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 ?
8251	2^199522+82875	60063	Lelio R Paula	10/2012
8252	5^85928-72	60062	Lelio R Paula	10/2012
8253	39^37749+38	60062	Norbert Schneider	05/2014
8254	6^77182-143	60060	Lelio R Paula	10/2012
8255	2^199502-2145	60057	Lelio R Paula	06/2011
8256	2^199493+4257	60054	Lelio R Paula	06/2011
8257	2^199488+40755	60052	Lelio R Paula	06/2011
8258	(2^199451+9)/25619	60037	Lelio R Paula	02/2012
8259	2^199425-61	60033	Lelio R Paula	05/2011
8260	(85*10^60026+23)/9	60027	Robert Price	11/2015
8261	65^33107+62	60021	Lelio R Paula	01/2016
8263	2^199362-1215	60014	Lelio R Paula	06/2011
8262	2^199362-111633	60014	Enzo Doria	05/2014
8264	1537^18832+18832^1537	60012	Serge Batalov	05/2014
8265	2^199324-17433	60003	Enzo Doria	05/2013
8267	10^60000+204331	60001	Milton L. Brown	04/2006
8268	10^60000+87129	60001	Milton L. Brown	04/2006
8266	143^27838-2	60001	Lelio R Paula	10/2017
8269	10^59999+65197	60000	Patrick De Geest	04/2005
8283	10^60000-32529	60000	Patrick De Geest	08/2009
8284	(10^60000+2249)/9	60000	Makoto Morimoto	09/2016
8285	((2^43112609)/10^24296)%10^60000	60000	Michael Vang	10/2016
8286	(2^57885161/10^105090)%10^60000	60000	Michael Vang	10/2016
8287	(2^42643801/10^58945)%10^60000	60000	Michael Vang	10/2016
8270	(2^37156667/10^243655)%10^60000	60000	Michael Vang	10/2016
8271	(2^30402457/10^69028)%10^60000	60000	Michael Vang	11/2016
8272	(2^32582657/10^248088)%10^60000	60000	Michael Vang	11/2016
8273	(2^32582657/10^238942)%10^60000	60000	Michael Vang	11/2016
8274	(2^24036583/10^13547)%10^60000	60000	Michael Vang	11/2016
8275	(2^20996011/10^131008)%10^60000	60000	Michael Vang	11/2016
8276	(2^13466917/10^79774)%10^60000	60000	Michael Vang	11/2016
8277	(2^13466917/10^102581)%10^60000	60000	Michael Vang	11/2016
8278	(2^6972593/10^339640)%10^60000	60000	Michael Vang	11/2016
8279	(2^2976221/10^65464)%10^60000	60000	Michael Vang	12/2016
8280	(2^1398269/10^61138)%10^60000	60000	Michael Vang	12/2016
8281	(2^3021377/10^418881)%10^60000	60000	Michael Vang	12/2016
8282	(2^1257787/10^164080)%10^60000	60000	Michael Vang	12/2016
8291	10^59999-516267	59999	Patrick De Geest	06/2009
8290	20^46116-41	59999	Lelio R Paula	03/2013
8288	(2^74207281/10^184638)%10^60000	59999	Michael Vang	10/2016
8289	(2^25964951/10^135429)%10^60000	59999	Michael Vang	11/2016
8292	6^77100-55	59996	Lelio R Paula	10/2012
8294	(19*2^199274+1)/161	59987	Lelio R Paula	07/2012
8293	(23^44053+1)/24	59987	Robert Price	06/2013
8295	9^62848+6^62848-2^62848	59973	Mike Oakes	08/2010
8296	15852^6061+6061^15852	59961	Hans Havermann	08/2016
8297	19^46880-20	59948	Lelio R Paula	03/2013
8298	2^199107-17737	59938	Enzo Doria	05/2013
8299	(13*10^59928+83)/3	59929	Robert Price	09/2016
8300	10^59913+108931431	59914	Marisa Kirisame	02/2015
8301	10^59913+48619	59914	Patrick De Geest	04/2016
8302	10^59913-74123	59913	Patrick De Geest	03/2016
8303	t(199528)	59890	Robert Price	01/2015
8304	2^198903-17901	59876	Enzo Doria	05/2013
8305	9*10^59862-19	59863	Robert Price	10/2017
8306	gcd(V(776555),5F(155311)(F(155311)+1)+1)	59858	Serge Batalov	04/2015
8307	(3^125447+7)/2	59854	Lelio R Paula	04/2012
8308	5^85630+4^(85630-1)	59853	Robert Price	03/2016
8309	2^198824-2135	59852	Yves Minet	06/2013
8310	(124^28591-1)/123	59851	Richard Fischer	10/2017
8311	2^198799-16117	59845	Enzo Doria	04/2013
8312	7^70811+6^(70811+1)	59843	Robert Price	07/2016
8313	2^198774-15945	59837	Enzo Doria	04/2013
8314	2^198753-15873	59831	Enzo Doria	04/2013
8315	(31*2^198748-1)/45	59829	Lelio R Paula	01/2014
8316	2^198725+69	59823	Lelio R Paula	04/2011
8317	(68*10^59821+31)/9	59822	Robert Price	10/2015
8318	(37*25^42785+1867)/8	59812	Curtis Bright	05/2015
8319	3^125354+2660	59810	Lelio R Paula	10/2012
8320	105^29591-104	59810	Norbert Schneider	08/2013
8321	4*5^85565-3	59808	Lelio R Paula	09/2014
8322	13963842222*Bern(19550)/55727275	59803	Thomas Ritschel	03/2014
8324	125330^3+3^125330	59798	Anatoly F. Selevich	06/2010
8323	2^198643-3189	59798	Yves Minet	10/2014
8325	(13*10^59797+191)/3	59798	Robert Price	08/2017
8326	(7*10^59796-1)/3	59797	Erik Branger	03/2014
8327	2^198595+153	59784	Lelio R Paula	04/2011
8328	(19*10^59766+161)/9	59767	Robert Price	07/2016
8329	2^198510-1965	59758	Lelio R Paula	06/2011
8330	2^198506-19077	59757	Enzo Doria	05/2013
8331	2^198484-16005	59750	Enzo Doria	04/2013
8332	2^198473-16821	59747	Enzo Doria	05/2013
8333	(2^198481-5)/28311	59745	Lelio R Paula	02/2012
8334	2^198400-189	59725	Lelio R Paula	04/2011
8335	2^198384-12837	59720	Enzo Doria	10/2012
8336	42694!3-729	59719	Robert Price	09/2014
8337	2^198320-18717	59701	Enzo Doria	05/2013
8338	20^45881-1183	59693	Enzo Doria	03/2013
8339	2^198224-6855	59672	Lelio R Paula	05/2011
8340	2^198181-19101	59659	Enzo Doria	05/2013
8341	5*10^59650+41	59651	Robert Price	08/2017
8342	2^198149-112213	59649	Enzo Doria	06/2014
8343	2^198138+73699	59646	Enzo Doria	04/2016
8344	2^198129-55	59643	Lelio R Paula	04/2011
8345	5^85318-14636	59635	Enzo Doria	02/2013
8346	(2^198119+47)/1560935	59634	Lelio R Paula	02/2012
8347	2^198090-16097	59632	Enzo Doria	04/2013
8348	9*10^59617+89	59618	Robert Price	11/2016
8349	42625!3+81	59612	Robert Price	09/2014
8350	5^85277-84	59607	Lelio R Paula	10/2012
8351	(871*10^59599-7)/9	59601	Robert Price	11/2017
8352	2^197984-18245	59600	Enzo Doria	05/2013
8353	2^197951-2137	59590	Yves Minet	06/2013
8354	(38*10^59589+187)/9	59590	Robert Price	11/2017
8355	66^32749-65^32749	59589	Robert Price	09/2013
8356	5*10^59586-3	59587	Dmitry Domanov	11/2010
8357	(35*10^59584-197)/9	59585	Robert Kinser	10/2017
8358	2^197932-3959	59584	Yves Minet	04/2017
8359	2^197909-18961	59577	Enzo Doria	05/2013
8360	(3^124871+2)/45031	59574	Lelio R Paula	04/2012
8361	2^197872+81	59566	Henri Lifchitz	10/2005
8362	2^197873-18469	59566	Enzo Doria	05/2013
8363	(22*10^59558-31)/9	59559	Robert Price	04/2015
8365	2^197840-465	59556	Lelio R Paula	05/2011
8364	(31*2^197856-1)/3889605	59556	Lelio R Paula	01/2014
8366	2^197808-17805	59547	Enzo Doria	05/2013
8367	2^197781-17905	59539	Enzo Doria	05/2013
8368	2^197777-17473	59537	Enzo Doria	05/2013
8369	6^76507-149	59535	Lelio R Paula	10/2012
8371	Phi(61456,109)	59526	Enzo Doria	05/2012
8370	18^47420+23	59526	Lelio R Paula	03/2013
8372	(59^33613+1)/60	59522	Paul Bourdelais	08/2017
8373	3^124747+94	59520	Lelio R Paula	10/2012
8374	17^48370+18	59517	Lelio R Paula	03/2013
8375	20^45740-1523	59510	Enzo Doria	03/2013
8376	(47*10^59509+493)/9	59510	Robert Price	11/2017
8377	(7*2^197642-1)/3051	59494	Lelio R Paula	01/2014
8378	18^47390-1853	59488	Enzo Doria	03/2013
8379	(2^197581-7)/1915	59475	Lelio R Paula	02/2012
8380	(24737*2^197559+1)/77	59474	Lelio R Paula	06/2014
8381	2^197540-2459	59466	Yves Minet	07/2014
8382	(44*10^59454+1)/9	59455	Serge Batalov	11/2010
8383	2^197494-17805	59452	Enzo Doria	05/2013
8384	2^197482-16821	59449	Enzo Doria	05/2013
8385	2^197485+75767	59449	Enzo Doria	04/2016
8386	(3*2^197483+1)/25	59448	Lelio R Paula	07/2012
8387	2^197466-1868351	59444	Enzo Doria	04/2016
8388	2^197411-17781	59427	Enzo Doria	05/2013
8389	(F(142164)^3-F(142163)^3)/F(142162)	59421	Wayne Halsdorf	03/2012
8390	2^197392-114629	59421	Enzo Doria	05/2015
8391	2^197355-157	59410	Lelio R Paula	04/2011
8392	5^84992-84	59407	Lelio R Paula	10/2012
8393	2*3^124504-5	59404	Lelio R Paula	04/2014
8394	2^197307-19165	59396	Enzo Doria	05/2013
8396	2^197303+32769	59395	Lelio R Paula	05/2011
8395	2*10^59394-69	59395	Robert Price	07/2017
8397	(53*10^59389+1)/9	59390	Serge Batalov	11/2010
8398	6^76316-35	59386	Lelio R Paula	10/2012
8399	2^197259-2929	59381	Yves Minet	09/2014
8400	lucasU(46,1,35715)-lucasU(46,1,35714)	59377	Mike Oakes	04/2009
8401	17^48253-6	59373	Lelio R Paula	03/2013
8402	2^197156-15837	59350	Enzo Doria	04/2013
8403	2^197152-4295	59349	Yves Minet	08/2018
8404	2^197149-18481	59348	Enzo Doria	05/2013
8405	2^197142-17157	59346	Enzo Doria	05/2013
8407	(F(6)^65707-F(5)^65707)/F(4)	59339	Wayne Halsdorf	04/2010
8406	(8^65707-5^65707)/3	59339	Robert Price	12/2012
8408	(2*14283^14283+1)/7925497975	59334	David Broadhurst	09/2010
8409	2^197012-111719	59307	Enzo Doria	05/2014
8410	2^196975+513	59296	Lelio R Paula	05/2011
8411	(61*10^59294+119)/9	59295	Robert Price	09/2017
8412	4*10^59292+39	59293	Robert Price	11/2017
8413	2^196960+97	59291	Lelio R Paula	04/2011
8414	9^62116+8^(62116-1)	59274	Robert Price	03/2016
8415	2^196900-97305	59273	Lelio R Paula	09/2011
8416	5*6^76155+7	59261	Lelio R Paula	09/2014
8417	15^50385-14	59258	Wojciech Florek	06/2006
8418	(136777#-1)/8823581477	59254	Donovan Johnson	05/2006
8419	(2^196744-3)*6-7	59227	Gilbert Mozzo	05/2016
8420	(67607*2^196696+1)/3	59216	Lelio R Paula	05/2014
8421	2^196696-112967	59212	Enzo Doria	06/2014
8422	20^45508-4223	59208	Enzo Doria	03/2013
8423	gcd(Phi(325820,10),(10^16291+1)^3(10^16291+1-10^8146)+(10^32582+10^16291)(10^8146+1)+10^48873)	59201	Serge Batalov	04/2015
8424	14^51651-81	59199	Lelio R Paula	03/2013
8425	2^196650-1451	59198	Yves Minet	08/2012
8426	2^196636-2797799	59194	Enzo Doria	04/2016
8427	1111*2^196610-555	59189	Henri Lifchitz	04/2005
8428	3^124041+658	59183	Lelio R Paula	10/2012
8429	2^196590-111797	59180	Enzo Doria	05/2014
8430	(10^59174-13)/3	59174	Robert Price	02/2017
8431	(2*10^59174-113)/3	59174	Robert Price	09/2017
8432	(9179*2^196533-1)/783	59164	Lelio R Paula	04/2015
8433	379*10^59152+9	59155	Arkadiusz Wesolowski	10/2011
8434	(404*10^59149-53)/9	59151	Robert Price	11/2017
8435	13^53095+40	59145	Lelio R Paula	03/2013
8437	2*F(282999)-1	59144	Henri Lifchitz	12/2009
8436	4*7^69984+3	59144	Lelio R Paula	09/2014
8438	(5*10^59142+1)/3	59143	Erik Branger	12/2013
8439	2^196463+5711	59142	Lelio R Paula	10/2011
8440	2^196453-97305	59139	Lelio R Paula	09/2011
8441	(28*10^59135+53)/9	59136	Serge Batalov	11/2008
8442	(28*10^59133+113)/3	59134	Robert Price	03/2016
8443	2^196434+7	59133	Lelio R Paula	04/2011
8444	(8*10^59127-29)/3	59128	Robert Price	05/2016
8445	2^196414+255	59127	Lelio R Paula	05/2011
8446	5^84586-92	59124	Lelio R Paula	10/2012
8447	2^196388-17177	59119	Enzo Doria	05/2013
8448	79427!6-6	59119	Robert Price	08/2018
8449	3^123890+20	59111	Lelio R Paula	10/2012
8450	2^196355-1021777	59109	Paul Bourdelais	11/2012
8451	11^56754-1410	59104	Enzo Doria	11/2012
8452	(7*2^196297-1)/1200407	59087	Lelio R Paula	01/2014
8453	(16*10^59062-19)/3	59063	Robert Price	03/2016
8454	35^38249-1228	59060	Enzo Doria	03/2013
8455	5^84475-18	59046	Lelio R Paula	10/2012
8456	2^196123-17701	59039	Enzo Doria	05/2013
8457	12^54702-31	59034	Lelio R Paula	03/2013
8458	2^196101-175	59033	Lelio R Paula	04/2011
8459	2^196085+5775	59028	Lelio R Paula	05/2011
8460	2^196034+11715	59013	Lelio R Paula	05/2011
8461	2^196018-18485	59008	Enzo Doria	05/2013
8462	2^195984-2163	58998	Yves Minet	08/2013
8463	3^123645-16	58994	Lelio R Paula	10/2012
8464	39^37078-38	58994	Norbert Schneider	05/2014
8465	2^195958-16853	58990	Enzo Doria	05/2013
8466	2^195930-3071	58981	Yves Minet	10/2014
8467	2^195924+513	58980	Lelio R Paula	05/2011
8468	2^195863+155	58961	Lelio R Paula	04/2011
8469	(28*10^58956+113)/3	58957	Robert Price	03/2016
8470	11^56612-9300	58956	Enzo Doria	02/2013
8471	2^195833-17173	58952	Enzo Doria	05/2013
8472	(27*2^195833-1)/53	58952	Lelio R Paula	01/2014
8473	(13*2^195821-1)/122425	58945	Lelio R Paula	01/2014
8474	139^27504-138	58942	Norbert Schneider	10/2015
8475	(418*10^58923+23)/9	58925	Robert Price	08/2017
8476	3^123495+44	58923	Lelio R Paula	10/2012
8477	2^195737-18565	58923	Enzo Doria	05/2013
8478	79185!6-16	58921	Robert Price	08/2018
8479	14^51407+47	58920	Lelio R Paula	03/2013
8480	2^195691-99	58909	Lelio R Paula	04/2011
8481	2^195667-1859827	58902	Enzo Doria	04/2016
8482	2^195642+75499	58895	Enzo Doria	04/2016
8483	(299*10^58893+1)/3	58895	Robert Price	11/2017
8484	8*6^75678+5	58890	Lelio R Paula	09/2014
8486	2^195618+73189	58887	Enzo Doria	04/2016
8485	(3928^20480+1)/(3928^4096+1)	58887	Serge Batalov	01/2017
8487	t(197953)	58881	Robert Price	12/2014
8488	2^195581-16105	58876	Enzo Doria	04/2013
8489	(8*10^58872+67)/3	58873	Robert Price	01/2017
8490	7*2^195542-5	58865	Lelio R Paula	03/2014
8491	2*10^58861+9^58861	58862	Mike Oakes	04/2011
8492	11^56513-1620	58853	Enzo Doria	11/2012
8493	2^195496+165	58851	Lelio R Paula	04/2011
8494	5^84187+66	58845	Lelio R Paula	10/2012
8495	(28*10^58843-43)/3	58844	Robert Price	04/2016
8496	2^195462-17565	58840	Enzo Doria	05/2013
8497	2^195449-4171	58837	Yves Minet	02/2018
8498	2^195435+59273	58832	Yves Minet	01/2011
8499	2^195424-18605	58829	Enzo Doria	05/2013
8500	2^195385-111	58817	Lelio R Paula	04/2011

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Probable Primes Top 10000

(224660 PRPs in the top)