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	10^126919-100001	126919	Robert Price	07/2020
2502	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
2503	(5*10^126871-119)/3	126872	Robert Price	03/2018
2504	331^50339-10004	126846	Enzo Doria	07/2012
2505	2^421363-2790757	126843	Enzo Doria	03/2016
2506	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
2507	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
2508	(14*10^126784-83)/3	126785	Robert Price	12/2018
2509	2^421161-286183	126783	Enzo Doria	06/2015
2510	2^420939-113935	126716	Enzo Doria	10/2014
2511	177^56363-2	126703	Lelio R Paula	10/2017
2512	2^420741-113659	126656	Enzo Doria	08/2014
2513	2^420694-21	126642	Lelio R Paula	05/2017
2514	(13*10^126638+437)/9	126639	Robert Price	04/2018
2515	(167*10^126637-17)/3	126639	Robert Price	03/2020
2516	4*10^126625+87	126626	Robert Price	08/2018
2518	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
2517	7*10^126600-99	126601	Robert Price	06/2019
2519	2^420424-59189	126561	Enzo Doria	10/2015
2520	2^420126+71893	126471	Enzo Doria	04/2016
2521	(43*10^126441+47)/9	126442	Robert Price	12/2018
2522	2^419866+1877059	126393	Enzo Doria	07/2016
2523	F(604711)	126377	Henri Lifchitz	02/2005
2524	2^419757+72707	126360	Enzo Doria	04/2016
2525	2^419720-21569	126349	Enzo Doria	07/2013
2526	2^419637+29	126324	Henri Lifchitz	02/2006
2527	2^419612+1876741	126316	Enzo Doria	07/2016
2528	2^419520+2793271	126289	Enzo Doria	03/2016
2529	(2^419447-5)/369	126264	Lelio R Paula	05/2014
2530	2^419328-1859939	126231	Enzo Doria	03/2016
2531	2^419282-1851507	126217	Enzo Doria	08/2015
2532	2^419251+1866143	126208	Enzo Doria	03/2016
2533	11^121185+2	126202	Robert Price	05/2014
2534	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
2535	2^418851+23	126087	Robert Price	09/2015
2536	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
2537	2^418829+167	126081	Lelio R Paula	01/2012
2538	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
2539	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
2540	2^418319-109501	125927	Enzo Doria	04/2014
2541	2^418316-112373	125926	Enzo Doria	06/2014
2542	(8*10^125894-29)/3	125895	Robert Price	07/2018
2543	(26*10^125886-413)/9	125887	Robert Price	05/2018
2544	2^417968+1869811	125821	Enzo Doria	06/2016
2545	2^417902+63	125802	Lelio R Paula	09/2015
2546	(10^125792-91)/9	125792	Serge Batalov	12/2014
2547	(35*10^125754-593)/9	125755	Robert Price	07/2018
2548	(32*10^125751-77)/9	125752	Robert Price	06/2018
2549	2^417704+77011	125742	Enzo Doria	05/2016
2550	(10^125706+149)/3	125706	Serge Batalov	12/2014
2551	2^417419-115309	125656	Enzo Doria	07/2015
2552	2^417300+77281	125620	Enzo Doria	05/2016
2553	2^417095-1657	125559	Yves Minet	07/2014
2554	2^416773-25	125462	Lelio R Paula	09/2015
2555	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
2556	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
2557	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
2558	2^416641-2*416641+1	125422	Robert Price	05/2018
2559	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
2560	2^416530+1870429	125389	Enzo Doria	05/2016
2561	(56*10^125385+691)/9	125386	Robert Price	05/2019
2562	2^416490+1875109	125376	Enzo Doria	09/2016
2563	2^416416-114929	125354	Enzo Doria	05/2015
2564	(77*10^125330-293)/9	125331	Robert Price	09/2019
2565	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
2566	2^416134+1865899	125269	Enzo Doria	03/2016
2567	153^57337-152	125264	Norbert Schneider	12/2018
2568	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
2569	(23^91943-1)/22	125201	Robert Price	01/2012
2570	43125^27010-106	125185	Enzo Doria	08/2012
2571	(38*10^125166+349)/9	125167	Robert Price	10/2018
2572	2^415765-112603	125158	Enzo Doria	06/2014
2573	8*10^125088-13	125089	Robert Price	08/2019
2574	(25*10^125076-13)/3	125077	Robert Price	09/2019
2575	(29*10^125021-113)/3	125022	Robert Price	10/2019
2576	2^415290-113591	125015	Enzo Doria	08/2014
2577	2^415276-460919	125011	Enzo Doria	06/2015
2578	2^415259+77243	125006	Enzo Doria	05/2016
2579	2^415144-3683	124971	Yves Minet	10/2011
2580	2^414874+79	124890	Lelio R Paula	01/2015
2581	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
2582	2^414618+79459	124813	Enzo Doria	06/2016
2583	(61*10^124809-1)/3	124811	Robert Price	01/2020
2584	2^414432-1846709	124757	Enzo Doria	07/2015
2585	2*10^124751-51	124752	Robert Price	04/2018
2586	(56*10^124735+367)/9	124736	Robert Price	06/2019
2587	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
2588	56*10^124656-3	124658	Robert Price	03/2020
2589	(7*10^124648+197)/3	124649	Robert Price	07/2018
2591	2^414032-5	124637	Henri Lifchitz	07/2006
2590	2^414032+1872331	124637	Enzo Doria	05/2016
2592	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
2593	64^68909-63^68909	124463	Robert Price	07/2013
2594	2^413387+76253	124442	Enzo Doria	04/2016
2595	2^413352+524287	124432	Paul Underwood	09/2018
2596	287117#+391613	124424	Nicolas PALAU	01/2017
2597	(4*10^124420+83)/3	124421	Robert Price	02/2018
2598	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
2599	(41*10^124335-383)/9	124336	Robert Price	11/2018
2600	(304*10^124329-43)/9	124331	Robert Price	02/2020
2601	2^412868-120599	124286	Paul Bourdelais	02/2012
2602	10^124248-1000001	124248	Robert Price	08/2020
2603	45^75145-2	124231	Lelio R Paula	08/2015
2604	2^412645-112213	124219	Enzo Doria	06/2014
2605	2^412248+74611	124100	Enzo Doria	04/2016
2606	(22*10^124096-13)/9	124097	Robert Price	06/2018
2607	2^412192-3329	124083	Yves Minet	12/2014
2608	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
2609	(25*10^124076-67)/3	124077	Robert Price	06/2019
2610	F(593689)	124074	Henri Lifchitz	01/2005
2611	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
2612	(266*10^124022-11)/3	124024	Robert Price	04/2020
2613	2^411884-113279	123990	Enzo Doria	07/2014
2614	(2^411832+1)/257	123972	Lelio R Paula	05/2014
2615	(2^411833+2)/514	123972	Stefano Morozzi	03/2020
2616	(26*10^123970-89)/9	123971	Robert Price	06/2018
2617	2^411790-1853531	123962	Enzo Doria	08/2015
2618	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
2619	2^411711-113257	123938	Enzo Doria	07/2014
2620	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
2621	(11*10^123899-179)/3	123900	Robert Price	09/2018
2622	2^411325-351103	123822	Enzo Doria	06/2015
2623	2^411052+1872481	123739	Enzo Doria	05/2016
2624	2^410997+39	123723	Lelio R Paula	05/2014
2625	(649^43987-1)/648	123700	Michael Stocker	05/2020
2626	(148*10^123688-1)/3	123690	Robert Price	03/2020
2627	8*10^123657+87	123658	Robert Price	10/2019
2628	155^56438+154	123618	Norbert Schneider	01/2019
2629	2^410596-39	123602	Lelio R Paula	05/2014
2630	2^410540-115079	123585	Enzo Doria	06/2015
2631	(7*10^123563+107)/3	123564	Robert Price	02/2018
2632	9*10^123549+89	123550	Robert Price	11/2019
2633	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
2634	2^410206-113081	123485	Enzo Doria	07/2014
2635	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
2636	2^409909-189	123395	Enzo Doria	05/2014
2637	2^409896-109043	123391	Enzo Doria	04/2014
2638	2^409890+75409	123390	Enzo Doria	04/2016
2639	133^58076-2	123345	Lelio R Paula	10/2017
2640	F(590041)	123311	Henri Lifchitz	01/2005
2641	2^409566-113501	123292	Enzo Doria	08/2014
2642	2^409533+77747	123282	Enzo Doria	05/2016
2643	2^409436-112799	123253	Enzo Doria	06/2014
2644	2^409225+1873787	123189	Enzo Doria	06/2016
2645	2^409174+73009	123174	Enzo Doria	04/2016
2646	2^409058-112685	123139	Enzo Doria	06/2014
2647	(13*10^123137-61)/3	123138	Robert Price	11/2018
2648	4*10^123113+21	123114	Robert Price	12/2018
2649	2^408778+77689	123055	Enzo Doria	05/2016
2650	2^408690-75	123028	Lelio R Paula	11/2013
2651	(29*10^122996+673)/9	122997	Robert Price	12/2018
2652	2^408574-2787341	122994	Enzo Doria	03/2016
2653	3*10^122977+37	122978	Robert Price	08/2018
2654	Phi(157825,10)	122961	Maksym Voznyy	06/2015
2655	(68*10^122933-419)/9	122934	Robert Price	07/2019
2656	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
2657	(266*10^122872-17)/3	122874	Robert Price	07/2020
2658	(16*10^122871+77)/3	122872	Robert Price	03/2019
2659	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
2660	(19*10^122836-43)/3	122837	Robert Price	05/2019
2661	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
2662	(32*10^122733-77)/9	122734	Robert Price	06/2018
2663	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
2664	(22*10^122681+161)/3	122682	Robert Price	05/2019
2665	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
2666	(26*10^122625-131)/3	122626	Robert Price	10/2019
2667	(73*10^122592-1)/9	122593	Robert Price	01/2015
2668	(5*10^122592+91)/3	122593	Robert Price	04/2018
2669	(85*10^122585-1)/3	122587	Robert Price	02/2020
2670	2^407179-112075	122574	Enzo Doria	06/2014
2671	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
2672	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
2673	2^407008-1867919	122522	Enzo Doria	04/2016
2674	11^117642-300	122512	Enzo Doria	10/2012
2675	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
2676	2^406949+72197	122504	Enzo Doria	04/2016
2677	(19*10^122501+149)/3	122502	Robert Price	05/2019
2678	2^406826-65	122467	Lelio R Paula	11/2013
2679	2^406821-2797363	122466	Enzo Doria	04/2016
2680	2^406758-17	122447	Lelio R Paula	11/2013
2681	(30^82883-1)/29	122427	Robert Price	12/2011
2682	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
2683	4*10^122377+19	122378	Robert Price	10/2018
2684	Phi(246362,10)	122365	Makoto Kamada	09/2019
2685	3*10^122345-97	122346	Robert Price	07/2018
2686	97^61575-2	122336	Lelio R Paula	12/2014
2687	2^406298+2799109	122308	Enzo Doria	04/2016
2688	7*10^122294+57	122295	Robert Price	06/2019
2689	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
2690	2^406229-1849993	122288	Enzo Doria	08/2015
2691	3*10^122274+7	122275	Robert Price	07/2015
2692	2^406117+1876577	122254	Enzo Doria	07/2016
2693	3^256199-2^256199	122238	Mike Oakes	06/2005
2694	2^405992-78557	122216	Jorge Menendez	03/2018
2695	(8*10^122203+43)/3	122204	Robert Price	06/2018
2696	(58*10^122170+329)/9	122171	Robert Price	05/2019
2697	2^405774+179149	122151	Enzo Doria	06/2016
2698	34*10^122082-9	122084	Robert Price	06/2020
2699	5*10^122082+41	122083	Robert Price	03/2019
2701	2^405514-3311	122072	Yves Minet	12/2014
2702	2^405514-115511	122072	Enzo Doria	07/2015
2700	23*10^122070-7	122072	Robert Price	02/2020
2703	2^405422-113261	122045	Enzo Doria	07/2014
2704	2^405173+71237	121970	Enzo Doria	04/2016
2705	(2^405016+1)/257	121920	Lelio R Paula	04/2014
2706	2^404858+71329	121875	Enzo Doria	04/2016
2707	2^404813-114703	121861	Enzo Doria	04/2015
2708	2^404764+77791	121847	Enzo Doria	05/2016
2709	317^48694+48694^317	121787	Norbert Schneider	08/2015
2710	2^404536-115259	121778	Enzo Doria	06/2015
2711	2^404501-631	121767	Yves Minet	07/2012
2712	63^67620+2	121672	Lelio R Paula	08/2015
2713	(16*10^121633+167)/3	121634	Robert Price	06/2019
2714	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
2715	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
2716	(10^121543-79)/3	121543	Robert Price	01/2018
2717	2^403676+76831	121519	Enzo Doria	05/2016
2718	(7*10^121487+143)/3	121488	Robert Price	03/2018
2719	2^403363-113635	121425	Enzo Doria	08/2014
2720	2^403336-1861469	121417	Enzo Doria	03/2016
2721	p(24442)#/2-64	121381	Robert Price	04/2017
2722	11^116555-720	121380	Enzo Doria	11/2012
2723	2^403100-461267	121346	Enzo Doria	07/2015
2724	2^403093-112213	121344	Enzo Doria	06/2014
2725	(316^48539+1)/317	121330	Eric Chen	10/2017
2726	(23*10^121320-71)/3	121321	Robert Price	07/2020
2727	2^403004+1866361	121317	Enzo Doria	03/2016
2728	2^402953+89	121301	Lelio R Paula	10/2013
2729	2^402944-2788319	121299	Enzo Doria	03/2016
2730	(44*10^121297-719)/9	121298	Robert Price	12/2018
2731	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
2732	2^402828-113183	121264	Enzo Doria	07/2014
2733	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
2734	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
2735	2^402715+1874223	121230	Enzo Doria	06/2016
2736	(35*10^121229-593)/9	121230	Robert Price	07/2018
2737	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
2738	7*10^121144+9	121145	Robert Price	09/2015
2739	2^401725-113251	120932	Enzo Doria	07/2014
2740	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
2741	2^401652+73711	120910	Enzo Doria	04/2016
2742	(2^401632+3)/79	120902	Lelio R Paula	04/2014
2743	10^120841+88417	120842	Patrick De Geest	04/2020
2744	10^120841-123456789	120841	Robert Price	02/2020
2745	10^120841-176853	120841	Patrick De Geest	04/2020
2746	2^401406-2791331	120836	Enzo Doria	03/2016
2747	(28^83497+1)/29	120832	Robert Price	07/2013
2748	(22*10^120828+161)/3	120829	Robert Price	05/2019
2749	2^401369+1867367	120825	Enzo Doria	03/2016
2750	(10^120782+29)/3	120782	Serge Batalov	12/2014

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Probable Primes Top 10000

(271019 PRPs in the top)