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 ?
7251	2^235793-112555	70981	Enzo Doria	06/2014
7252	49936!3-3^49936	70981	Robert Price	08/2015
7253	2^235787-78795	70979	Lelio R Paula	05/2012
7254	Perrin(581132)	70970	Eric W. Weisstein	02/2011
7255	14^61913-97	70961	Lelio R Paula	01/2015
7256	2^235720+16321	70959	Yves Minet	03/2010
7257	2^235718+16095	70959	Lelio R Paula	05/2012
7258	163841#+349933	70957	Nicolas PALAU	11/2016
7259	2^235710+7	70956	Lelio R Paula	02/2012
7260	(175^31627+1)/176	70939	Eric Chen	10/2017
7261	2^235635-112087	70934	Enzo Doria	06/2014
7262	153^32467+152	70931	Norbert Schneider	11/2018
7264	2^235575-1965	70916	Lelio R Paula	05/2012
7263	6^91133+101	70916	Lelio R Paula	01/2015
7265	(21181*2^235505+1)/3	70898	Lelio R Paula	06/2014
7266	(14*10^70896+211)/9	70897	Robert Price	11/2017
7267	5^101425+84	70894	Lelio R Paula	07/2014
7268	177^31536+2	70893	Lelio R Paula	05/2013
7269	43*71^38292+4	70891	Serge Batalov	03/2016
7270	(29*2^235506-1)/112029785	70888	Lelio R Paula	01/2014
7271	11^68045-1530	70862	Enzo Doria	12/2012
7272	5*10^70858+21	70859	Robert Price	01/2017
7274	2^235326+3	70841	Donovan Johnson	02/2006
7273	34523!2+4	70841	Robert Price	02/2015
7275	(31*2^235307+1)/3	70836	Lelio R Paula	06/2012
7276	2^235308+135	70835	Lelio R Paula	02/2012
7277	r(35414,90)*1000+911	70831	Patrick De Geest	07/2004
7278	2^235274+159	70825	Lelio R Paula	02/2012
7279	3^148409+70	70810	Lelio R Paula	11/2014
7280	(19*10^70794+17)/9	70795	Robert Price	03/2015
7281	2^235108-232709	70775	Paul Bourdelais	03/2013
7282	(2^235099-2^117550+1)/5	70772		11/2006
7283	19^55325-6	70748	Lelio R Paula	08/2014
7284	257^29356+29356^257	70746	Norbert Schneider	10/2014
7285	22*10^70729+3	70731	Robert Price	10/2017
7286	2^234956+11715	70729	Lelio R Paula	05/2012
7287	(7*10^70727-43)/9	70727	Robert Price	10/2014
7288	2^234890-30341	70709	Enzo Doria	11/2012
7289	17^57461+14	70703	Lelio R Paula	01/2015
7290	(9179*2^234834-1)/5	70696	Lelio R Paula	04/2015
7291	2*10^70688+51	70689	Robert Price	10/2017
7292	123^33822-122	70685	Norbert Schneider	01/2015
7293	7*10^70680-99	70681	Robert Price	11/2017
7294	(21*2^234772-1)/2095	70672	Lelio R Paula	01/2014
7295	(29*2^234686-1)/21145	70645	Lelio R Paula	01/2014
7296	(15*2^234688-1)/5278141	70643	Lelio R Paula	01/2014
7298	2^234655-67	70639	Lelio R Paula	02/2012
7297	(79*10^70638-61)/9	70639	Robert Price	10/2015
7299	2^234652-173	70638	Lelio R Paula	02/2012
7300	2^234618-3645	70628	Lelio R Paula	05/2012
7301	(2^234610-5)/19	70624	Lelio R Paula	05/2012
7302	4*5^101038+9	70624	Lelio R Paula	10/2014
7303	2^234603+71963	70623	Enzo Doria	04/2016
7304	2^234600-113129	70622	Enzo Doria	07/2014
7305	2^234586+9	70618	Lelio R Paula	02/2012
7306	3^148008+26	70618	Robert Price	11/2013
7307	(7*10^70616-151)/9	70616	Robert Price	09/2017
7308	65^38947+32	70608	Lelio R Paula	01/2016
7309	(2^234488-3)/11	70587	Lelio R Paula	05/2012
7310	(3*2^234451+1)/35	70576	Lelio R Paula	08/2012
7311	Phi(159495,10)	70560	Maksym Voznyy	09/2015
7312	2^234383-4035	70557	Lelio R Paula	05/2012
7313	2^234315-111241	70536	Enzo Doria	05/2014
7314	14^61526+97	70517	Lelio R Paula	01/2015
7315	(3*2^234170+1)/13	70492	Lelio R Paula	08/2012
7316	51^41281-50^41281	70491	Robert Price	02/2013
7317	2^234141-112123	70484	Enzo Doria	06/2014
7318	2^234139+12285	70483	Lelio R Paula	04/2012
7319	2^234133-3163	70482	Yves Minet	04/2009
7320	2^234115+83	70476	Lelio R Paula	02/2012
7321	2^234114-1595	70476	Lelio R Paula	05/2012
7322	24^51061-23^51061	70475	Robert Price	07/2012
7323	19471^16428-2	70467	Faysal YAtim	09/2005
7324	7^83381+12	70466	Robert Price	01/2014
7325	2^234067-111427	70462	Enzo Doria	05/2014
7326	(266*10^70457+1)/3	70459	Robert Price	02/2016
7327	(31*2^234041-1)/97	70453	Lelio R Paula	01/2014
7328	2^234026+12909	70449	Lelio R Paula	04/2012
7329	2^233965-19	70431	Lelio R Paula	02/2012
7330	(5*2^233932-1)/179	70419	Lelio R Paula	01/2014
7331	2^233908-17109	70414	Enzo Doria	05/2013
7332	695^24772+24772^695	70402	Norbert Schneider	09/2016
7333	3*5^100719-2	70401	Lelio R Paula	10/2014
7334	2^233829-111355	70390	Enzo Doria	05/2014
7335	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
7336	7*3^147519+8	70386	Lelio R Paula	04/2014
7337	141^32749-2	70385	Lelio R Paula	10/2017
7338	5*7^83265+2	70368	Lelio R Paula	10/2014
7339	(23*10^70363+97)/3	70364	Robert Price	02/2017
7340	(23*2^233749-1)/35325	70363	Lelio R Paula	01/2014
7342	5^100652-13916	70353	Enzo Doria	02/2013
7341	45^42555-2	70353	Lelio R Paula	08/2013
7343	2^233661-61	70339	Lelio R Paula	02/2012
7344	2^233523-112249	70298	Enzo Doria	06/2014
7345	5*3^147324-8	70293	Lelio R Paula	04/2014
7346	2^233488-13065	70287	Enzo Doria	11/2012
7347	(3^147322+8)/42851	70286	Lelio R Paula	06/2012
7348	(22*10^70259+161)/3	70260	Robert Price	02/2017
7350	2^233388+465	70257	Lelio R Paula	11/2012
7349	14^61299+59	70257	Lelio R Paula	01/2015
7351	2^233383+94065	70256	Lelio R Paula	04/2012
7352	49471!3-6561	70253	Robert Price	11/2015
7353	7^83121+6^(83121-1)	70246	Robert Price	03/2016
7354	(197*10^70241-11)/3	70243	Robert Price	10/2017
7355	23*10^70240-7	70242	Robert Price	03/2016
7356	(71*10^70227-53)/9	70228	Robert Price	10/2015
7357	10815^17408+17408^10815	70225	Norbert Schneider	05/2019
7358	(2^233247-9)/17	70214	Lelio R Paula	05/2012
7359	(11^67421-2^67421)/9	70211	Robert Price	01/2013
7360	(23*10^70209-41)/9	70210	Robert Price	03/2015
7361	(29*10^70194-11)/9	70195	Robert Price	04/2015
7362	3^147109+196	70189	Lelio R Paula	05/2014
7363	(34*10^70191-7)/9/3/40583/573047	70181	Makoto Morimoto	05/2016
7364	9^73538+8^(73538+1)	70174	Robert Price	06/2016
7365	2*5^100391+7	70171	Lelio R Paula	10/2014
7366	99^35156-2	70159	Lelio R Paula	08/2013
7367	(68*10^70148+7)/3	70150	Robert Price	03/2016
7368	11^67360-6030	70149	Enzo Doria	01/2013
7369	(35*10^70130-377)/9	70131	Robert Price	12/2017
7370	49391!3+3^49391	70128	Robert Price	09/2015
7371	(229*10^70122-1)/3	70124	Robert Price	12/2016
7372	7^82975-92	70123	Lelio R Paula	07/2014
7373	65^38670+58	70106	Lelio R Paula	01/2016
7374	105^34684+34684^105	70103	Serge Batalov	05/2014
7375	134^32955-133	70099	Norbert Schneider	03/2015
7377	2^232836-227903	70091	Enzo Doria	12/2012
7376	2^232837-1859173	70091	Enzo Doria	03/2016
7378	3*2^232820+5	70087	Lelio R Paula	04/2014
7380	2^232799+90195	70080	Lelio R Paula	02/2013
7379	2^232799-112237	70080	Enzo Doria	06/2014
7381	2^232759+262145	70068	Lelio R Paula	04/2012
7382	3*2^232750+7	70066	Lelio R Paula	04/2014
7383	12^64918-11	70059	Lelio R Paula	01/2015
7384	7^82899-12	70058	Lelio R Paula	09/2013
7385	(22*10^70051-13)/9	70052	Robert Price	03/2015
7386	(2^232685-7)/2514625	70039	Lelio R Paula	04/2012
7387	18^55786-5363	70027	Enzo Doria	03/2013
7388	(2^(77537*3+1)+243)/7	70023	Kevin Acres	11/2013
7389	2^232602+169	70021	Lelio R Paula	02/2012
7390	(137^32768+29^32768)/2	70016	Jeppe Stig Nielsen	04/2018
7391	2^232580+72133	70014	Enzo Doria	04/2016
7392	4*6^89958-7	70002	Lelio R Paula	09/2014
7393	10^70000+80487	70001	Milton L. Brown	05/2006
7394	10^69999+134857	70000	Patrick De Geest	02/2007
7398	10^70000-9273	70000	Patrick De Geest	08/2009
7397	(79*10^69999-7)/9	70000	Robert Price	01/2015
7399	((2^43112609)/10^38420)%10^70000	70000	Michael Vang	10/2016
7395	(2^756839/10^36014)%10^70000	70000	Michael Vang	12/2016
7396	(2^74207281/10^32641)%10^70000	70000	Michael Vang	12/2016
7400	10^69999-88251	69999	Patrick De Geest	08/2009
7401	2^232507+1089	69992	Lelio R Paula	04/2012
7402	(17*2^232445+1)/5	69974	Lelio R Paula	08/2012
7403	(529^25693+1)/530	69972	Richard Fischer	12/2017
7404	7^82778+48	69956	Lelio R Paula	09/2013
7405	7*2^232381+3	69955	Lelio R Paula	04/2014
7406	2^232362-110541	69948	Enzo Doria	05/2014
7407	2^232326-112391	69938	Enzo Doria	06/2014
7408	3^146575+236	69935	Lelio R Paula	09/2013
7409	30^47341-29	69929	Norbert Schneider	02/2014
7410	5^100040-68	69925	Lelio R Paula	09/2013
7411	9946^17491+17491^9946	69923	Norbert Schneider	07/2019
7412	(35*10^69866-593)/9	69867	Robert Price	08/2017
7413	2^232045-17295	69853	Lelio R Paula	04/2012
7414	(2^231987+78557)/95	69834	Lelio R Paula	05/2012
7415	2^231955+74243	69826	Yves Minet	03/2011
7416	2^231946-15873	69823	Enzo Doria	04/2013
7417	18^55618+95	69816	Lelio R Paula	09/2013
7418	6^89712+5^(89712-1)	69810	Robert Price	02/2016
7419	2^231870+135	69800	Lelio R Paula	02/2012
7420	(23*2^231827-1)/4179	69785	Lelio R Paula	01/2014
7421	2^231778+54615	69773	Lelio R Paula	04/2012
7422	(19*2^231780+1)/235	69772	Lelio R Paula	08/2012
7423	14^60866+27	69761	Lelio R Paula	09/2013
7424	13^62619-44	69755	Lelio R Paula	09/2013
7425	(2^231715-509203)/35	69752	Lelio R Paula	05/2012
7426	2^231711-110467	69752	Enzo Doria	05/2014
7427	(19^54547+18^54547)/37	69751	Robert Price	08/2013
7428	(23*2^231697-1)/45	69748	Lelio R Paula	01/2014
7429	2^231696-1861499	69748	Enzo Doria	03/2016
7430	2^231684-147	69744	Lelio R Paula	02/2012
7431	(23*2^231686-1)/1183	69743	Lelio R Paula	01/2014
7432	2^231591-477397	69716	Paul Bourdelais	03/2013
7433	11^66916-420	69686	Enzo Doria	08/2012
7434	5^99680-13706	69674	Enzo Doria	02/2013
7435	(8*10^69674-53)/9	69674	Robert Price	11/2014
7436	(44*10^69663-413)/9	69664	Robert Price	10/2017
7437	(77*10^69656-23)/9	69657	Robert Price	10/2015
7438	6^89509+131	69652	Lelio R Paula	09/2013
7439	(78557*2^231349+1)/35	69647	Lelio R Paula	06/2014
7440	(11*10^69645+19)/3	69646	Robert Price	03/2016
7441	11^66875-28	69644	Lelio R Paula	09/2013
7442	2^231347+71483	69643	Enzo Doria	04/2016
7443	(14^60763+3^60763)/17	69641	Robert Price	04/2013
7444	(4*10^69626+173)/3	69627	Robert Price	01/2017
7445	2^231289+255	69625	Lelio R Paula	04/2012
7446	2^231234-112913	69609	Enzo Doria	06/2014
7447	(265*10^69602-7)/3	69604	Robert Price	07/2016
7448	2^231182-112841	69593	Enzo Doria	06/2014
7449	(15*2^231129+1)/23	69577	Lelio R Paula	08/2012
7450	3^145806-28	69568	Lelio R Paula	09/2013
7451	(265*10^69554-7)/3	69556	Robert Price	07/2016
7452	2^231052-113159	69554	Enzo Doria	07/2014
7453	(10^9+1)(10^129+1)(10^831+1)*(10^107199+1)/1001/(10^387+1)/(10^2493+1)/(10^35733+1)	69552	Makoto Kamada	03/2019
7454	11^66784-8	69549	Lelio R Paula	09/2013
7455	Phi(104409,10)/2296999	69546	Maksym Voznyy	07/2015
7456	2^231016-110523	69543	Enzo Doria	05/2014
7457	2^231014+577294575	69543	Lelio R Paula	02/2016
7458	14^60658+67	69522	Lelio R Paula	09/2013
7459	5^99418+36	69491	Lelio R Paula	06/2013
7460	7^82203-30	69470	Lelio R Paula	09/2013
7461	(63^38609-1)/62	69469	Paul Bourdelais	08/2017
7462	5^99359-2^99360	69449	Mike Oakes	12/2010
7463	(29*2^230684+1)/1395	69442	Lelio R Paula	08/2012
7464	(19*10^69424+77)/3	69425	Robert Price	08/2016
7465	19^54287-96	69420	Lelio R Paula	09/2013
7466	2^230541+58905	69400	Lelio R Paula	04/2012
7467	2^230506+12705	69390	Lelio R Paula	02/2013
7468	8*6^89156-5	69378	Lelio R Paula	09/2014
7469	2^230438-111347	69369	Enzo Doria	05/2014
7470	2^230428-99	69366	Lelio R Paula	02/2012
7471	(62^38699+1)/63	69362	Paul Bourdelais	08/2017
7472	3*10^69354+17	69355	Robert Price	03/2017
7473	(493*10^69340-7)/9	69342	Robert Price	07/2016
7474	(41*10^69321+373)/9	69322	Robert Price	04/2017
7475	6^89072+53	69312	Lelio R Paula	09/2013
7476	155^31639+2	69300	Lelio R Paula	05/2013
7477	3*7^81965-4	69269	Lelio R Paula	09/2014
7478	(16*10^69265+41)/3	69266	Robert Price	10/2017
7479	(86*10^69260-77)/9	69261	Robert Price	05/2016
7480	9*5^99087+4	69260	Lelio R Paula	09/2014
7481	3^145145+2660	69252	Lelio R Paula	09/2013
7483	11^66492-1140	69245	Enzo Doria	11/2012
7482	5*3^145129-4	69245	Lelio R Paula	04/2014
7484	7*3^145126+8	69244	Lelio R Paula	04/2014
7485	11^66480-2370	69232	Enzo Doria	12/2012
7486	2^229962-65	69226	Lelio R Paula	02/2012
7487	2^229958-110733	69225	Enzo Doria	05/2014
7488	V(332407)	69225	Serge Batalov	03/2015
7489	6^88959+7	69224	Lelio R Paula	09/2013
7490	15^58855-94	69219	Lelio R Paula	09/2013
7491	159773#-p(159773)	69212	Henri Lifchitz	12/2018
7492	(2^229838+47)/12081	69185	Lelio R Paula	04/2012
7493	3^144952+98	69160	Lelio R Paula	09/2013
7494	5^98941-72	69157	Lelio R Paula	06/2013
7495	(17*2^229604-1)/229	69117	Lelio R Paula	01/2014
7496	2^229585-1063	69112	Yves Minet	11/2012
7497	(13*2^229567-1)/19	69107	Lelio R Paula	01/2014
7498	(13*2^229393-1)/5	69055	Lelio R Paula	01/2014
7499	(53*10^69050-17)/9	69051	Robert Price	09/2015
7500	(43*10^69048+47)/9	69049	Robert Price	12/2017

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PRP Records

Probable Primes Top 10000

(253466 PRPs in the top)