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 ?
8501	2^189671+131	57097	Lelio R Paula	04/2011
8502	(67607*2^189651+1)/43727	57091	Lelio R Paula	05/2014
8503	(29*2^189619-1)/393	57080	Lelio R Paula	01/2014
8504	3^119587+80	57058	Lelio R Paula	10/2012
8505	2^189502-113453	57046	Enzo Doria	07/2014
8506	2^189455+153	57032	Lelio R Paula	04/2011
8507	24^41317-41317^24	57027	Norbert Schneider	07/2016
8508	2^189414-17	57020	Lelio R Paula	03/2011
8509	24^41311+23	57018	Norbert Schneider	12/2013
8510	(4*10^56989-31)/9	56989	Erik Branger	05/2011
8511	11^54712-1620	56977	Enzo Doria	11/2012
8512	2^189237-112231	56967	Enzo Doria	06/2014
8514	17^46285-48	56952	Lelio R Paula	02/2013
8513	2^189188+75241	56952	Enzo Doria	04/2016
8515	2^189181+94395	56950	Henri Lifchitz	01/2005
8516	7001^14808-108	56940	Enzo Doria	07/2012
8517	2^189147-112639	56939	Enzo Doria	06/2014
8518	(19*10^56933-43)/3	56934	Robert Price	10/2017
8519	2^189110-3	56928	M. Frind & P. Underwood	11/2002
8520	2^189069+12909	56916	Lelio R Paula	04/2011
8521	(13*10^56909+191)/3	56910	Robert Price	08/2017
8522	(35*10^56898-17)/9	56899	Serge Batalov	02/2009
8523	2^189011-5955	56898	Lelio R Paula	04/2011
8524	6^73119-5	56898	Lelio R Paula	10/2012
8525	13^51076-90	56896	Lelio R Paula	02/2013
8526	2^188997+56897	56894	Yves Minet	02/2010
8527	5^81388-13766	56888	Enzo Doria	02/2013
8528	(156^25933+1)/157	56873	Eric Chen	12/2017
8529	20^43713-6403	56872	Enzo Doria	03/2013
8530	(71*10^56858-287)/9	56859	Robert Price	05/2017
8531	2^188857-254233	56852	Gary Barnes	09/2009
8532	15^48338-88	56850	Lelio R Paula	02/2013
8533	10^56849+136437	56850	Patrick De Geest	07/2017
8534	10^56849-701	56849	Robert Price	06/2017
8535	(2^188788+78557)/3	56831	Lelio R Paula	05/2012
8536	2^188771+16095	56826	Lelio R Paula	04/2011
8537	7*2^188742-9	56818	Lelio R Paula	03/2014
8538	12^52646-65	56815	Lelio R Paula	02/2013
8539	5003^15358-158	56813	Enzo Doria	07/2012
8540	2^188713+577294575	56809	Lelio R Paula	03/2013
8541	2^188693-112099	56803	Enzo Doria	05/2014
8542	(7^67211+4^67211)/11	56799	Robert Price	10/2012
8543	2^188678-94395	56798	Lelio R Paula	09/2011
8544	20^43651-8503	56792	Enzo Doria	03/2013
8545	2^188657-2371	56792	Yves Minet	10/2013
8546	(14^49549+5^49549)/19	56789	Robert Price	05/2013
8547	(45^34351-1)/44	56788	Robert Price	05/2014
8548	7*10^56785-23	56786	Robert Price	04/2016
8549	(10^56781-31)/3	56781	Serge Batalov	12/2014
8550	7*10^56779+3	56780	Erik Branger	11/2009
8551	10^56765+259179	56766	Patrick De Geest	09/2013
8552	10^56765-249497	56765	Patrick De Geest	09/2013
8553	t(188706)	56764	Robert Price	04/2015
8554	2^188551-904327	56760	Paul Bourdelais	11/2012
8556	(64*10^56756+17)/9	56757	Robert Price	09/2015
8555	131101#+146291	56757	Makoto Morimoto	02/2016
8557	2^188539-112519	56756	Enzo Doria	06/2014
8558	6^72927+101	56749	Lelio R Paula	10/2012
8559	20^43617-1603	56748	Enzo Doria	03/2013
8560	(3^118892-8)/91358929	56718	Lelio R Paula	03/2012
8561	(509203*2^188338-1)/3	56701	Lelio R Paula	03/2015
8562	20^43567-5623	56682	Enzo Doria	03/2013
8563	2^188234-113183	56665	Enzo Doria	07/2014
8564	(139^26437+1)/140	56653	Richard Fischer	03/2018
8565	(7*2^188215-1)/1497315125	56651	Lelio R Paula	01/2014
8566	(1017*2^188171-1)/35	56647	Lelio R Paula	03/2015
8567	(34*10^56647-7)/9/37/263	56644	Makoto Morimoto	04/2016
8568	(2^188176-1017)/453814543	56638	Lelio R Paula	02/2012
8569	33*10^56634+7	56636	Robert Price	07/2016
8570	(F(31)^9241-F(30)^9241)/F(29)	56634	Wayne Halsdorf	08/2010
8571	14^49413+33	56634	Lelio R Paula	02/2013
8572	3^118680+110	56625	Lelio R Paula	10/2012
8573	(13*10^56624+161)/3	56625	Robert Price	04/2017
8574	(3^118676-2)/7516653263	56613	Lelio R Paula	03/2012
8575	(13*2^188062+1)/17	56613	Lelio R Paula	07/2012
8576	2^188056-1313	56611	Yves Minet	08/2012
8577	20^43510-5583	56608	Enzo Doria	03/2013
8578	2^188032+12285	56604	Lelio R Paula	03/2011
8579	(19*10^56597-43)/3	56598	Robert Price	10/2017
8580	(265*10^56588+17)/3	56590	Robert Price	05/2016
8581	2^187959+5775	56582	Lelio R Paula	03/2011
8582	(5*2^187959+1)/53	56581	Lelio R Paula	07/2012
8583	3*10^56575-13	56576	Robert Price	11/2017
8584	(11*2^187889-1)/351	56559	Lelio R Paula	01/2014
8585	(100049^11311+1)/100050	56553	Faysal YAtim	09/2007
8586	(19*10^56544-1)/9	56545	Serge Batalov	03/2009
8587	20^43447-8923	56526	Enzo Doria	03/2013
8588	2^187743-112177	56517	Enzo Doria	06/2014
8589	(F(5879)^47-F(5878)^47)/F(5877)	56502	Wayne Halsdorf	08/2010
8590	5^80831-22	56499	Lelio R Paula	10/2012
8591	5^80828-13166	56497	Enzo Doria	02/2013
8592	7*2^187590-5	56472	Lelio R Paula	03/2014
8593	2^187555+75473	56460	Enzo Doria	04/2016
8594	2^187541-283	56456	Yves Minet	01/2012
8595	(55*10^56453-1)/9	56454	Serge Batalov	03/2009
8596	2^187506-1451	56445	Yves Minet	08/2012
8597	189^24794-2	56443	Lelio R Paula	10/2017
8598	6^72522+143	56434	Lelio R Paula	10/2012
8599	(15185*2^187452-1)/949	56430	Lelio R Paula	03/2015
8600	2^187390+79	56411	Lelio R Paula	03/2011
8601	2^187386+12909	56409	Lelio R Paula	03/2011
8602	2^187382+613	56408	Jason Earls	04/2008
8603	(34*10^56392-7)/9/37/883/23887	56384	Makoto Morimoto	04/2016
8604	20^43337-9	56383	Lelio R Paula	02/2013
8605	(26*10^56371-173)/3	56372	Robert Price	10/2017
8606	(F(1008)^269-F(1007)^269)/F(1006)	56364	Wayne Halsdorf	08/2010
8608	2^187230+427	56362	Henri Lifchitz	01/2005
8607	11^54121-9480	56362	Enzo Doria	02/2013
8609	(21*2^187202-1)/43	56354	Lelio R Paula	01/2014
8610	2^187173-91	56345	Lelio R Paula	03/2011
8611	(23*2^187174-1)/20719883	56340	Lelio R Paula	01/2014
8612	2^187125-2833	56331	Yves Minet	09/2014
8613	9*7^66655-4	56331	Lelio R Paula	09/2014
8614	18^44874-97	56330	Lelio R Paula	02/2013
8615	60*79^29679+19	56322	Serge Batalov	03/2016
8616	5^80571+56	56317	Lelio R Paula	10/2012
8617	5^80551-22	56303	Lelio R Paula	10/2012
8618	(76*10^56281+41)/9	56282	Robert Price	10/2015
8619	(88*10^56271-43)/9	56272	Robert Price	11/2015
8620	(5*10^56256-119)/3	56257	Robert Price	04/2016
8621	1508^17691+17691^1508	56230	Serge Batalov	05/2014
8622	3^117844-58	56226	Lelio R Paula	10/2012
8623	(19*10^56224+737)/9	56225	Robert Price	10/2017
8624	95^28427+2	56221	Lelio R Paula	05/2013
8625	2^186713+76817	56207	Enzo Doria	05/2016
8626	16534^2505+2505^16534	56196	Hans Havermann	06/2016
8627	14428^7849+7849^14428	56195	Hans Havermann	06/2016
8628	2*10^56194-51	56195	Robert Price	11/2017
8629	14898^5909+5909^14898	56189	Hans Havermann	06/2016
8630	18^44758+95	56184	Lelio R Paula	02/2013
8631	2^186555-741	56159	Lelio R Paula	05/2011
8632	(4*10^56156+173)/3	56157	Robert Price	01/2017
8634	(3^117708+7)/447896	56156	Lelio R Paula	03/2012
8633	15711^3752+3752^15711	56156	Hans Havermann	06/2016
8635	(23*2^186549-1)/2429025	56152	Lelio R Paula	01/2014
8636	387^21694+21694^387	56138	Norbert Schneider	08/2014
8637	2^186422+17239	56119	Yves Minet	01/2010
8638	2^186418+4242429	56118	Jason Earls	10/2008
8639	136^26300+135	56113	Norbert Schneider	04/2015
8640	5*2^186392+9	56111	Lelio R Paula	03/2014
8641	14345^8152+8152^14345	56108	Hans Havermann	07/2016
8642	(5*2^186351-1)/39	56097	Lelio R Paula	01/2014
8643	2^186319-541237	56088	Paul Bourdelais	11/2012
8644	2*10^56083-43	56084	Robert Price	07/2017
8645	(16*10^56082-61)/9	56083	Serge Batalov	05/2009
8646	(14*10^56080-143)/3	56081	Robert Price	01/2017
8647	(265*10^56076+17)/3	56078	Robert Price	05/2016
8648	7^66346-50	56069	Lelio R Paula	10/2012
8649	20^43094-33	56067	Lelio R Paula	02/2013
8650	20^43090-1383	56062	Enzo Doria	03/2013
8651	3^117482+2660	56054	Lelio R Paula	10/2012
8652	(22699*2^186193+1)/111	56052	Lelio R Paula	05/2014
8653	(68*10^56042+13)/9	56043	Ray Chandler	09/2010
8654	3*6^71992+5^71992	56022	Mike Oakes	03/2010
8655	13691^12352+12352^13691	56020	Hans Havermann	07/2016
8656	(2^186095+7)/75	56019	Lelio R Paula	02/2012
8657	247^23412+23412^247	56018	Norbert Schneider	08/2014
8658	1839^17156+17156^1839	56008	Serge Batalov	05/2014
8659	13736^11949+11949^13736	56007	Hans Havermann	04/2016
8660	(5*2^186036-1)/11	56003	Lelio R Paula	01/2014
8661	(299*10^55998-17)/3	56000	Robert Price	01/2017
8662	p(12103)#/2-128	55994	Robert Price	05/2017
8664	2^186003-174337	55993	Gary Barnes	09/2009
8663	(2^186010+78557)/123	55993	Lelio R Paula	05/2012
8665	20^43037-93	55993	Lelio R Paula	02/2013
8666	16375^2626+2626^16375	55991	Hans Havermann	03/2016
8667	15631^3816+3816^15631	55985	Hans Havermann	03/2016
8668	21^42335-2	55977	Lelio R Paula	08/2013
8669	Phi(64736,139)	55959	Enzo Doria	07/2012
8670	15215^4762+4762^15215	55958	Hans Havermann	03/2016
8671	19317^788+788^19317	55953	Anatoly F. Selevich	12/2006
8672	13582^13165+13165^13582	55950	Hans Havermann	08/2016
8673	(78557*2^185842+1)/189	55947	Lelio R Paula	06/2014
8674	15^47562-86	55938	Lelio R Paula	02/2013
8675	4*10^55932+91	55933	Robert Price	11/2017
8676	3^117222+4	55930	Lelio R Paula	03/2012
8677	24^40519-23^40519	55925	Robert Price	07/2012
8678	13636^12623+12623^13636	55924	Hans Havermann	07/2016
8679	2^185767-99	55922	Lelio R Paula	03/2011
8680	(19*2^185750-1)/15	55917	Lelio R Paula	01/2014
8682	15^47542-58	55914	Lelio R Paula	02/2013
8681	52211!4+2	55914	Robert Price	08/2017
8683	20^42973-5583	55910	Enzo Doria	03/2013
8684	4*10^55906+21	55907	Robert Price	08/2016
8685	2^185713-111	55906	Lelio R Paula	03/2011
8686	13^50174+88	55891	Lelio R Paula	01/2013
8687	14569^6846+6846^14569	55879	Hans Havermann	08/2016
8688	Pell-LucasQ(145969)/2	55874	Eric W. Weisstein	08/2006
8689	3^117087-80	55865	Lelio R Paula	10/2012
8690	(7*10^55851-43)/9	55851	Robert Price	10/2014
8691	2^185519-169	55847	Lelio R Paula	03/2011
8692	7^66074+10	55840	Lelio R Paula	10/2012
8693	(19*10^55833-49)/3	55834	Robert Price	02/2017
8694	(2*10^55834-59)/3	55834	Robert Price	05/2017
8695	12^51732+5	55829	Lelio R Paula	01/2013
8696	3*2^185429+7	55821	Lelio R Paula	03/2014
8697	(60^31393+1)/61	55820	Paul Bourdelais	08/2017
8698	(9787*2^185420-1)/381	55819	Lelio R Paula	04/2015
8699	14427^7396+7396^14427	55819	Hans Havermann	08/2016
8700	10^55811+21	55812	Robert Price	01/2011
8701	10^55811-74103	55811	Patrick De Geest	12/2012
8702	11^53591-1530	55810	Enzo Doria	11/2012
8703	(5^79841-5^39921+1)/15334159	55800	Lelio R Paula	09/2017
8704	2^185355-2145	55798	Lelio R Paula	03/2011
8705	14531^6912+6912^14531	55794	Hans Havermann	07/2016
8706	2^185327-1615	55789	Lelio R Paula	03/2011
8707	2^185280-12779	55775	Enzo Doria	10/2012
8708	15504^3955+3955^15504	55771	Hans Havermann	07/2016
8709	(2*10^55762-59)/3	55762	Robert Price	05/2017
8710	5^79770-44	55757	Lelio R Paula	10/2012
8711	18^44416-85	55755	Lelio R Paula	02/2013
8712	2^185208-459995	55754	Enzo Doria	06/2015
8713	2^185200+1185	55751	Lelio R Paula	03/2011
8714	(536*10^55748-23)/9	55750	Robert Price	11/2017
8715	7^65964+6^(65964-1)	55747	Robert Price	03/2016
8716	2^185151-237157	55737	Gary Barnes	09/2009
8717	110017^11055-102	55734	Enzo Doria	07/2012
8718	14754^5987+5987^14754	55729	Hans Havermann	07/2016
8719	40090!3-9	55711	Robert Price	09/2014
8720	9*10^55707+89	55708	Robert Price	11/2016
8721	2^185023-2257	55698	Yves Minet	06/2009
8722	18628^977+977^18628	55696	Anatoly F. Selevich	01/2007
8723	2^185006-93	55693	Lelio R Paula	03/2011
8724	2^185003-2515	55692	Yves Minet	07/2014
8725	2^184992-78557	55689	Jorge Menendez	02/2018
8726	3*10^55679+37	55680	Robert Price	10/2017
8727	6^71524-19	55657	Lelio R Paula	10/2012
8728	2^184872-2195	55653	Yves Minet	08/2013
8729	507^20572+20572^507	55648	Norbert Schneider	06/2016
8730	(86*10^55645-311)/9	55646	Robert Price	10/2017
8731	134^26151-133	55626	Norbert Schneider	03/2015
8732	15340^4221+4221^15340	55614	Hans Havermann	07/2016
8733	27743!2+2	55612	Robert Price	01/2013
8734	20^42744+81	55612	Lelio R Paula	02/2013
8735	14609^6406+6406^14609	55611	Hans Havermann	07/2016
8736	2^184724-112883	55608	Enzo Doria	06/2014
8737	13507^13074+13074^13507	55601	Hans Havermann	07/2016
8738	2^184689+129	55597	Lelio R Paula	03/2011
8739	(9179*2^184672-1)/193	55594	Lelio R Paula	03/2015
8740	(22*10^55592-19)/3	55593	Robert Price	02/2017
8741	Phi(59984,89)	55582	Enzo Doria	05/2012
8742	11^53368+16	55578	Lelio R Paula	01/2013
8743	20^42717-1923	55577	Enzo Doria	03/2013
8744	117^26870+26870^117	55573	Serge Batalov	05/2014
8745	12^51488+55	55565	Lelio R Paula	01/2013
8746	(44*10^55558-17)/9	55559	Robert Price	06/2015
8747	(2*10^55559-23)/3	55559	Robert Price	09/2017
8748	10^55555+32857	55556	Patrick De Geest	06/2010
8749	10^55555-136721	55555	Patrick De Geest	06/2010
8750	(11*2^184541-1)/351	55551	Lelio R Paula	01/2014

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PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)