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 ?
8251	10^65537+27	65538	Robert Price	01/2011
8252	10^65537-76859	65537	Patrick De Geest	05/2013
8253	(28*10^65532+359)/9	65533	Robert Price	11/2017
8254	(10223*2^217676+1)/3	65531	Lelio R Paula	06/2014
8255	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
8256	5*10^65509+23	65510	Robert Price	11/2017
8257	(8*10^65507-83)/3	65508	Robert Price	10/2017
8258	7*10^65492-47	65493	Robert Price	02/2017
8259	2^217547-1868407	65489	Enzo Doria	04/2016
8260	2^217531-111769	65484	Enzo Doria	05/2014
8261	7^77484-18	65482	Lelio R Paula	06/2013
8262	5754^17413+17413^5754	65473	Norbert Schneider	05/2019
8263	2^217488-113285	65471	Enzo Doria	07/2014
8264	151153#/30-30	65468	Henri Lifchitz	12/2011
8265	2^217466+4257	65464	Lelio R Paula	10/2011
8266	46396!3-81	65455	Robert Price	09/2014
8267	2^217421-113185	65451	Enzo Doria	07/2014
8268	(6883*2^217440-1)/1061193295893	65448	Lelio R Paula	04/2015
8269	2^217408-2145	65447	Lelio R Paula	10/2011
8270	2^217398-16947	65444	Enzo Doria	05/2013
8271	16097^11628+11628^16097	65443	Hans Havermann	07/2019
8272	8*5^93613+3	65434	Lelio R Paula	09/2014
8273	15929^12810+12810^15929	65430	Hans Havermann	07/2019
8274	11^62828-5310	65429	Enzo Doria	01/2013
8275	10^65426+13	65427	Robert Price	01/2011
8276	2^217341-6555	65427	Lelio R Paula	10/2011
8277	10^65426-54849	65426	Patrick De Geest	05/2013
8278	(21*2^217363-1)/56003626667	65424	Lelio R Paula	01/2014
8279	30011^14608-108	65405	Enzo Doria	07/2012
8280	119^31504-2	65389	Lelio R Paula	10/2017
8281	(43^40031-1)/42	65388	Robert Price	04/2014
8282	2^217190+94395	65381	Henri Lifchitz	02/2005
8283	15^55587+46	65376	Lelio R Paula	08/2013
8284	18443^3502+3502^18443	65368	Hans Havermann	07/2019
8285	2^217088-111833	65350	Enzo Doria	05/2014
8286	(13*2^217069-1)/1682945	65340	Lelio R Paula	01/2014
8287	(10^65340+47)/3	65340	Robert Price	11/2017
8288	(62*10^65331+1)/9	65332	Serge Batalov	11/2010
8289	2^216947-111351	65308	Enzo Doria	05/2014
8290	-E(18022)/775201845682685322943949235068359	65307	Thomas Ritschel	02/2017
8291	(13*10^65297+83)/3	65298	Robert Price	09/2016
8292	16413^9502+9502^16413	65288	Hans Havermann	07/2019
8293	5^93400-8	65284	Lelio R Paula	06/2013
8294	2^216802-165	65264	Lelio R Paula	08/2011
8295	2^216799-28635	65264	Lelio R Paula	10/2011
8296	5*10^65255+51	65256	Robert Price	01/2017
8297	2^216762-167	65252	Lelio R Paula	08/2011
8298	11^62657-5790	65251	Enzo Doria	01/2013
8299	3^136756-112880	65250	Enzo Doria	06/2014
8300	2^216752+21	65249	Lelio R Paula	08/2011
8301	3*10^65247+11	65248	Robert Price	11/2017
8302	11^62651-2700	65245	Enzo Doria	12/2012
8303	15130^15609-15609^15130	65244	Norbert Schneider	07/2018
8305	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
8304	gcd(V(790525),5F(158105)(F(158105)+1)+1)	65230	Serge Batalov	04/2015
8306	(2^216676-1017)/637	65224	Lelio R Paula	04/2012
8307	2^216652-2327	65219	Yves Minet	10/2013
8308	(9179*2^216648-1)/4667	65218	Lelio R Paula	04/2015
8309	(5*10^65203-119)/3	65204	Robert Price	04/2016
8310	15977^12034+12034^15977	65193	Hans Havermann	07/2019
8311	2^216555-113269	65190	Enzo Doria	07/2014
8313	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
8312	15753^13730+13730^15753	65181	Hans Havermann	07/2019
8314	2^216474+12915	65166	Lelio R Paula	02/2013
8315	19^50958-32	65163	Lelio R Paula	08/2013
8316	2^216442-112133	65156	Enzo Doria	06/2014
8317	2^216437-112213	65155	Enzo Doria	06/2014
8318	2^216435-112767	65154	Enzo Doria	06/2014
8319	2^216420+12705	65149	Lelio R Paula	02/2013
8320	8*3^136507-7	65132	Lelio R Paula	04/2014
8321	(-lucasV(1,2,432719)-2)/(5*461)	65128	Mike Oakes	03/2017
8322	16803^7496+7496^16803	65109	Hans Havermann	07/2019
8323	15132^15575-15575^15132	65102	Norbert Schneider	07/2018
8324	5*10^65086-51	65087	Robert Price	10/2017
8325	2^216197-111769	65082	Enzo Doria	05/2014
8327	6^83631-79	65078	Lelio R Paula	07/2013
8326	572^23601+23601^572	65078	Norbert Schneider	08/2016
8328	(3^136399-7)/544220	65074	Lelio R Paula	04/2012
8329	15592^14911+14911^15592	65074	Hans Havermann	07/2019
8330	2^216154-1421	65069	Yves Minet	01/2013
8331	2^216145-112663	65067	Enzo Doria	06/2014
8332	(7*10^65064+53)/3	65065	Robert Price	10/2017
8333	132013*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
8334	132019*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
8335	148918*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
8336	194014*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
8337	223864*10^65050+2^216091-1	65056	Gilbert Mozzo	04/2014
8339	82090*10^65050+2^216091-1	65055	Gilbert Mozzo	07/2012
8340	95133*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
8338	98142*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
8341	((2^216091-1)*34009-48)/25	65054	Serge Batalov	01/2012
8342	5977*10^65050+2^216091-1	65054	Gilbert Mozzo	03/2012
8343	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
8344	2^216091+2*29208-1	65050	Makoto Morimoto	10/2013
8345	15845^12736+12736^15845	65045	Hans Havermann	07/2019
8346	(10^(232521+1)-610^32521-1)/3	65043	Robert Price	02/2016
8347	p(13861)#/2+256	65039	Robert Price	05/2017
8348	(2^216091-2096)/(2^432918437*5220283)	65036	Makoto Morimoto	10/2017
8349	11^62439-4380	65024	Enzo Doria	01/2013
8350	16489^8776+8776^16489	65022	Hans Havermann	07/2019
8351	3^136244+2	65005	Mike Oakes	11/2009
8352	13^58343-50	64991	Lelio R Paula	07/2013
8353	331^25791-10002	64989	Enzo Doria	07/2012
8354	2^215877+131	64986	Lelio R Paula	08/2011
8355	4*5^92959+9	64977	Lelio R Paula	09/2014
8356	2^215789-18825	64959	Lelio R Paula	09/2011
8357	(2^215801-509203)/41327	64958	Lelio R Paula	05/2012
8358	U(315311)	64954	Serge Batalov	03/2015
8359	46072!3-59049	64951	Robert Price	12/2015
8360	2^215750-5955	64948	Lelio R Paula	09/2011
8361	13^58281+46	64922	Lelio R Paula	07/2013
8362	15633^14212+14212^15633	64919	Hans Havermann	07/2019
8363	2^215623+183	64909	Lelio R Paula	08/2011
8364	(46*10^64904+521)/9	64905	Robert Price	08/2017
8365	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
8366	5*2^215554+3	64889	Lelio R Paula	04/2014
8367	2^215541-112075	64885	Enzo Doria	06/2014
8368	2*10^64882-3	64883	Dmitry Domanov	11/2010
8369	16592^8121+8121^16592	64869	Hans Havermann	07/2019
8370	10^64862+342339	64863	Patrick De Geest	05/2013
8371	10^64862-47	64862	Robert Price	05/2011
8372	19^50718-84	64856	Lelio R Paula	08/2013
8373	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
8374	86413!6-12	64846	Robert Price	08/2018
8375	10^64843+4278697839	64844	Robert Price	05/2015
8376	10^64843+21967	64844	Patrick De Geest	03/2016
8377	10^64843-340073	64843	Patrick De Geest	03/2016
8378	11^62254+70	64831	Lelio R Paula	07/2013
8379	2^215351-111925	64828	Enzo Doria	05/2014
8380	2^215310-117	64815	Lelio R Paula	08/2011
8381	124^30958-123	64809	Norbert Schneider	02/2015
8382	(7*10^64807+17)/3	64808	Erik Branger	03/2014
8383	59703!4-256	64806	Robert Price	11/2019
8384	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
8385	2^215243-15949	64795	Enzo Doria	04/2013
8386	23^47581-22^47581	64793	Robert Price	08/2012
8387	(62*10^64783-17)/9	64784	Robert Price	09/2015
8388	5*3^135747-4	64769	Lelio R Paula	04/2014
8389	(59*10^64767-41)/9	64768	Robert Price	09/2015
8391	(2^215140+3)/19	64763	Lelio R Paula	04/2012
8390	2^215135-17169	64763	Enzo Doria	05/2013
8392	16078^10665+10665^16078	64762	Hans Havermann	07/2019
8393	2^215115-111277	64757	Enzo Doria	05/2014
8394	9*5^92641+2	64755	Lelio R Paula	09/2014
8395	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
8396	5791^17200+17200^5791	64720	Norbert Schneider	12/2018
8397	(5*10^64715-23)/9	64715	Robert Price	11/2014
8398	2^214938-1781	64703	Yves Minet	03/2013
8399	21003^1202+1202^21003	64688	Hans Havermann	07/2019
8400	11^62111-420	64682	Enzo Doria	08/2012
8401	18870^2677+2677^18870	64680	Hans Havermann	07/2019
8402	5^92525+42	64673	Lelio R Paula	06/2013
8403	2^214824+71893	64669	Enzo Doria	04/2016
8404	19157^2374+2374^19157	64665	Hans Havermann	08/2019
8405	2^214799-2221	64661	Yves Minet	08/2013
8406	18393^3274+3274^18393	64653	Hans Havermann	07/2019
8407	5939^17128+17128^5939	64637	Norbert Schneider	10/2018
8408	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
8409	92^32907+32907^92	64623	Serge Batalov	05/2014
8410	17650^4579+4579^17650	64613	Hans Havermann	07/2019
8411	(89*10^64608-539)/9	64609	Robert Price	11/2017
8412	6^83013+101	64597	Lelio R Paula	07/2013
8413	p(13775)#/2+8	64594	Robert Price	01/2017
8414	(7*10^64568-43)/9	64568	Robert Price	10/2014
8415	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
8416	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014
8417	(47*2^214463+1)/7	64561	Lelio R Paula	04/2015
8418	2^214458+54615	64559	Lelio R Paula	10/2011
8419	(3^135322+7)/122911408	64557	Lelio R Paula	04/2012
8420	2^214389-683113	64538	Paul Bourdelais	03/2013
8421	(76*10^64534+113)/9	64535	Robert Price	11/2017
8422	2^214369-111241	64532	Enzo Doria	05/2014
8423	(19^50461+3^50461)/22	64526	Robert Price	07/2013
8424	11^61954-3660	64519	Enzo Doria	12/2012
8425	(23*2^214319-1)/21	64517	Lelio R Paula	01/2014
8426	(58695*2^214310-1)/571	64516	Lelio R Paula	04/2015
8427	2^214300-4547	64511	Yves Minet	03/2019
8428	35^41779-34	64510	Norbert Schneider	04/2014
8429	(159^29303+1)/160	64506	Eric Chen	12/2017
8430	(89*10^64504-179)/9	64505	Robert Price	11/2017
8431	11^61939-5220	64503	Enzo Doria	01/2013
8432	(2^214271+78557)/35	64501	Lelio R Paula	05/2012
8433	L(308604)+P(308604)	64495	Robert Price	12/2017
8434	126^30706-125	64494	Norbert Schneider	02/2015
8435	gcd(V(1157265),5F(231453)(F(231453)-1)+1)	64492	Serge Batalov	04/2015
8436	2^214215+12909	64486	Lelio R Paula	10/2011
8437	16581^7738+7738^16581	64478	Hans Havermann	07/2019
8438	5^92225+66	64463	Lelio R Paula	06/2013
8439	2^214126-240551	64459	Paul Bourdelais	03/2013
8440	8*6^82827+5	64453	Lelio R Paula	09/2014
8441	(31*2^214120-1)/2170485	64452	Lelio R Paula	01/2014
8442	(31*2^214088-1)/5955	64445	Lelio R Paula	01/2014
8443	14^56227+89	64444	Lelio R Paula	08/2013
8446	2^214055-159	64437	Lelio R Paula	08/2011
8444	10^64436+2667	64437	Patrick De Geest	05/2013
8445	65^35543-64^35543	64437	Robert Price	08/2013
8447	10^64436-53	64436	Robert Price	05/2011
8448	(3^135043-lucasV(1,3,135043)+1)/3	64432	Paul Vanderveen	11/2017
8449	Phi(128878,10)/39503297927	64428	Maksym Voznyy	11/2015
8450	3^135027+100	64425	Lelio R Paula	05/2013
8451	(3^134972-7)/2	64398	Lelio R Paula	04/2012
8452	6*10^64387+7	64388	Dmitry Domanov	11/2010
8453	2^213864-18377	64380	Enzo Doria	05/2013
8454	17929^3892+3892^17929	64369	Hans Havermann	06/2019
8455	(2^213821+9)/209	64365	Lelio R Paula	04/2012
8456	2^213788+135	64357	Lelio R Paula	08/2011
8457	17703^4316+4316^17703	64352	Hans Havermann	06/2019
8458	(3^134883+2)/48313	64351	Lelio R Paula	04/2012
8459	(49^38069-46^38069)/3	64344	Serge Batalov	12/2016
8460	(11^61781+2^61781)/13	64338	Robert Price	02/2013
8461	6^82670+37	64330	Lelio R Paula	07/2013
8462	(3^134839+4)/32312959	64328	Lelio R Paula	04/2012
8463	(22*10^64326+161)/3	64327	Robert Price	02/2017
8464	11^61767-4050	64324	Enzo Doria	12/2012
8465	2^213645-114853	64314	Enzo Doria	05/2015
8466	13^57733+18	64312	Lelio R Paula	07/2013
8467	2^213621+72707	64307	Enzo Doria	04/2016
8468	10^64305+136791	64306	Patrick De Geest	05/2011
8469	10^64305-9	64305	Alexander Gramolin	01/2011
8470	V(307652)	64295	Serge Batalov	03/2015
8471	4*10^64286-89	64287	Robert Price	08/2017
8472	(2^213546-5)/2221	64281	Lelio R Paula	04/2012
8473	2^213438-58695	64252	Lelio R Paula	10/2011
8474	2^213367-105	64230	Lelio R Paula	08/2011
8475	595^23148+23148^595	64225	Norbert Schneider	07/2016
8477	3^134601+8680	64221	Lelio R Paula	05/2013
8476	(26*10^64220+61)/3	64221	Robert Price	06/2017
8478	500^23793+23793^500	64217	Norbert Schneider	08/2016
8479	179^28504-2	64216	Lelio R Paula	10/2017
8481	2^213314-455	64214	Yves Minet	02/2012
8480	39^40359-38	64214	Norbert Schneider	05/2014
8482	2^213292-16085	64208	Enzo Doria	04/2013
8483	(72524!5+1)/25	64203	Joe McLean	10/2018
8484	2^213274-77	64202	Lelio R Paula	08/2011
8485	19^50203+78	64198	Lelio R Paula	08/2013
8486	(44*10^64192-233)/9	64193	Robert Price	10/2017
8487	2^213240-112865	64192	Enzo Doria	06/2014
8488	2^213190-112391	64177	Enzo Doria	06/2014
8489	(9913*2^213184-1)/9657	64175	Lelio R Paula	04/2015
8490	14^55991+27	64173	Lelio R Paula	07/2013
8491	2^213158-112581	64167	Enzo Doria	06/2014
8492	2^213148+91	64164	Lelio R Paula	08/2011
8493	(96^32369+1)/97	64163	Paul Bourdelais	08/2017
8495	6^82439+125	64151	Lelio R Paula	07/2013
8494	7*2^213102+9	64151	Lelio R Paula	04/2014
8496	L(306854)+F(306855)	64129	Henri Lifchitz	01/2007
8497	15621^12736+12736^15621	64125	Hans Havermann	07/2019
8498	15633^12622+12622^15633	64113	Hans Havermann	07/2019
8499	610^23017+23017^610	64110	Norbert Schneider	07/2016
8500	2^212950-64875	64105	Lelio R Paula	10/2011

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Probable Primes Top 10000

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