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	(19*10^143129-43)/3	143130	Robert Price	05/2019
2502	31830^31373+31373^31830	143126	Hans Havermann	05/2021
2503	6*10^143105-53	143106	Robert Price	05/2021
2504	(14*10^143097+73)/3	143098	Robert Price	12/2018
2505	2^475299-111937	143080	Enzo Doria	05/2014
2506	35488^10753+10753^35488	143071	Hans Havermann	04/2021
2507	2^475160-2797859	143038	Enzo Doria	04/2016
2508	(2^475069+3)/395	143008	Lelio R Paula	08/2015
2509	2^475027-461437	142998	Enzo Doria	07/2015
2510	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
2511	(8*10^142932+43)/3	142933	Robert Price	06/2018
2512	35055^11942+11942^35055	142922	Hans Havermann	05/2021
2513	37650^6239+6239^37650	142887	Hans Havermann	05/2021
2514	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
2515	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
2516	2^474417-59923	142814	Enzo Doria	10/2015
2517	4*10^142810-21	142811	Robert Price	09/2018
2518	32287^26494+26494^32287	142811	Hans Havermann	06/2021
2519	37162^6965+6965^37162	142811	Hans Havermann	06/2021
2520	37456^6493+6493^37456	142799	Hans Havermann	05/2021
2521	35141^11572+11572^35141	142793	Hans Havermann	05/2021
2522	32231^26908+26908^32231	142780	Hans Havermann	05/2021
2523	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
2524	2^474053+2897	142705	Lelio R Paula	08/2012
2525	(10^142699+359)/9	142699	Serge Batalov	12/2014
2526	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
2527	2^473740-1856639	142610	Enzo Doria	09/2015
2528	(25*10^142573-403)/9	142574	Robert Price	12/2020
2529	2^473617-114223	142573	Enzo Doria	12/2014
2530	36115^8856+8856^36115	142555	Hans Havermann	05/2021
2531	2^473257+1873217	142465	Enzo Doria	06/2016
2532	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
2533	32750^22371+22371^32750	142453	Hans Havermann	06/2021
2534	(61*10^142446-1)/3	142448	Robert Price	01/2020
2535	(14*10^142440+61)/3	142441	Robert Price	12/2018
2536	(10^142425+359)/9	142425	Serge Batalov	12/2014
2537	2^473101+773027	142418	Enzo Doria	05/2016
2538	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
2539	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
2540	36915^7162+7162^36915	142309	Hans Havermann	05/2021
2541	2^472634-109511	142278	Enzo Doria	04/2014
2542	31870^28997+28997^31870	142216	Hans Havermann	06/2021
2543	(48^84589+1)/49	142213	Robert Price	01/2014
2544	7*10^142189+87	142190	Robert Price	07/2019
2545	2^472258+7	142164	Lelio R Paula	08/2015
2546	40135^3484+3484^40135	142162	Hans Havermann	05/2021
2547	(23*10^142105+91)/3	142106	Robert Price	08/2019
2548	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
2549	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
2550	(16*10^142058+197)/3	142059	Robert Price	04/2019
2551	9*10^142037+91	142038	Robert Price	10/2020
2552	2^471792+1880881	142024	Enzo Doria	11/2016
2553	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
2554	(4*10^141926-79)/3	141927	Robert Price	02/2018
2555	2^471464-111546435	141925	Paul Bourdelais	10/2021
2556	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
2557	(14*10^141853+37)/3	141854	Robert Price	12/2018
2558	(41*10^141836-59)/9	141837	Robert Price	10/2018
2559	4*5^202913-9	141831	Lelio R Paula	04/2015
2560	2*7^167812-3	141818	Lelio R Paula	12/2014
2561	2^471043+35	141799	Robert Price	11/2015
2562	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
2563	43636^1773+1773^43636	141761	Hans Havermann	05/2021
2564	(11*10^141718-131)/3	141719	Robert Price	09/2018
2565	2^470692+76771	141693	Enzo Doria	05/2016
2566	50160^667+667^50160	141659	Hans Havermann	05/2021
2567	31522^31181+31181^31522	141657	Hans Havermann	05/2021
2568	33076^19135+19135^33076	141626	Hans Havermann	04/2021
2569	(91*10^141610+71)/9	141612	Robert Price	01/2022
2570	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
2571	31932^27155+27155^31932	141582	Hans Havermann	05/2021
2572	36449^7660+7660^36449	141577	Hans Havermann	05/2021
2573	2^470305-459373	141576	Enzo Doria	05/2015
2574	32195^24936+24936^32195	141556	Hans Havermann	05/2021
2575	2^470183+72623	141540	Enzo Doria	04/2016
2576	2^470173-16465	141537	Enzo Doria	04/2013
2577	37297^6234+6234^37297	141534	Hans Havermann	05/2021
2578	44*10^141476+9	141478	Robert Price	10/2020
2579	2^469974-1841	141477	Enzo Doria	05/2014
2580	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
2581	2*10^141448+63	141449	Robert Price	05/2018
2582	2^469824+43	141432	Lelio R Paula	09/2017
2583	2*10^141407-27	141408	Robert Price	05/2018
2584	(214*10^141385-1)/3	141387	Robert Price	01/2021
2585	2^469630-59711	141373	Enzo Doria	10/2015
2586	35277^10172+10172^35277	141370	Hans Havermann	04/2021
2587	33397^17100+17100^33397	141370	Hans Havermann	04/2021
2588	(25*10^141366-331)/9	141367	Robert Price	08/2018
2589	36986^6639+6639^36986	141365	Hans Havermann	06/2021
2590	34572^12271+12271^34572	141361	Hans Havermann	06/2021
2591	37179^6338+6338^37179	141353	Hans Havermann	05/2021
2592	(2^469564-3)/611	141351	Lelio R Paula	08/2015
2593	197^61601+2	141342	Lelio R Paula	08/2017
2594	33420^16951+16951^33420	141340	Hans Havermann	05/2021
2595	31623^29458+29458^31623	141330	Hans Havermann	05/2021
2596	48112^865+865^48112	141306	Hans Havermann	05/2021
2597	2^469372-112949	141296	Enzo Doria	07/2014
2598	5*10^141294-63	141295	Robert Price	04/2021
2599	3^296115+4	141283	Tyler NeSmith	01/2021
2600	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
2601	143^65536+106^65536	141253	Serge Batalov	03/2018
2602	(11*10^141243-23)/3	141244	Robert Price	09/2021
2604	2^469198+782569	141243	Enzo Doria	10/2016
2603	38129^5062+5062^38129	141243	Hans Havermann	05/2021
2605	2^469076-2786939	141206	Enzo Doria	11/2015
2606	38630^4521+4521^38630	141202	Hans Havermann	05/2021
2607	31755^27836+27836^31755	141139	Hans Havermann	05/2021
2608	35554^9325+9325^35554	141137	Hans Havermann	05/2021
2609	2^468804+1874941	141125	Enzo Doria	06/2016
2610	2^468787+81353	141119	Enzo Doria	08/2016
2611	2^468595-350407	141062	Enzo Doria	06/2015
2612	2^468564+87855	141052	Lelio R Paula	01/2016
2613	2^468551-21987	141048	Enzo Doria	07/2013
2614	2^468523-7	141040	Lelio R Paula	08/2015
2615	(25*10^141019-13)/3	141020	Robert Price	09/2019
2616	2^468405+87855	141004	Lelio R Paula	01/2016
2617	39338^3831+3831^39338	140961	Hans Havermann	05/2021
2618	31458^30239+30239^31458	140950	Hans Havermann	05/2021
2619	8*10^140932+29	140933	Robert Price	11/2021
2620	33166^17691+17691^33166	140881	Hans Havermann	06/2021
2621	2^467978-113051	140876	Enzo Doria	07/2014
2622	2^467780-344429	140816	Enzo Doria	07/2015
2623	9*10^140802-89	140803	Robert Price	04/2020
2624	2^467605-1855603	140764	Enzo Doria	09/2015
2625	5*10^140744-7	140745	Robert Price	09/2015
2626	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
2627	2^467401-1850023	140702	Enzo Doria	08/2015
2628	(266*10^140681-17)/3	140683	Robert Price	07/2020
2629	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
2630	32138^23781+23781^32138	140644	Hans Havermann	05/2021
2631	31654^27735+27735^31654	140640	Hans Havermann	05/2021
2632	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
2633	2^467166-1854941	140631	Enzo Doria	09/2015
2634	(203*10^140615-11)/3	140617	Robert Price	12/2020
2635	(85*10^140609+473)/9	140610	Robert Price	01/2020
2636	39231^3836+3836^39231	140600	Hans Havermann	06/2021
2637	2^466866-1840571	140541	Enzo Doria	06/2015
2638	2^466829-459523	140530	Enzo Doria	05/2015
2639	2^466692-113213	140489	Enzo Doria	07/2014
2640	23*10^140464-3	140466	Robert Price	10/2021
2641	31335^30364+30364^31335	140455	Hans Havermann	05/2021
2642	32795^19126+19126^32795	140416	Hans Havermann	05/2021
2643	(44*10^140410-503)/9	140411	Robert Price	12/2018
2644	153^64265-2	140400	Lelio R Paula	11/2017
2645	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
2646	(29*10^140337-17)/3	140338	Robert Price	09/2019
2647	2^466181-112735	140335	Enzo Doria	07/2014
2648	(16*10^140290-37)/3	140291	Robert Price	05/2021
2649	(5*10^140281-119)/3	140282	Robert Price	03/2018
2650	34568^11415+11415^34568	140259	Hans Havermann	05/2021
2651	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
2652	33632^14781+14781^33632	140236	Hans Havermann	05/2021
2653	31803^25670+25670^31803	140233	Hans Havermann	05/2021
2654	2^465803-114817	140221	Enzo Doria	05/2015
2655	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
2656	2^465503-112735	140131	Enzo Doria	07/2014
2657	(16*10^140091+167)/3	140092	Robert Price	06/2019
2658	6^179964+179964^6-1	140040	Robert Price	04/2014
2659	(89*10^140008-179)/9	140009	Robert Price	12/2019
2660	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
2661	2^465072-344789	140001	Enzo Doria	07/2015
2662	34742^10683+10683^34742	139965	Hans Havermann	05/2021
2663	5*10^139945+81	139946	Robert Price	03/2019
2664	32648^19335+19335^32648	139941	Hans Havermann	05/2021
2665	2^464864-17	139939	Lelio R Paula	09/2017
2666	8*10^139920+51	139921	Robert Price	08/2019
2667	(85*10^139913-1)/3	139915	Robert Price	02/2020
2668	31203^30436+30436^31203	139896	Hans Havermann	04/2021
2669	4*10^139839-27	139840	Robert Price	08/2021
2670	33582^14573+14573^33582	139821	Hans Havermann	05/2021
2671	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
2673	2*10^139800-21	139801	Robert Price	09/2020
2672	32628^19261+19261^32628	139801	Hans Havermann	04/2021
2674	(13*10^139782+191)/3	139783	Robert Price	11/2018
2675	(64*10^139776+791)/9	139777	Robert Price	01/2022
2676	(695*10^139772+7)/9	139774	Robert Price	12/2021
2677	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
2678	(74*10^139723+133)/9	139724	Robert Price	06/2019
2679	3*10^139722+13	139723	Robert Price	07/2018
2680	31577^26592+26592^31577	139721	Hans Havermann	05/2021
2681	77*10^139692+3	139694	Robert Price	06/2020
2682	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
2683	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
2684	39640^3321+3321^39640	139584	Hans Havermann	05/2021
2685	36663^6410+6410^36663	139571	Hans Havermann	05/2021
2686	2^463633-2788423	139568	Enzo Doria	11/2015
2687	33659^13978+13978^33659	139532	Hans Havermann	05/2021
2688	31811^24318+24318^31811	139521	Hans Havermann	04/2021
2689	34149^12172+12172^34149	139512	Hans Havermann	04/2021
2690	(29*10^139476+313)/9	139477	Robert Price	04/2021
2691	31721^24940+24940^31721	139474	Hans Havermann	05/2021
2692	32833^17698+17698^32833	139473	Hans Havermann	05/2021
2693	2^463271-109501	139459	Enzo Doria	04/2014
2694	(5*10^139457+79)/3	139458	Robert Price	03/2018
2695	2^463237-99	139449	Lelio R Paula	09/2017
2696	(49*10^139442+383)/9	139443	Robert Price	04/2019
2697	31155^29902+29902^31155	139441	Hans Havermann	05/2021
2698	(7*10^139417-547)/9	139417	Robert Price	01/2018
2699	(10^139398+191)/3	139398	Robert Price	02/2018
2700	23*10^139386-3	139388	Robert Price	10/2021
2701	2^463019+79463	139383	Enzo Doria	06/2016
2702	3^292129-112756	139381	Enzo Doria	07/2014
2703	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
2704	31922^23205+23205^31922	139359	Hans Havermann	05/2021
2706	2^462855-1865707	139334	Enzo Doria	02/2016
2705	31237^28876+28876^31237	139334	Hans Havermann	05/2021
2707	(86*10^139315+121)/9	139316	Robert Price	08/2019
2708	2^462786-292043	139313	Enzo Doria	08/2015
2709	38915^3798+3798^38915	139299	Hans Havermann	05/2021
2710	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
2711	34065^12248+12248^34065	139260	Hans Havermann	05/2021
2712	36425^6654+6654^36425	139256	Hans Havermann	05/2021
2713	39252^3527+3527^39252	139243	Hans Havermann	05/2021
2714	(17*10^139239+67)/3	139240	Robert Price	01/2019
2715	31887^23248+23248^31887	139231	Hans Havermann	05/2021
2716	(25*10^139210-97)/9	139211	Robert Price	01/2022
2717	2^462238-935	139148	Yves Minet	02/2014
2718	(29*10^139134-119)/9	139135	Robert Price	12/2021
2719	(109*10^139100-7)/3	139102	Robert Price	03/2021
2720	38744^3885+3885^38744	139068	Hans Havermann	05/2021
2721	31112^29499+29499^31112	139065	Hans Havermann	05/2021
2722	2*10^139043-63	139044	Robert Price	01/2022
2723	36390^6613+6613^36390	139025	Hans Havermann	04/2021
2724	2*10^138975+33	138976	Robert Price	11/2021
2725	42437^1882+1882^42437	138966	Hans Havermann	05/2021
2726	32151^20990+20990^32151	138958	Hans Havermann	05/2021
2727	32154^20933+20933^32154	138933	Hans Havermann	04/2021
2728	31082^29499+29499^31082	138931	Hans Havermann	04/2021
2729	2^461228+1870441	138844	Enzo Doria	05/2016
2730	2^461204-113675	138837	Enzo Doria	08/2014
2731	(2^461139-7)/47	138815	Lelio R Paula	08/2015
2732	(17*10^138812-521)/9	138813	Robert Price	04/2018
2733	3*10^138811-11	138812	Robert Price	07/2018
2734	(28*10^138768+173)/3	138769	Robert Price	12/2019
2735	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
2736	(379*10^138737-1)/9	138739	Robert Price	02/2020
2737	(43*10^138648+101)/9	138649	Robert Price	11/2018
2738	2^460567-113541	138645	Enzo Doria	08/2014
2739	(10^138622+161)/9	138622	Robert Price	09/2021
2740	7*10^138604+3	138605	Robert Price	08/2015
2741	(133*10^138600+17)/3	138602	Robert Price	11/2021
2742	33912^12203+12203^33912	138581	Hans Havermann	05/2021
2743	2^460330+69	138574	Lelio R Paula	09/2017
2744	(17*10^138569-77)/3	138570	Robert Price	08/2019
2745	31186^27725+27725^31186	138556	Hans Havermann	05/2021
2746	(16*10^138545+89)/3	138546	Robert Price	03/2021
2747	39753^3056+3056^39753	138546	Hans Havermann	05/2021
2748	31282^26847+26847^31282	138545	Hans Havermann	05/2021
2749	6*10^138520-37	138521	Robert Price	02/2021
2750	31830^22447+22447^31830	138498	Hans Havermann	05/2021

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PRP Records

Probable Primes Top 10000

(288949 PRPs in the top)