10^111111+163849	111112	Patrick De Geest	03/2017
2608	10^111111-312911	111111	Patrick De Geest	03/2017
2609	2^369092-216923	111108	Enzo Doria	05/2014
2610	2^369081-55	111105	Lelio R Paula	02/2013
2611	88^57124-87	111077	Norbert Schneider	11/2015
2612	2^368980+753	111075	Lelio R Paula	05/2013
2613	2^368946-3623	111064	Yves Minet	03/2017
2614	2^368929+29835	111059	Lelio R Paula	05/2017
2615	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
2616	111^54298+110	111057	Norbert Schneider	04/2017
2617	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
2618	2^368641-460303	110972	Enzo Doria	06/2015
2619	2^368619-109087	110966	Enzo Doria	04/2014
2620	3*2^368489+7	110927	Lelio R Paula	09/2014
2621	(14*10^110922+61)/3	110923	Robert Price	12/2018
2622	97411!4-2	110913	Robert Price	07/2017
2623	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
2624	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
2625	2^368050-64875	110795	Lelio R Paula	05/2017
2626	2^368048+25	110794	Lelio R Paula	02/2013
2627	69^60239-2	110771	Lelio R Paula	10/2013
2628	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
2629	2^367924-69	110757	Lelio R Paula	02/2013
2630	2^367709-109723	110692	Enzo Doria	04/2014
2631	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
2632	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
2633	2^367215+1879223	110543	Enzo Doria	09/2016
2634	2^367141+41	110521	Lelio R Paula	02/2013
2635	2^367126+29835	110516	Lelio R Paula	05/2017
2636	(11*10^110496+49)/3	110497	Robert Price	07/2018
2637	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
2638	2^366853+5711	110434	Lelio R Paula	05/2017
2639	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
2640	2^366816+315	110423	Lelio R Paula	05/2017
2641	2^366775-2787037	110411	Enzo Doria	03/2016
2642	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
2643	2^366751+2797553	110404	Enzo Doria	03/2016
2644	2^366748+255	110403	Lelio R Paula	05/2017
2645	2^366738-2985	110400	Yves Minet	09/2014
2646	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
2647	2^366716+1871791	110393	Enzo Doria	05/2016
2648	2^366649+1871687	110373	Enzo Doria	05/2016
2649	2^366629-351205	110367	Enzo Doria	06/2015
2650	2^366558+1874479	110345	Enzo Doria	06/2016
2651	18^87853-4409	110280	Enzo Doria	03/2013
2652	2^366218-23	110243	Lelio R Paula	02/2013
2653	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
2654	2^366178-343991	110231	Enzo Doria	07/2015
2655	2^365944+1871341	110161	Enzo Doria	05/2016
2656	2^365838-461267	110129	Enzo Doria	07/2015
2657	2^365763-6555	110106	Lelio R Paula	04/2017
2658	(2^365689+2^182845+1)/5	110083		11/2006
2659	2^365666-459161	110077	Enzo Doria	05/2015
2660	3*10^110076-7	110077	Robert Price	08/2015
2661	13^98785-72	110041	Lelio R Paula	03/2017
2662	(25^78707+1)/26	110027	Robert Price	06/2013
2663	(7*10^110006-151)/9	110006	Robert Price	02/2018
2664	6^141361-7	110001	Lelio R Paula	11/2014
2665	20^84536+81	109984	Lelio R Paula	03/2017
2666	5*2^365347-9	109982	Lelio R Paula	09/2014
2667	9*6^141303+7	109957	Lelio R Paula	11/2014
2668	78^58099+77	109929	Norbert Schneider	02/2015
2669	2*10^109928-7	109929	Robert Price	10/2015
2670	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
2671	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
2672	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
2673	18^87533-11	109878	Lelio R Paula	04/2017
2674	2^364982-5	109871	Henri Lifchitz	04/2006
2675	3*10^109861+59	109862	Robert Price	08/2018
2676	2^364936-1867979	109857	Enzo Doria	04/2016
2677	2^364867-112087	109836	Enzo Doria	06/2014
2678	4^182415-85061	109825	Mike Oakes	06/2011
2679	(17^89227+16^89227)/33	109788	Robert Price	08/2013
2680	2^364687-187	109782	Lelio R Paula	01/2012
2681	2^364644+67	109769	Lelio R Paula	01/2012
2682	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
2683	(2^364616+5)/9	109760	Lelio R Paula	01/2014
2684	12^101694+73	109747	Lelio R Paula	03/2017
2685	13^98518-66	109744	Lelio R Paula	03/2017
2686	2^364478-113261	109719	Enzo Doria	07/2014
2687	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
2688	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
2689	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
2690	3^229824+340	109654	Lelio R Paula	03/2017
2691	(2*10^109645-71)/3	109645	Robert Price	12/2017
2692	2^364169-112813	109626	Enzo Doria	06/2014
2693	10^109615+21	109616	Lelio R Paula	03/2017
2694	10^109615-456267	109615	Patrick De Geest	03/2017
2695	2^364094-113	109604	Lelio R Paula	01/2012
2696	(4^182026+11)/3	109591	Robert Price	02/2017
2697	2^364041-6883	109588	Lelio R Paula	09/2011
2698	12^101545+11	109586	Lelio R Paula	03/2017
2699	2^363842-2787101	109528	Enzo Doria	03/2016
2700	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
2701	2^363769+5711	109506	Lelio R Paula	04/2017
2702	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
2703	p(22245)#/2-8	109462	Robert Price	01/2017
2704	2^363556+55	109442	Lelio R Paula	01/2012
2705	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
2706	2^363406+1871569	109397	Enzo Doria	05/2016
2707	(2^363349+7)/9	109378	Lelio R Paula	01/2014
2708	3^229236+100	109374	Lelio R Paula	03/2017
2709	2^363268-58695	109355	Lelio R Paula	04/2017
2710	2^363191-112321	109332	Enzo Doria	06/2014
2711	4*10^109316-63	109317	Robert Price	10/2018
2712	2^363120+3	109311	Donovan Johnson	04/2006
2713	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
2714	2^363042-114641	109287	Enzo Doria	04/2015
2715	2^363020-112793	109280	Enzo Doria	06/2014
2716	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
2717	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
2718	5^156181+38	109166	Lelio R Paula	02/2017
2719	4*10^109142+91	109143	Robert Price	08/2018
2720	3^228750+68	109142	Lelio R Paula	03/2017
2721	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
2722	65^60167-64^60167	109078	Robert Price	08/2013
2723	7*3^228589-2	109066	Lelio R Paula	09/2014
2724	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
2725	2*7^129008+9	109025	Lelio R Paula	11/2014
2726	(5*10^108960+91)/3	108961	Robert Price	04/2018
2727	2^361957+76367	108960	Enzo Doria	05/2016
2728	2^361873-1411	108935	Yves Minet	01/2013
2729	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
2730	115^52842-114	108892	Norbert Schneider	07/2018
2731	13^97745-24	108883	Lelio R Paula	03/2017
2732	17^88475+8	108864	Lelio R Paula	04/2017
2733	2^361567+51	108843	Lelio R Paula	01/2012
2734	2^361563-109501	108842	Enzo Doria	04/2014
2735	12^100852+83	108838	Lelio R Paula	03/2017
2736	2^361497+767	108822	Lelio R Paula	01/2012
2737	2^361280-112349	108757	Enzo Doria	06/2014
2738	2^361271-5955	108754	Lelio R Paula	04/2017
2739	12^100757+19	108736	Lelio R Paula	03/2017
2740	14^94849-61	108710	Lelio R Paula	05/2017
2741	(19^85009-5^85009)/14	108705	Robert Price	07/2013
2742	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
2743	2^360973+1299	108664	Lelio R Paula	04/2017
2744	2^360959-109101	108660	Enzo Doria	04/2014
2745	6*5^155454+7	108659	Lelio R Paula	11/2014
2746	10^108656+79	108657	Lelio R Paula	02/2017
2747	10^108656-50001	108656	Patrick De Geest	03/2017
2748	2^360918-35	108648	Lelio R Paula	01/2012
2749	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
2750	3*10^108624-49	108625	Robert Price	07/2018

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PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)