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	2^440846+1870909	132708	Enzo Doria	05/2016
2502	2^440656-113489	132651	Enzo Doria	08/2014
2503	numbpart(14180123587)	132646	Serge Batalov	04/2017
2504	(19*10^132550+191)/3	132551	Robert Price	05/2019
2505	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
2506	(38^83891+1)/39	132529	Robert Price	09/2013
2507	2*10^132493-43	132494	Robert Price	04/2018
2508	(418*10^132441+23)/9	132443	Robert Price	02/2020
2509	2^439931-21	132433	Lelio R Paula	08/2017
2510	47^79201-46^79201	132432	Robert Price	10/2012
2511	2^439897-113653	132423	Enzo Doria	08/2014
2512	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
2513	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
2514	2^439576-113247	132326	Enzo Doria	07/2014
2515	2^439497-29143	132302	Enzo Doria	07/2015
2516	2^439409-114193	132276	Enzo Doria	12/2014
2517	(44*10^132233-233)/9	132234	Robert Price	01/2019
2518	9*10^132148-7	132149	Robert Price	09/2015
2519	(47*10^132125-119)/9	132126	Robert Price	05/2019
2520	2^438845+1870217	132106	Enzo Doria	05/2016
2521	2^438789+87855	132089	Lelio R Paula	01/2016
2522	2^438774-2786411	132085	Enzo Doria	03/2016
2523	2^438755-1848205	132079	Enzo Doria	07/2015
2524	2^438739-112087	132074	Enzo Doria	06/2014
2525	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
2526	L(631181)	131910	Henri Lifchitz	09/2008
2527	(47*10^131886-119)/9	131887	Robert Price	05/2019
2528	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
2529	2^438079-1863877	131875	Enzo Doria	03/2016
2530	(2^438067+5)/329	131869	Lelio R Paula	06/2015
2531	2^437908-113855	131824	Enzo Doria	09/2014
2532	2^437884-286349	131817	Enzo Doria	07/2015
2533	(11*10^131784-17)/3	131785	Robert Price	06/2018
2534	4*10^131719-93	131720	Robert Price	07/2020
2535	3^276062-112292	131716	Enzo Doria	07/2014
2536	(7*10^131682+89)/3	131683	Robert Price	08/2020
2537	2^437343+75953	131654	Enzo Doria	04/2016
2538	35^85243-34^85243	131621	Robert Price	05/2012
2539	(203*10^131457+1)/3	131459	Robert Price	03/2020
2540	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
2541	2^436451+1884713	131385	Enzo Doria	03/2017
2542	2^436365+35	131359	Robert Price	11/2015
2544	2^436300+1866871	131340	Enzo Doria	03/2016
2543	(7*10^131339+179)/3	131340	Robert Price	09/2018
2545	14^114592-3	131338	Paul Bourdelais	12/2020
2546	(37*10^131270+341)/9	131271	Robert Price	08/2018
2547	(5*10^131223-29)/3	131224	Robert Price	03/2018
2548	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
2549	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
2551	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
2550	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
2554	2^435773+1875557	131181	Enzo Doria	06/2016
2552	(16*10^131180+167)/3	131181	Robert Price	06/2019
2553	(26*10^131180-77)/3	131181	Robert Price	11/2019
2555	(25*10^131144-7)/9	131145	Robert Price	05/2018
2556	2^435612-2789939	131133	Enzo Doria	12/2015
2557	66^72047-65^72047	131093	Robert Price	09/2013
2558	(5*10^131090+37)/3	131091	Robert Price	03/2018
2559	2^435468+75631	131089	Enzo Doria	04/2016
2560	37^83588-2	131083	Lelio R Paula	08/2015
2561	(4^217720+11)/3	131081	Robert Price	02/2017
2562	2^435202-113193	131009	Enzo Doria	07/2014
2563	9*10^130998-19	130999	Robert Price	07/2019
2564	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
2565	2^434835-111937	130899	Enzo Doria	05/2014
2566	2^434685+72257	130854	Enzo Doria	04/2016
2567	(7*10^130825+113)/3	130826	Robert Price	02/2018
2568	2^434539-29317	130810	Enzo Doria	07/2015
2569	2^434469-114259	130789	Enzo Doria	01/2015
2570	2^434246+33	130722	Robert Price	11/2015
2571	9*10^130638+41	130639	Robert Price	08/2020
2572	2^433911-91	130621	Lelio R Paula	06/2017
2573	2^433744-114419	130570	Enzo Doria	02/2015
2575	2^433708+1869451	130560	Enzo Doria	05/2016
2574	2^433710+93	130560	Lelio R Paula	06/2017
2576	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
2577	3^273521+10	130503	Tyler NeSmith	01/2021
2578	4*10^130480+9	130481	Robert Price	05/2015
2579	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
2580	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
2581	2^433023-113497	130353	Enzo Doria	08/2014
2582	2^433002+1179379	130347	Enzo Doria	06/2016
2583	2^432974+19	130339	Robert Price	08/2015
2584	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
2585	2^432217+41	130111	Lelio R Paula	06/2017
2586	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
2587	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
2588	97^65480-2	130094	Lelio R Paula	05/2017
2589	4*10^130088-89	130089	Robert Price	11/2018
2590	2^432117-113215	130081	Enzo Doria	07/2014
2591	2^431804+72511	129986	Enzo Doria	04/2016
2592	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
2593	(47*10^129789-119)/9	129790	Robert Price	05/2019
2594	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
2595	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
2596	2^430807+1869563	129686	Enzo Doria	05/2016
2597	2^430721-21429	129660	Enzo Doria	07/2013
2598	2^430415-276271	129568	Enzo Doria	07/2015
2599	(199*10^129487-7)/3	129489	Robert Price	05/2020
2600	2^430142-2791721	129486	Enzo Doria	03/2016
2601	(7*10^129472-13)/3	129473	Robert Price	07/2018
2602	(8*10^129469+79)/3	129470	Robert Price	10/2020
2603	2^429568-21017	129313	Enzo Doria	07/2013
2604	(11*10^129239-179)/3	129240	Robert Price	09/2018
2605	2^429194-112685	129201	Enzo Doria	06/2014
2606	2^429145-2780449	129186	Enzo Doria	04/2016
2607	2^428892-113453	129110	Enzo Doria	07/2014
2608	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
2609	2^428727-113959	129060	Enzo Doria	10/2014
2610	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
2611	(10^129051-31)/3	129051	Serge Batalov	12/2014
2612	(134*10^129038+7)/3	129040	Robert Price	02/2020
2613	2^428564+71161	129011	Enzo Doria	04/2016
2614	2^428502-113285	128992	Enzo Doria	07/2014
2615	2^428421-21373	128968	Enzo Doria	06/2013
2616	L(616787)	128901	Henri Lifchitz	09/2008
2617	20^99055-3	128874	Paul Bourdelais	12/2020
2618	91^65772-2	128851	Lelio R Paula	05/2017
2619	2^428022+43	128848	Lelio R Paula	05/2017
2620	2^427999-459397	128841	Enzo Doria	05/2015
2621	2^427993+76847	128839	Enzo Doria	05/2016
2622	2^427824-1851507	128788	Enzo Doria	08/2015
2623	2^427807-21469	128783	Enzo Doria	07/2013
2624	11^123594-240	128710	Enzo Doria	09/2012
2625	2^427504-21503	128692	Enzo Doria	07/2013
2626	2^427420+91	128667	Lelio R Paula	05/2017
2627	(68*10^128645-257)/9	128646	Robert Price	07/2019
2628	2^427269-113635	128621	Enzo Doria	08/2014
2629	2^427130+1877569	128579	Enzo Doria	08/2016
2630	2^427016-115349	128545	Enzo Doria	07/2015
2631	(4*10^128510+137)/3	128511	Robert Price	03/2018
2632	2^426889-112879	128507	Enzo Doria	06/2014
2633	2^426804+1869931	128481	Enzo Doria	05/2016
2634	2^426750+77635	128465	Enzo Doria	05/2016
2635	2^426425-91	128367	Lelio R Paula	05/2017
2636	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
2637	2^426352+74971	128345	Enzo Doria	04/2016
2638	(199*10^128343-7)/3	128345	Robert Price	05/2020
2639	4*10^128343-21	128344	Robert Price	09/2018
2640	2^426300-1863689	128330	Enzo Doria	03/2016
2641	2^426293+1881017	128327	Enzo Doria	11/2016
2642	(88*10^128324-637)/9	128325	Robert Price	11/2020
2643	2^426043+35	128252	Robert Price	11/2015
2644	(4*10^128244-19)/3	128245	Robert Price	03/2018
2645	(305*10^128198+1)/9	128200	Robert Price	02/2020
2646	2^425808-459959	128181	Enzo Doria	06/2015
2647	2^425627-113605	128127	Enzo Doria	08/2014
2648	(22*10^128094+53)/3	128095	Robert Price	07/2019
2649	(86*10^128086-221)/9	128087	Robert Price	09/2019
2650	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
2651	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
2652	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
2653	2^425205+4911	128000	Marek Hubal	02/2017
2654	2^425118-113663	127974	Enzo Doria	08/2014
2655	(86*10^127967-329)/9	127968	Robert Price	01/2020
2656	2^425061+1869761	127957	Enzo Doria	05/2016
2657	746^44541+44541^746	127955	Norbert Schneider	07/2019
2658	2^424918-21141	127914	Enzo Doria	07/2013
2659	2^424864-29489	127897	Enzo Doria	08/2015
2660	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
2661	2^424632-2786639	127827	Enzo Doria	03/2016
2662	2^424577-113755	127811	Enzo Doria	09/2014
2663	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
2664	(56*10^127752+691)/9	127753	Robert Price	05/2019
2665	11^122629-720	127705	Enzo Doria	11/2012
2666	22*10^127645+3	127647	Robert Price	01/2020
2667	(5*36^81995+821)/7	127609	Eric Chen	01/2021
2668	4*10^127562-39	127563	Robert Price	09/2020
2669	2^423696-21429	127546	Enzo Doria	07/2013
2670	2^423664-1864559	127536	Enzo Doria	03/2016
2671	3^267267-4	127519	Henri Lifchitz	10/2014
2672	(103*10^127491+17)/3	127493	Robert Price	08/2020
2673	(19^99689+5^99689)/24	127477	Robert Price	09/2013
2674	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
2675	2^423328-21537	127435	Enzo Doria	07/2013
2676	(67*10^127413-7)/3	127415	Robert Price	01/2020
2677	(2*10^127407+73)/3	127407	Robert Price	09/2020
2678	(2^423165-7)/25	127384	Lelio R Paula	05/2015
2679	(112*10^127324+17)/3	127326	Robert Price	03/2020
2680	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
2681	(16*10^127259+197)/3	127260	Robert Price	04/2019
2682	(26*10^127240+61)/3	127241	Robert Price	10/2019
2683	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
2684	2^422515-114997	127190	Enzo Doria	06/2015
2685	5*10^127179-3	127180	Robert Price	07/2015
2686	(44*10^127169-233)/9	127170	Robert Price	01/2019
2687	5*10^127153+77	127154	Robert Price	12/2018
2688	736^44335+44335^736	127104	Norbert Schneider	07/2019
2689	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
2690	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
2691	2^421860-113285	126993	Enzo Doria	07/2014
2692	(2^421827-7)/11	126982	Lelio R Paula	05/2015
2693	11^121910-840	126957	Enzo Doria	12/2012
2694	(29*10^126928-77)/3	126929	Robert Price	02/2020
2695	(259*10^126919-1)/3	126921	Robert Price	12/2020
2696	10^126919-100001	126919	Robert Price	07/2020
2697	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
2698	(5*10^126871-119)/3	126872	Robert Price	03/2018
2699	331^50339-10004	126846	Enzo Doria	07/2012
2700	2^421363-2790757	126843	Enzo Doria	03/2016
2701	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
2702	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
2703	(14*10^126784-83)/3	126785	Robert Price	12/2018
2704	2^421161-286183	126783	Enzo Doria	06/2015
2705	2^420939-113935	126716	Enzo Doria	10/2014
2706	177^56363-2	126703	Lelio R Paula	10/2017
2707	2^420741-113659	126656	Enzo Doria	08/2014
2708	2^420694-21	126642	Lelio R Paula	05/2017
2709	(13*10^126638+437)/9	126639	Robert Price	04/2018
2710	(167*10^126637-17)/3	126639	Robert Price	03/2020
2711	4*10^126625+87	126626	Robert Price	08/2018
2712	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
2713	7*10^126600-99	126601	Robert Price	06/2019
2714	2^420424-59189	126561	Enzo Doria	10/2015
2715	2^420126+71893	126471	Enzo Doria	04/2016
2716	(43*10^126441+47)/9	126442	Robert Price	12/2018
2717	2^419866+1877059	126393	Enzo Doria	07/2016
2718	F(604711)	126377	Henri Lifchitz	02/2005
2719	2^419757+72707	126360	Enzo Doria	04/2016
2720	2^419720-21569	126349	Enzo Doria	07/2013
2721	2^419637+29	126324	Henri Lifchitz	02/2006
2722	2^419612+1876741	126316	Enzo Doria	07/2016
2723	2^419520+2793271	126289	Enzo Doria	03/2016
2724	(2^419447-5)/369	126264	Lelio R Paula	05/2014
2725	2^419328-1859939	126231	Enzo Doria	03/2016
2726	2^419282-1851507	126217	Enzo Doria	08/2015
2727	2^419251+1866143	126208	Enzo Doria	03/2016
2728	11^121185+2	126202	Robert Price	05/2014
2729	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
2730	2^418851+23	126087	Robert Price	09/2015
2731	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
2732	2^418829+167	126081	Lelio R Paula	01/2012
2733	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
2734	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
2735	2^418319-109501	125927	Enzo Doria	04/2014
2736	2^418316-112373	125926	Enzo Doria	06/2014
2737	(8*10^125894-29)/3	125895	Robert Price	07/2018
2738	(26*10^125886-413)/9	125887	Robert Price	05/2018
2739	2^417968+1869811	125821	Enzo Doria	06/2016
2740	2^417902+63	125802	Lelio R Paula	09/2015
2741	(10^125792-91)/9	125792	Serge Batalov	12/2014
2742	(35*10^125754-593)/9	125755	Robert Price	07/2018
2743	(32*10^125751-77)/9	125752	Robert Price	06/2018
2744	2^417704+77011	125742	Enzo Doria	05/2016
2745	(10^125706+149)/3	125706	Serge Batalov	12/2014
2746	2^417419-115309	125656	Enzo Doria	07/2015
2747	2^417300+77281	125620	Enzo Doria	05/2016
2748	2^417095-1657	125559	Yves Minet	07/2014
2749	(88*10^125492-637)/9	125493	Robert Price	11/2020
2750	2^416773-25	125462	Lelio R Paula	09/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(277054 PRPs in the top)