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 (> 30000)	Who ?	When ?
6501	(31*2^235307+1)/3	70836	Lelio R Paula	06/2012
6502	2^235308+135	70835	Lelio R Paula	02/2012
6503	r(35414,90)*1000+911	70831	Patrick De Geest	07/2004
6504	2^235274+159	70825	Lelio R Paula	02/2012
6505	3^148409+70	70810	Lelio R Paula	11/2014
6506	(19*10^70794+17)/9	70795	Robert Price	03/2015
6507	2^235108-232709	70775	Paul Bourdelais	03/2013
6508	(2^235099-2^117550+1)/5	70772		11/2006
6509	19^55325-6	70748	Lelio R Paula	08/2014
6510	257^29356+29356^257	70746	Norbert Schneider	10/2014
6511	22*10^70729+3	70731	Robert Price	10/2017
6512	2^234956+11715	70729	Lelio R Paula	05/2012
6513	(7*10^70727-43)/9	70727	Robert Price	10/2014
6514	2^234890-30341	70709	Enzo Doria	11/2012
6515	17^57461+14	70703	Lelio R Paula	01/2015
6516	(9179*2^234834-1)/5	70696	Lelio R Paula	04/2015
6517	2*10^70688+51	70689	Robert Price	10/2017
6518	123^33822-122	70685	Norbert Schneider	01/2015
6519	7*10^70680-99	70681	Robert Price	11/2017
6520	(21*2^234772-1)/2095	70672	Lelio R Paula	01/2014
6521	(29*2^234686-1)/21145	70645	Lelio R Paula	01/2014
6522	(15*2^234688-1)/5278141	70643	Lelio R Paula	01/2014
6524	2^234655-67	70639	Lelio R Paula	02/2012
6523	(79*10^70638-61)/9	70639	Robert Price	10/2015
6525	2^234652-173	70638	Lelio R Paula	02/2012
6526	2^234618-3645	70628	Lelio R Paula	05/2012
6527	(2^234610-5)/19	70624	Lelio R Paula	05/2012
6528	4*5^101038+9	70624	Lelio R Paula	10/2014
6529	2^234603+71963	70623	Enzo Doria	04/2016
6530	2^234600-113129	70622	Enzo Doria	07/2014
6531	2^234586+9	70618	Lelio R Paula	02/2012
6532	3^148008+26	70618	Robert Price	11/2013
6533	(7*10^70616-151)/9	70616	Robert Price	09/2017
6534	65^38947+32	70608	Lelio R Paula	01/2016
6535	(2^234488-3)/11	70587	Lelio R Paula	05/2012
6536	(3*2^234451+1)/35	70576	Lelio R Paula	08/2012
6537	Phi(159495,10)	70560	Maksym Voznyy	09/2015
6538	2^234383-4035	70557	Lelio R Paula	05/2012
6539	2^234315-111241	70536	Enzo Doria	05/2014
6540	14^61526+97	70517	Lelio R Paula	01/2015
6541	(3*2^234170+1)/13	70492	Lelio R Paula	08/2012
6542	51^41281-50^41281	70491	Robert Price	02/2013
6543	2^234141-112123	70484	Enzo Doria	06/2014
6544	2^234139+12285	70483	Lelio R Paula	04/2012
6545	2^234133-3163	70482	Yves Minet	04/2009
6546	2^234115+83	70476	Lelio R Paula	02/2012
6547	2^234114-1595	70476	Lelio R Paula	05/2012
6548	24^51061-23^51061	70475	Robert Price	07/2012
6549	19471^16428-2	70467	Faysal YAtim	09/2005
6550	7^83381+12	70466	Robert Price	01/2014
6551	2^234067-111427	70462	Enzo Doria	05/2014
6552	(266*10^70457+1)/3	70459	Robert Price	02/2016
6553	(31*2^234041-1)/97	70453	Lelio R Paula	01/2014
6554	2^234026+12909	70449	Lelio R Paula	04/2012
6555	2^233965-19	70431	Lelio R Paula	02/2012
6556	(5*2^233932-1)/179	70419	Lelio R Paula	01/2014
6557	2^233908-17109	70414	Enzo Doria	05/2013
6558	695^24772+24772^695	70402	Norbert Schneider	09/2016
6559	3*5^100719-2	70401	Lelio R Paula	10/2014
6560	2^233829-111355	70390	Enzo Doria	05/2014
6561	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
6562	7*3^147519+8	70386	Lelio R Paula	04/2014
6563	141^32749-2	70385	Lelio R Paula	10/2017
6564	5*7^83265+2	70368	Lelio R Paula	10/2014
6565	(23*10^70363+97)/3	70364	Robert Price	02/2017
6566	(23*2^233749-1)/35325	70363	Lelio R Paula	01/2014
6567	5^100652-13916	70353	Enzo Doria	02/2013
6568	45^42555-2	70353	Lelio R Paula	08/2013
6569	2^233661-61	70339	Lelio R Paula	02/2012
6570	2^233523-112249	70298	Enzo Doria	06/2014
6571	5*3^147324-8	70293	Lelio R Paula	04/2014
6572	2^233488-13065	70287	Enzo Doria	11/2012
6573	(3^147322+8)/42851	70286	Lelio R Paula	06/2012
6574	(22*10^70259+161)/3	70260	Robert Price	02/2017
6575	2^233388+465	70257	Lelio R Paula	11/2012
6576	14^61299+59	70257	Lelio R Paula	01/2015
6577	2^233383+94065	70256	Lelio R Paula	04/2012
6578	49471!3-6561	70253	Robert Price	11/2015
6579	7^83121+6^(83121-1)	70246	Robert Price	03/2016
6580	(197*10^70241-11)/3	70243	Robert Price	10/2017
6581	23*10^70240-7	70242	Robert Price	03/2016
6582	(71*10^70227-53)/9	70228	Robert Price	10/2015
6583	(2^233247-9)/17	70214	Lelio R Paula	05/2012
6584	(11^67421-2^67421)/9	70211	Robert Price	01/2013
6585	(23*10^70209-41)/9	70210	Robert Price	03/2015
6586	(29*10^70194-11)/9	70195	Robert Price	04/2015
6587	3^147109+196	70189	Lelio R Paula	05/2014
6588	(34*10^70191-7)/9/3/40583/573047	70181	Makoto Morimoto	05/2016
6589	9^73538+8^(73538+1)	70174	Robert Price	06/2016
6590	2*5^100391+7	70171	Lelio R Paula	10/2014
6591	99^35156-2	70159	Lelio R Paula	08/2013
6592	(68*10^70148+7)/3	70150	Robert Price	03/2016
6593	11^67360-6030	70149	Enzo Doria	01/2013
6594	(35*10^70130-377)/9	70131	Robert Price	12/2017
6595	49391!3+3^49391	70128	Robert Price	09/2015
6596	(229*10^70122-1)/3	70124	Robert Price	12/2016
6597	7^82975-92	70123	Lelio R Paula	07/2014
6598	65^38670+58	70106	Lelio R Paula	01/2016
6599	105^34684+34684^105	70103	Serge Batalov	05/2014
6600	134^32955-133	70099	Norbert Schneider	03/2015
6601	2^232836-227903	70091	Enzo Doria	12/2012
6602	2^232837-1859173	70091	Enzo Doria	03/2016
6603	3*2^232820+5	70087	Lelio R Paula	04/2014
6605	2^232799+90195	70080	Lelio R Paula	02/2013
6604	2^232799-112237	70080	Enzo Doria	06/2014
6606	2^232759+262145	70068	Lelio R Paula	04/2012
6607	3*2^232750+7	70066	Lelio R Paula	04/2014
6608	12^64918-11	70059	Lelio R Paula	01/2015
6609	7^82899-12	70058	Lelio R Paula	09/2013
6610	(22*10^70051-13)/9	70052	Robert Price	03/2015
6611	(2^232685-7)/2514625	70039	Lelio R Paula	04/2012
6612	18^55786-5363	70027	Enzo Doria	03/2013
6613	(2^(77537*3+1)+243)/7	70023	Kevin Acres	11/2013
6614	2^232602+169	70021	Lelio R Paula	02/2012
6615	(137^32768+29^32768)/2	70016	Jeppe Stig Nielsen	04/2018
6616	2^232580+72133	70014	Enzo Doria	04/2016
6617	4*6^89958-7	70002	Lelio R Paula	09/2014
6618	10^70000+80487	70001	Milton L. Brown	05/2006
6619	10^69999+134857	70000	Patrick De Geest	02/2007
6624	10^70000-9273	70000	Patrick De Geest	08/2009
6623	(79*10^69999-7)/9	70000	Robert Price	01/2015
6622	((2^43112609)/10^38420)%10^70000	70000	Michael Vang	10/2016
6620	(2^756839/10^36014)%10^70000	70000	Michael Vang	12/2016
6621	(2^74207281/10^32641)%10^70000	70000	Michael Vang	12/2016
6625	10^69999-88251	69999	Patrick De Geest	08/2009
6626	2^232507+1089	69992	Lelio R Paula	04/2012
6627	(17*2^232445+1)/5	69974	Lelio R Paula	08/2012
6628	(529^25693+1)/530	69972	Richard Fischer	12/2017
6629	7^82778+48	69956	Lelio R Paula	09/2013
6630	7*2^232381+3	69955	Lelio R Paula	04/2014
6631	2^232362-110541	69948	Enzo Doria	05/2014
6632	2^232326-112391	69938	Enzo Doria	06/2014
6633	3^146575+236	69935	Lelio R Paula	09/2013
6634	30^47341-29	69929	Norbert Schneider	02/2014
6635	5^100040-68	69925	Lelio R Paula	09/2013
6636	(35*10^69866-593)/9	69867	Robert Price	08/2017
6637	2^232045-17295	69853	Lelio R Paula	04/2012
6638	(2^231987+78557)/95	69834	Lelio R Paula	05/2012
6639	2^231955+74243	69826	Yves Minet	03/2011
6640	2^231946-15873	69823	Enzo Doria	04/2013
6641	18^55618+95	69816	Lelio R Paula	09/2013
6642	6^89712+5^(89712-1)	69810	Robert Price	02/2016
6643	2^231870+135	69800	Lelio R Paula	02/2012
6644	(23*2^231827-1)/4179	69785	Lelio R Paula	01/2014
6645	2^231778+54615	69773	Lelio R Paula	04/2012
6646	(19*2^231780+1)/235	69772	Lelio R Paula	08/2012
6647	14^60866+27	69761	Lelio R Paula	09/2013
6648	13^62619-44	69755	Lelio R Paula	09/2013
6649	(2^231715-509203)/35	69752	Lelio R Paula	05/2012
6650	2^231711-110467	69752	Enzo Doria	05/2014
6651	(19^54547+18^54547)/37	69751	Robert Price	08/2013
6652	(23*2^231697-1)/45	69748	Lelio R Paula	01/2014
6653	2^231696-1861499	69748	Enzo Doria	03/2016
6654	2^231684-147	69744	Lelio R Paula	02/2012
6655	(23*2^231686-1)/1183	69743	Lelio R Paula	01/2014
6656	2^231591-477397	69716	Paul Bourdelais	03/2013
6657	11^66916-420	69686	Enzo Doria	08/2012
6659	5^99680-13706	69674	Enzo Doria	02/2013
6658	(8*10^69674-53)/9	69674	Robert Price	11/2014
6660	(44*10^69663-413)/9	69664	Robert Price	10/2017
6661	(77*10^69656-23)/9	69657	Robert Price	10/2015
6662	6^89509+131	69652	Lelio R Paula	09/2013
6663	(78557*2^231349+1)/35	69647	Lelio R Paula	06/2014
6664	(11*10^69645+19)/3	69646	Robert Price	03/2016
6665	11^66875-28	69644	Lelio R Paula	09/2013
6666	2^231347+71483	69643	Enzo Doria	04/2016
6667	(14^60763+3^60763)/17	69641	Robert Price	04/2013
6668	(4*10^69626+173)/3	69627	Robert Price	01/2017
6669	2^231289+255	69625	Lelio R Paula	04/2012
6670	2^231234-112913	69609	Enzo Doria	06/2014
6671	(265*10^69602-7)/3	69604	Robert Price	07/2016
6672	2^231182-112841	69593	Enzo Doria	06/2014
6673	(15*2^231129+1)/23	69577	Lelio R Paula	08/2012
6674	3^145806-28	69568	Lelio R Paula	09/2013
6675	(265*10^69554-7)/3	69556	Robert Price	07/2016
6676	2^231052-113159	69554	Enzo Doria	07/2014
6677	11^66784-8	69549	Lelio R Paula	09/2013
6678	Phi(104409,10)/2296999	69546	Maksym Voznyy	07/2015
6679	2^231016-110523	69543	Enzo Doria	05/2014
6680	2^231014+577294575	69543	Lelio R Paula	02/2016
6681	14^60658+67	69522	Lelio R Paula	09/2013
6682	5^99418+36	69491	Lelio R Paula	06/2013
6683	7^82203-30	69470	Lelio R Paula	09/2013
6684	(63^38609-1)/62	69469	Paul Bourdelais	08/2017
6685	5^99359-2^99360	69449	Mike Oakes	12/2010
6686	(29*2^230684+1)/1395	69442	Lelio R Paula	08/2012
6687	(19*10^69424+77)/3	69425	Robert Price	08/2016
6688	19^54287-96	69420	Lelio R Paula	09/2013
6689	2^230541+58905	69400	Lelio R Paula	04/2012
6690	2^230506+12705	69390	Lelio R Paula	02/2013
6691	8*6^89156-5	69378	Lelio R Paula	09/2014
6692	2^230438-111347	69369	Enzo Doria	05/2014
6693	2^230428-99	69366	Lelio R Paula	02/2012
6694	(62^38699+1)/63	69362	Paul Bourdelais	08/2017
6695	3*10^69354+17	69355	Robert Price	03/2017
6696	(493*10^69340-7)/9	69342	Robert Price	07/2016
6697	(41*10^69321+373)/9	69322	Robert Price	04/2017
6698	6^89072+53	69312	Lelio R Paula	09/2013
6699	155^31639+2	69300	Lelio R Paula	05/2013
6700	3*7^81965-4	69269	Lelio R Paula	09/2014
6701	(16*10^69265+41)/3	69266	Robert Price	10/2017
6702	(86*10^69260-77)/9	69261	Robert Price	05/2016
6703	9*5^99087+4	69260	Lelio R Paula	09/2014
6704	3^145145+2660	69252	Lelio R Paula	09/2013
6706	11^66492-1140	69245	Enzo Doria	11/2012
6705	5*3^145129-4	69245	Lelio R Paula	04/2014
6707	7*3^145126+8	69244	Lelio R Paula	04/2014
6708	11^66480-2370	69232	Enzo Doria	12/2012
6709	2^229962-65	69226	Lelio R Paula	02/2012
6710	2^229958-110733	69225	Enzo Doria	05/2014
6711	V(332407)	69225	Serge Batalov	03/2015
6712	6^88959+7	69224	Lelio R Paula	09/2013
6713	15^58855-94	69219	Lelio R Paula	09/2013
6714	(2^229838+47)/12081	69185	Lelio R Paula	04/2012
6715	3^144952+98	69160	Lelio R Paula	09/2013
6716	5^98941-72	69157	Lelio R Paula	06/2013
6717	(17*2^229604-1)/229	69117	Lelio R Paula	01/2014
6718	2^229585-1063	69112	Yves Minet	11/2012
6719	(13*2^229567-1)/19	69107	Lelio R Paula	01/2014
6720	(13*2^229393-1)/5	69055	Lelio R Paula	01/2014
6721	(53*10^69050-17)/9	69051	Robert Price	09/2015
6722	(43*10^69048+47)/9	69049	Robert Price	12/2017
6723	2^229305-1868533	69028	Enzo Doria	04/2016
6724	2^229297+1385	69026	Lelio R Paula	04/2012
6725	18^54986-2441	69023	Enzo Doria	03/2013
6726	(34*10^69021-7)/9/3/67	69020	Makoto Morimoto	04/2016
6727	5^98736-14636	69014	Enzo Doria	02/2013
6728	(13^61949-5^61949)/8	69007	Robert Price	03/2013
6729	(2^229227+5)/611	69002	Lelio R Paula	04/2012
6730	2^229216-113279	69001	Enzo Doria	07/2014
6731	10^68994+51913	68995	Patrick De Geest	03/2016
6733	10^68994-10^5814-1	68994	Serge Batalov	01/2011
6732	10^68994-82947	68994	Patrick De Geest	03/2016
6734	(17*2^229136-1)/2381	68975	Lelio R Paula	01/2014
6735	2^229113+107	68970	Lelio R Paula	02/2012
6736	11^66202-4410	68943	Enzo Doria	01/2013
6737	12^63883+5	68942	Lelio R Paula	07/2013
6738	(9913*2^229002-1)/399903	68935	Lelio R Paula	04/2015
6739	2^228962-111581	68925	Enzo Doria	05/2014
6740	2^228944+81	68920	Henri Lifchitz	01/2007
6741	11^66174-54	68914	Lelio R Paula	09/2013
6742	2^228913-111265	68910	Enzo Doria	05/2014
6743	2^228902+73519	68907	Enzo Doria	04/2016
6744	(47*2^228884+1)/63	68901	Lelio R Paula	04/2015
6745	2^228821+76427	68882	Enzo Doria	05/2016
6746	3^144340+50	68868	Lelio R Paula	09/2013
6747	2^228758-112967	68864	Enzo Doria	06/2014
6748	2^228743-111379	68859	Enzo Doria	05/2014
6749	2^228741-110911	68858	Enzo Doria	05/2014
6750	3*5^98511-8	68857	Lelio R Paula	09/2014

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PRP Records

Probable Primes Top 10000

(218736 PRPs in the top)