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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	2^498623+1866983	150101	Enzo Doria	03/2016
2502	(25*10^150050-403)/9	150051	Robert Price	12/2020
2503	numbpart(18140942830)	150033	Serge Batalov	04/2017
2504	10^150029+4381	150030	Patrick De Geest	05/2016
2505	10^150029-41	150029	Serge Batalov	12/2014
2506	10^150000+1158603	150001	Patrick De Geest	09/2018
2507	10^150000-245703	150000	Patrick De Geest	09/2018
2508	(38*10^149999+691)/9	150000	Robert Price	10/2018
2509	2043563126843649194^8192+2043563126843649185^8192	150000	Youcef Lemsafer	01/2023
2510	(2043563126843649232^8192+2043563126843649201^8192)/147457	149994	Youcef Lemsafer	01/2023
2511	2^498238-53	149985	Lelio R Paula	12/2017
2512	45728^1905+1905^45728	149984	Hans Havermann	10/2020
2513	5*10^149907+23	149908	Robert Price	03/2019
2514	39347^6442+6442^39347	149874	Hans Havermann	09/2020
2515	2^497850+81049	149868	Enzo Doria	07/2016
2516	37228^10575+10575^37228	149816	Hans Havermann	10/2020
2517	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
2518	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
2519	(2*10^149803-143)/3	149803	Robert Price	03/2018
2520	33845^26604+26604^33845	149763	Hans Havermann	09/2020
2521	2^497434-2784191	149743	Enzo Doria	10/2015
2522	(865*10^149737-1)/9	149739	Robert Price	04/2020
2523	10^149695-7000001	149695	Robert Price	06/2021
2524	38237^8214+8214^38237	149681	Hans Havermann	09/2020
2525	(23*10^149655+19)/3	149656	Robert Price	07/2019
2526	2^497068-113579	149633	Enzo Doria	08/2014
2527	2^497037+73727	149624	Enzo Doria	04/2016
2528	11*10^149618+3	149620	Robert Price	07/2021
2529	34942^19067+19067^34942	149562	Hans Havermann	09/2020
2530	33696^27449+27449^33696	149561	Hans Havermann	09/2020
2531	2^496773+77747	149544	Enzo Doria	05/2016
2532	(7*10^149483-493)/9	149483	Robert Price	04/2021
2533	(206*10^149459+7)/3	149461	Robert Price	07/2020
2534	34589^20940+20940^34589	149459	Hans Havermann	09/2020
2535	2^496477-113485	149455	Enzo Doria	08/2014
2536	((10^74703-1)10000/9+7481)10^74703+(10^74703-1)/9	149410	Hans Havermann	09/2019
2537	2^496270-49451	149393	Enzo Doria	10/2015
2538	2^496238-1865081	149383	Enzo Doria	01/2016
2539	33831^26030+26030^33831	149380	Hans Havermann	09/2020
2540	34131^23780+23780^34131	149365	Hans Havermann	09/2020
2541	(5*10^149335-53)/3	149336	Robert Price	09/2020
2542	2^495968-1853699	149302	Enzo Doria	09/2015
2543	2^495935-4117	149292	Yves Minet	02/2018
2544	35816^14709+14709^35816	149267	Hans Havermann	09/2020
2545	(10^149264+7)/191/2683/80557	149254	Alfred Reich	07/2021
2546	10^149240-40000001	149240	Robert Price	07/2022
2547	2^495712-396765	149225	Enzo Doria	07/2013
2548	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
2549	2^495420+1880701	149137	Enzo Doria	10/2016
2550	2^495337-1847293	149112	Enzo Doria	07/2015
2551	(2^495193-7)/5	149068	Lelio R Paula	10/2015
2552	2^495163+111546435	149059	Paul Bourdelais	10/2021
2553	33282^30097+30097^33282	149055	Hans Havermann	09/2020
2554	37384^9705+9705^37384	149050	Hans Havermann	09/2020
2555	34808^19143+19143^34808	149049	Hans Havermann	09/2020
2556	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
2557	47^89113-46^89113	149006	Robert Price	10/2012
2558	2^494916+87855	148985	Lelio R Paula	01/2016
2559	6*10^148982+73	148983	Robert Price	04/2019
2560	10^148934+1530019	148935	Patrick De Geest	02/2021
2561	10^148934-1000000001	148934	Robert Price	11/2020
2562	10^148934-512057	148934	Patrick De Geest	02/2021
2563	39000^6571+6571^39000	148888	Hans Havermann	10/2020
2564	2^494586-2791991	148886	Enzo Doria	02/2016
2565	8*10^148860-3	148861	Ray Chandler	04/2011
2566	38262^7769+7769^38262	148854	Hans Havermann	10/2020
2567	10^148816-500001	148816	Robert Price	03/2022
2568	(53*10^148811-287)/9	148812	Robert Price	02/2022
2569	2^494333-286183	148810	Enzo Doria	06/2015
2570	2^494144-264119	148753	Enzo Doria	05/2014
2571	6*10^148734+47	148735	Robert Price	06/2022
2572	36502^11823+11823^36502	148663	Hans Havermann	11/2020
2573	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
2574	64239^206+206^64239	148641	Hans Havermann	10/2020
2575	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
2576	(23*10^148627-137)/3	148628	Robert Price	08/2021
2577	(151*10^148601-1)/3	148603	Robert Price	03/2020
2578	2^493636+82081	148600	Enzo Doria	09/2016
2579	((((((((((((((34251^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	148593	Serge Batalov	07/2016
2580	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
2581	(2*10^148460-23)/3	148460	Robert Price	04/2018
2582	(28*10^148445+101)/3	148446	Robert Price	09/2020
2583	36203^12556+12556^36203	148391	Hans Havermann	10/2020
2584	33912^23749+23749^33912	148387	Hans Havermann	10/2020
2585	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
2586	34294^21117+21117^34294	148309	Hans Havermann	10/2020
2587	(71*10^148306-539)/9	148307	Robert Price	07/2019
2588	38042^7875+7875^38042	148222	Hans Havermann	10/2020
2589	5^211959-12874	148153	Enzo Doria	05/2014
2590	34142^21831+21831^34142	148145	Hans Havermann	10/2020
2591	10^148112+34059	148113	Patrick De Geest	05/2021
2592	10^148112-70000001	148112	Robert Price	03/2021
2593	10^148112-106593	148112	Patrick De Geest	05/2021
2594	36303^12016+12016^36303	148108	Hans Havermann	10/2020
2595	(77*10^148089-149)/9	148090	Robert Price	03/2022
2596	(16*10^148071+41)/3	148072	Robert Price	03/2019
2597	187^65175-2	148068	Lelio R Paula	11/2017
2598	2^491851+1871453	148062	Enzo Doria	05/2016
2599	(68*10^148060-257)/9	148061	Robert Price	07/2019
2600	(151*10^148020-1)/3	148022	Robert Price	03/2020
2601	39153^6032+6032^39153	148017	Hans Havermann	10/2020
2602	36798^10507+10507^36798	147983	Hans Havermann	12/2020
2603	(26*10^147973-23)/3	147974	Robert Price	12/2019
2604	2^491521-1865323	147963	Enzo Doria	02/2016
2605	(2^491476+7)/71	147948	Lelio R Paula	10/2015
2606	2*10^147928+47	147929	Robert Price	12/2021
2607	2^491391-7807	147924	Lelio R Paula	01/2013
2608	39736^5279+5279^39736	147920	Hans Havermann	11/2020
2609	2^491370-113297	147918	Enzo Doria	07/2014
2610	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
2611	44368^2155+2155^44368	147899	Hans Havermann	12/2020
2612	(17*10^147890+79)/3	147891	Robert Price	04/2019
2613	94*10^147871-3	147873	Robert Price	05/2020
2614	10^147843+620967	147844	Patrick De Geest	05/2021
2615	10^147843-50000000001	147843	Robert Price	12/2020
2616	10^147843-182891	147843	Patrick De Geest	05/2021
2617	35805^13346+13346^35805	147709	Hans Havermann	11/2020
2618	2^490672+255255	147707	Paul Bourdelais	10/2021
2619	2^490660-17	147704	Lelio R Paula	12/2017
2620	(229*10^147699-1)/3	147701	Robert Price	07/2020
2621	40656^4289+4289^40656	147678	Hans Havermann	11/2020
2622	2^490550+1179439	147671	Enzo Doria	06/2016
2623	(23*10^147649-59)/9	147650	Robert Price	05/2018
2624	2^490303+2793653	147596	Enzo Doria	03/2016
2625	2^490266+255255	147585	Paul Bourdelais	10/2021
2626	199^64181-2	147543	Lelio R Paula	11/2017
2627	32849^30958+30958^32849	147518	Hans Havermann	11/2020
2628	2^489871-286987	147466	Enzo Doria	07/2015
2629	2^489864-351899	147464	Enzo Doria	07/2015
2630	175^65724-2	147422	Lelio R Paula	11/2017
2631	2^489712+1874851	147419	Enzo Doria	06/2016
2632	34473^18830+18830^34473	147367	Hans Havermann	11/2020
2633	63^81896-2	147359	Lelio R Paula	10/2017
2634	34580^18237+18237^34580	147344	Hans Havermann	11/2020
2635	(11*10^147313-107)/3	147314	Robert Price	09/2018
2636	(397*10^147310+17)/9	147312	Robert Price	03/2022
2637	2^489305-59815	147296	Enzo Doria	10/2015
2638	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
2639	2*10^147264-61	147265	Robert Price	10/2021
2640	2*10^147260+29	147261	Robert Price	02/2021
2641	33556^24457+24457^33556	147258	Hans Havermann	11/2020
2642	2^489125+80357	147242	Enzo Doria	06/2016
2643	10^147240-40000001	147240	Robert Price	07/2022
2644	32835^30452+30452^32835	147220	Hans Havermann	12/2020
2645	(19*10^147213-97)/3	147214	Robert Price	10/2021
2646	(148*10^147139-1)/3	147141	Robert Price	03/2020
2647	34338^19255+19255^34338	147123	Hans Havermann	11/2020
2648	2^488648-112799	147098	Enzo Doria	07/2014
2649	2^488627-350317	147092	Enzo Doria	06/2015
2650	33432^25075+25075^33432	147076	Hans Havermann	12/2020
2651	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
2652	2^488280-2165	146987	Yves Minet	07/2014
2653	2^488278+45	146987	Lelio R Paula	12/2017
2654	2^487927-39	146881	Lelio R Paula	12/2017
2655	(7*10^146860-13)/3	146861	Robert Price	07/2018
2656	(26*10^146856-77)/3	146857	Robert Price	11/2019
2657	32948^28611+28611^32948	146834	Hans Havermann	11/2020
2658	42596^2799+2799^42596	146829	Hans Havermann	12/2020
2659	2^487726-1863341	146821	Enzo Doria	12/2015
2660	43838^2229+2229^43838	146775	Hans Havermann	11/2020
2661	35005^15594+15594^35005	146775	Hans Havermann	11/2020
2662	(167*10^146764+7)/3	146766	Robert Price	04/2021
2663	53^85114+85114	146761	Kellen Shenton	05/2022
2664	(59*10^146738+157)/9	146739	Robert Price	12/2021
2665	((10^73362-1)10000/9+6701)10^73362+(10^73362-1)/9	146728	Hans Havermann	09/2019
2666	32963^28234+28234^32963	146711	Hans Havermann	12/2020
2667	(22*10^146661-19)/3	146662	Robert Price	04/2019
2668	33958^20825+20825^33958	146651	Hans Havermann	12/2020
2669	2^487121-39523	146639	Enzo Doria	09/2015
2670	61063^252+252^61063	146637	Hans Havermann	12/2020
2671	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
2672	34099^19900+19900^34099	146587	Hans Havermann	11/2020
2673	2^486893-79	146570	Yves Minet	09/2017
2674	36818^9567+9567^36818	146565	Hans Havermann	12/2020
2675	2^486840+1879141	146554	Enzo Doria	08/2016
2676	2^486774-87	146534	Lelio R Paula	12/2017
2677	38655^6176+6176^38655	146530	Hans Havermann	11/2020
2678	8*10^146522-81	146523	Robert Price	02/2021
2679	32820^29059+29059^32820	146485	Hans Havermann	12/2020
2680	37261^8530+8530^37261	146472	Hans Havermann	12/2020
2681	66953^154+154^66953	146462	Hans Havermann	12/2020
2682	96^73877-95^73877	146445	Robert Price	10/2015
2683	8*10^146421+81	146422	Robert Price	08/2019
2684	33153^26090+26090^33153	146420	Hans Havermann	11/2020
2685	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
2686	179^64935+2	146290	Lelio R Paula	10/2017
2687	32595^30758+30758^32595	146285	Hans Havermann	11/2020
2688	34972^15157+15157^34972	146205	Hans Havermann	12/2020
2689	(16*10^146200+131)/3	146201	Robert Price	03/2022
2690	(19*10^146181-49)/3	146182	Robert Price	05/2019
2691	2^485531-114621	146160	Enzo Doria	05/2015
2692	2^485473-933075	146142	Paul Bourdelais	06/2021
2693	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
2694	(22*10^146130-193)/9	146131	Robert Price	07/2022
2695	2^485389+81887	146117	Enzo Doria	08/2016
2696	32554^30773+30773^32554	146108	Hans Havermann	11/2020
2697	(10^146063+71)/9	146063	Serge Batalov	07/2015
2698	2*10^146051-63	146052	Robert Price	01/2022
2699	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
2700	(22*10^146029+257)/9	146030	Robert Price	06/2018
2701	7*10^145982-53	145983	Robert Price	06/2020
2702	2^484743+1872923	145923	Enzo Doria	05/2016
2703	33140^25287+25287^33140	145913	Hans Havermann	01/2021
2704	37875^7112+7112^37875	145895	Hans Havermann	01/2021
2705	32862^27473+27473^32862	145872	Hans Havermann	01/2021
2706	32836^27587+27587^32836	145815	Hans Havermann	01/2021
2707	2^484341+1879157	145802	Enzo Doria	08/2016
2708	2*10^145784-91	145785	Robert Price	04/2020
2709	2^484271-51	145781	Lelio R Paula	11/2017
2710	(188*10^145750-11)/3	145752	Robert Price	02/2022
2711	70^78989-69^78989	145743	Robert Price	01/2014
2712	51^85334+2	145714	Robert Price	07/2015
2713	2^483886-1857101	145665	Enzo Doria	10/2015
2714	33350^23307+23307^33350	145656	Hans Havermann	01/2021
2715	(19*10^145585+131)/3	145586	Robert Price	06/2020
2716	2^483563-1863457	145567	Enzo Doria	12/2015
2717	4*10^145563-69	145564	Robert Price	01/2022
2718	2^483516-1861409	145553	Enzo Doria	11/2015
2719	2^483384-115019	145514	Enzo Doria	06/2015
2720	(259*10^145501-1)/3	145503	Robert Price	12/2020
2721	(19*10^145499-61)/3	145500	Robert Price	05/2019
2722	2^483302-3221	145489	Lelio R Paula	12/2012
2723	(23*10^145463+61)/3	145464	Robert Price	01/2022
2724	35523^12434+12434^35523	145453	Hans Havermann	01/2021
2725	2^483046+1874029	145412	Enzo Doria	06/2016
2726	2^482991-2789317	145395	Enzo Doria	12/2015
2727	2^482978-2789711	145391	Enzo Doria	12/2015
2728	2^482966-2789711	145388	Enzo Doria	12/2015
2729	2^482817-1858843	145343	Enzo Doria	10/2015
2730	2^482751-113635	145323	Enzo Doria	08/2014
2731	2^482705-459763	145309	Enzo Doria	05/2015
2732	(4^241306+11)/3	145281	Robert Price	03/2017
2733	(238*10^145276-1)/3	145278	Robert Price	04/2020
2734	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
2735	53^84239-52^84239	145252	Robert Price	01/2013
2736	47952^1067+1067^47952	145207	Hans Havermann	01/2021
2737	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
2738	2^482087+72623	145123	Enzo Doria	04/2016
2739	2^482016-286565	145102	Enzo Doria	07/2015
2740	(19*10^145093+101)/3	145094	Robert Price	09/2019
2741	2^481956+121	145084	Stefano Morozzi	04/2021
2742	2^481840+15	145049	Robert Price	09/2015
2743	2^481801-481801	145037	Henri Lifchitz	03/2005
2744	2^481775+1869083	145029	Enzo Doria	05/2016
2745	29^99167+2	145022	Ray Chandler	08/2011
2746	2^481663+1875653	144996	Enzo Doria	07/2016
2747	8*10^144977+27	144978	Robert Price	09/2021
2748	36486^9379+9379^36486	144929	Hans Havermann	12/2020
2749	35111^13378+13378^35111	144882	Hans Havermann	01/2021
2750	2^481149-459073	144841	Enzo Doria	05/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(291910 PRPs in the top)