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 ?
9501	189^24794-2	56443	Lelio R Paula	10/2017
9502	13600^13653-13653^13600	56436	Norbert Schneider	08/2018
9503	6^72522+143	56434	Lelio R Paula	10/2012
9504	(15185*2^187452-1)/949	56430	Lelio R Paula	03/2015
9505	15992^3369+3369^15992	56412	Hans Havermann	03/2019
9506	2^187390+79	56411	Lelio R Paula	03/2011
9507	2^187386+12909	56409	Lelio R Paula	03/2011
9508	2^187382+613	56408	Jason Earls	04/2008
9509	13931^11188+11188^13931	56404	Hans Havermann	04/2019
9510	(34*10^56392-7)/9/37/883/23887	56384	Makoto Morimoto	04/2016
9511	20^43337-9	56383	Lelio R Paula	02/2013
9512	(26*10^56371-173)/3	56372	Robert Price	10/2017
9513	(F(1008)^269-F(1007)^269)/F(1006)	56364	Wayne Halsdorf	08/2010
9515	2^187230+427	56362	Henri Lifchitz	01/2005
9514	11^54121-9480	56362	Enzo Doria	02/2013
9516	10758^13979-13979^10758	56360	Norbert Schneider	09/2018
9517	10635^13996-13996^10635	56359	Norbert Schneider	09/2018
9518	(21*2^187202-1)/43	56354	Lelio R Paula	01/2014
9519	2^187173-91	56345	Lelio R Paula	03/2011
9520	(23*2^187174-1)/20719883	56340	Lelio R Paula	01/2014
9521	2^187125-2833	56331	Yves Minet	09/2014
9522	9*7^66655-4	56331	Lelio R Paula	09/2014
9524	18^44874-97	56330	Lelio R Paula	02/2013
9523	13304^13659-13659^13304	56330	Norbert Schneider	08/2018
9525	60*79^29679+19	56322	Serge Batalov	03/2016
9526	5^80571+56	56317	Lelio R Paula	10/2012
9527	5^80551-22	56303	Lelio R Paula	10/2012
9528	(76*10^56281+41)/9	56282	Robert Price	10/2015
9529	(88*10^56271-43)/9	56272	Robert Price	11/2015
9530	9191^14198-14198^9191	56272	Norbert Schneider	02/2019
9531	(5*10^56256-119)/3	56257	Robert Price	04/2016
9532	2^186840-4475	56245	Yves Minet	03/2019
9533	1508^17691+17691^1508	56230	Serge Batalov	05/2014
9534	3^117844-58	56226	Lelio R Paula	10/2012
9535	(19*10^56224+737)/9	56225	Robert Price	10/2017
9536	95^28427+2	56221	Lelio R Paula	05/2013
9537	2^186713+76817	56207	Enzo Doria	05/2016
9538	16534^2505+2505^16534	56196	Hans Havermann	06/2016
9539	14428^7849+7849^14428	56195	Hans Havermann	06/2016
9540	2*10^56194-51	56195	Robert Price	11/2017
9541	14898^5909+5909^14898	56189	Hans Havermann	06/2016
9542	18^44758+95	56184	Lelio R Paula	02/2013
9543	7478^14503-14503^7478	56182	Norbert Schneider	11/2018
9544	2^186555-741	56159	Lelio R Paula	05/2011
9545	(4*10^56156+173)/3	56157	Robert Price	01/2017
9547	(3^117708+7)/447896	56156	Lelio R Paula	03/2012
9546	15711^3752+3752^15711	56156	Hans Havermann	06/2016
9548	(23*2^186549-1)/2429025	56152	Lelio R Paula	01/2014
9549	387^21694+21694^387	56138	Norbert Schneider	08/2014
9550	2^186422+17239	56119	Yves Minet	01/2010
9551	2^186418+4242429	56118	Jason Earls	10/2008
9552	136^26300+135	56113	Norbert Schneider	04/2015
9553	5*2^186392+9	56111	Lelio R Paula	03/2014
9554	14345^8152+8152^14345	56108	Hans Havermann	07/2016
9555	(5*2^186351-1)/39	56097	Lelio R Paula	01/2014
9556	2^186319-541237	56088	Paul Bourdelais	11/2012
9557	2*10^56083-43	56084	Robert Price	07/2017
9558	(16*10^56082-61)/9	56083	Serge Batalov	05/2009
9559	(14*10^56080-143)/3	56081	Robert Price	01/2017
9560	(265*10^56076+17)/3	56078	Robert Price	05/2016
9561	7^66346-50	56069	Lelio R Paula	10/2012
9562	20^43094-33	56067	Lelio R Paula	02/2013
9563	20^43090-1383	56062	Enzo Doria	03/2013
9564	3^117482+2660	56054	Lelio R Paula	10/2012
9565	(22699*2^186193+1)/111	56052	Lelio R Paula	05/2014
9566	(68*10^56042+13)/9	56043	Ray Chandler	09/2010
9567	3*6^71992+5^71992	56022	Mike Oakes	03/2010
9568	13691^12352+12352^13691	56020	Hans Havermann	07/2016
9569	(2^186095+7)/75	56019	Lelio R Paula	02/2012
9570	247^23412+23412^247	56018	Norbert Schneider	08/2014
9571	1839^17156+17156^1839	56008	Serge Batalov	05/2014
9572	13736^11949+11949^13736	56007	Hans Havermann	04/2016
9573	(5*2^186036-1)/11	56003	Lelio R Paula	01/2014
9574	(299*10^55998-17)/3	56000	Robert Price	01/2017
9575	p(12103)#/2-128	55994	Robert Price	05/2017
9576	2^186003-174337	55993	Gary Barnes	09/2009
9577	(2^186010+78557)/123	55993	Lelio R Paula	05/2012
9578	20^43037-93	55993	Lelio R Paula	02/2013
9579	16375^2626+2626^16375	55991	Hans Havermann	03/2016
9580	11083^13842-13842^11083	55987	Norbert Schneider	11/2018
9581	15631^3816+3816^15631	55985	Hans Havermann	03/2016
9582	21^42335-2	55977	Lelio R Paula	08/2013
9583	Phi(64736,139)	55959	Enzo Doria	07/2012
9584	15215^4762+4762^15215	55958	Hans Havermann	03/2016
9585	19317^788+788^19317	55953	Anatoly F. Selevich	12/2006
9586	13582^13165+13165^13582	55950	Hans Havermann	08/2016
9587	(78557*2^185842+1)/189	55947	Lelio R Paula	06/2014
9588	11867^13730-13730^11867	55941	Norbert Schneider	09/2018
9589	15^47562-86	55938	Lelio R Paula	02/2013
9590	4*10^55932+91	55933	Robert Price	11/2017
9591	3^117222+4	55930	Lelio R Paula	03/2012
9592	24^40519-23^40519	55925	Robert Price	07/2012
9593	13636^12623+12623^13636	55924	Hans Havermann	07/2016
9594	2^185767-99	55922	Lelio R Paula	03/2011
9595	(19*2^185750-1)/15	55917	Lelio R Paula	01/2014
9596	15^47542-58	55914	Lelio R Paula	02/2013
9597	52211!4+2	55914	Robert Price	08/2017
9598	20^42973-5583	55910	Enzo Doria	03/2013
9599	4*10^55906+21	55907	Robert Price	08/2016
9600	2^185713-111	55906	Lelio R Paula	03/2011
9601	13^50174+88	55891	Lelio R Paula	01/2013
9602	14569^6846+6846^14569	55879	Hans Havermann	08/2016
9603	Pell-LucasQ(145969)/2	55874	Eric W. Weisstein	08/2006
9604	3^117087-80	55865	Lelio R Paula	10/2012
9605	8384^14237-14237^8384	55859	Norbert Schneider	03/2019
9606	(7*10^55851-43)/9	55851	Robert Price	10/2014
9607	2^185519-169	55847	Lelio R Paula	03/2011
9608	7^66074+10	55840	Lelio R Paula	10/2012
9609	(19*10^55833-49)/3	55834	Robert Price	02/2017
9610	(2*10^55834-59)/3	55834	Robert Price	05/2017
9611	2^185463-4237	55830	Yves Minet	08/2018
9612	12^51732+5	55829	Lelio R Paula	01/2013
9613	11252^13779-13779^11252	55822	Norbert Schneider	10/2018
9614	3*2^185429+7	55821	Lelio R Paula	03/2014
9615	(60^31393+1)/61	55820	Paul Bourdelais	08/2017
9617	(9787*2^185420-1)/381	55819	Lelio R Paula	04/2015
9616	14427^7396+7396^14427	55819	Hans Havermann	08/2016
9618	10^55811+21	55812	Robert Price	01/2011
9619	10^55811-74103	55811	Patrick De Geest	12/2012
9620	11^53591-1530	55810	Enzo Doria	11/2012
9621	(5^79841-5^39921+1)/15334159	55800	Lelio R Paula	09/2017
9622	2^185355-2145	55798	Lelio R Paula	03/2011
9623	14531^6912+6912^14531	55794	Hans Havermann	07/2016
9624	2^185327-1615	55789	Lelio R Paula	03/2011
9625	2^185280-12779	55775	Enzo Doria	10/2012
9626	15504^3955+3955^15504	55771	Hans Havermann	07/2016
9627	(2*10^55762-59)/3	55762	Robert Price	05/2017
9628	5^79770-44	55757	Lelio R Paula	10/2012
9629	18^44416-85	55755	Lelio R Paula	02/2013
9630	2^185208-459995	55754	Enzo Doria	06/2015
9631	2^185200+1185	55751	Lelio R Paula	03/2011
9632	(536*10^55748-23)/9	55750	Robert Price	11/2017
9633	7^65964+6^(65964-1)	55747	Robert Price	03/2016
9634	2^185151-237157	55737	Gary Barnes	09/2009
9635	110017^11055-102	55734	Enzo Doria	07/2012
9637	14754^5987+5987^14754	55729	Hans Havermann	07/2016
9636	12591^13592-13592^12591	55729	Norbert Schneider	07/2018
9638	40090!3-9	55711	Robert Price	09/2014
9639	9*10^55707+89	55708	Robert Price	11/2016
9640	2^185023-2257	55698	Yves Minet	06/2009
9641	18628^977+977^18628	55696	Anatoly F. Selevich	01/2007
9642	2^185006-93	55693	Lelio R Paula	03/2011
9643	2^185003-2515	55692	Yves Minet	07/2014
9644	2^184992-78557	55689	Jorge Menendez	02/2018
9645	3*10^55679+37	55680	Robert Price	10/2017
9646	6^71524-19	55657	Lelio R Paula	10/2012
9647	2^184872-2195	55653	Yves Minet	08/2013
9648	507^20572+20572^507	55648	Norbert Schneider	06/2016
9649	(86*10^55645-311)/9	55646	Robert Price	10/2017
9650	134^26151-133	55626	Norbert Schneider	03/2015
9651	15340^4221+4221^15340	55614	Hans Havermann	07/2016
9652	27743!2+2	55612	Robert Price	01/2013
9653	20^42744+81	55612	Lelio R Paula	02/2013
9654	14609^6406+6406^14609	55611	Hans Havermann	07/2016
9655	2^184724-112883	55608	Enzo Doria	06/2014
9656	13507^13074+13074^13507	55601	Hans Havermann	07/2016
9657	2^184689+129	55597	Lelio R Paula	03/2011
9658	(9179*2^184672-1)/193	55594	Lelio R Paula	03/2015
9659	(22*10^55592-19)/3	55593	Robert Price	02/2017
9660	Phi(59984,89)	55582	Enzo Doria	05/2012
9661	8815^14088-14088^8815	55581	Norbert Schneider	11/2018
9662	11^53368+16	55578	Lelio R Paula	01/2013
9663	20^42717-1923	55577	Enzo Doria	03/2013
9664	117^26870+26870^117	55573	Serge Batalov	05/2014
9665	12^51488+55	55565	Lelio R Paula	01/2013
9666	(44*10^55558-17)/9	55559	Robert Price	06/2015
9667	(2*10^55559-23)/3	55559	Robert Price	09/2017
9668	10^55555+32857	55556	Patrick De Geest	06/2010
9669	10^55555-136721	55555	Patrick De Geest	06/2010
9670	(11*2^184541-1)/351	55551	Lelio R Paula	01/2014
9671	20^42696-2043	55549	Enzo Doria	03/2013
9672	(35*10^55547-737)/9	55548	Robert Price	11/2017
9673	(2*10^55544+1)/3	55544	Serge Batalov	06/2009
9674	(-lucasV(1,2,369056)+2)/(389109*457)	55542	Mike Oakes	04/2017
9675	5003^15013-160	55537	Enzo Doria	07/2012
9676	39^34896-2	55522	Lelio R Paula	08/2013
9677	(6^71345-61)/5	55517	Lelio R Paula	05/2014
9678	2^184407-3019	55513	Yves Minet	10/2014
9679	(43*10^55512-61)/9	55513	Robert Price	06/2015
9680	20^42667-843	55512	Enzo Doria	03/2013
9681	133^26134-132	55505	Norbert Schneider	03/2015
9682	(31*2^184378-1)/711	55502	Lelio R Paula	01/2014
9683	9*7^65667-4	55497	Lelio R Paula	09/2014
9684	2^184342-173	55493	Lelio R Paula	03/2011
9685	15^47182+92	55491	Lelio R Paula	02/2013
9686	5^79378+6	55483	Lelio R Paula	10/2012
9687	581^20068+20068^581	55472	Norbert Schneider	06/2016
9688	(2^184232+1)/257	55457	Donovan Johnson	03/2005
9689	18^44177-1415	55455	Enzo Doria	03/2013
9690	2^184203-2797867	55451	Enzo Doria	04/2016
9691	2^184189+17	55447	Lelio R Paula	03/2011
9692	2^184183+26123	55445	Yves Minet	01/2010
9693	Phi(77077,10)	55441	Ray Chandler	05/2009
9694	2^184141-113251	55432	Enzo Doria	07/2014
9695	2^184093-504613	55418	Gary Barnes	09/2009
9696	6517^14528-14528^6517	55411	Norbert Schneider	12/2018
9697	(lucasV(1,2,368167)+2)/(1111031307*5647)	55404	Mike Oakes	04/2017
9698	2^184044-111269	55403	Enzo Doria	05/2014
9699	14051^8766+8766^14051	55401	Hans Havermann	07/2016
9700	98^27819+27819^98	55394	Serge Batalov	05/2014
9701	(178*10^55390-7)/9	55392	Robert Price	08/2017
9702	58046^9+9^58046	55390	Andrey Kulsha	02/2004
9703	7^65536+2*59232-2	55385	Jiahao He	07/2017
9704	2^183980+75241	55384	Enzo Doria	04/2016
9705	10^55372+37	55373	Robert Price	01/2011
9706	10^55372-49967	55372	Patrick De Geest	12/2012
9707	(13*10^55367+17)/3	55368	Robert Price	06/2015
9708	2*6^71150+7	55366	Lelio R Paula	09/2014
9709	19^43296-62	55365	Lelio R Paula	02/2013
9710	19^43295+10	55364	Lelio R Paula	02/2013
9711	(29*10^55362-11)/9	55363	Robert Price	04/2015
9712	(37*10^55359+53)/9	55360	Robert Price	05/2015
9713	19^43283+72	55349	Lelio R Paula	02/2013
9714	2^183800-65	55330	Lelio R Paula	03/2011
9715	21001^12801-110	55329	Enzo Doria	07/2012
9716	33^36433-32^36433	55325	Robert Price	04/2012
9717	(17*2^183729+1)/145	55308	Lelio R Paula	07/2012
9718	9932^13837-13837^9932	55307	Norbert Schneider	11/2018
9719	9^57952+8^(57952-1)	55301	Robert Price	03/2016
9720	14872^5229+5229^14872	55301	Hans Havermann	08/2016
9721	61^30972-2	55296	Lelio R Paula	08/2013
9722	2^183671-112537	55291	Enzo Doria	06/2014
9723	(2^183687+7)/497939745	55287	Lelio R Paula	02/2012
9724	3^115873+56	55286	Lelio R Paula	10/2012
9725	13^49629-84	55284	Lelio R Paula	01/2013
9726	2^183632-5	55279	Henri Lifchitz	08/2005
9727	13981^8988+8988^13981	55277	Hans Havermann	07/2016
9728	10688^13719-13719^10688	55273	Norbert Schneider	09/2018
9729	(5*2^183585+1)/13	55265	Lelio R Paula	07/2012
9730	2^183576+171	55262	Lelio R Paula	03/2011
9731	13^49604+82	55257	Lelio R Paula	01/2013
9732	(11*10^55254+1)/3	55255	Erik Branger	03/2014
9733	12609^13474-13474^12609	55253	Norbert Schneider	05/2018
9734	3^115802-26	55252	Lelio R Paula	10/2012
9735	2^183534-3645	55250	Lelio R Paula	01/2011
9736	(15*2^183533-1)/113	55249	Lelio R Paula	01/2014
9737	5^79032-13766	55241	Enzo Doria	02/2013
9738	8*3^115759-7	55232	Lelio R Paula	03/2014
9739	6^70974-137	55229	Lelio R Paula	10/2012
9740	2^183466+524287	55229	Paul Underwood	08/2018
9741	2^183446-113073	55223	Enzo Doria	07/2014
9742	2^183441+577294575	55222	Lelio R Paula	03/2013
9743	5^79000-6	55219	Lelio R Paula	10/2012
9744	2^183413-901	55213	Yves Minet	01/2012
9745	19^43168-50	55202	Lelio R Paula	02/2013
9746	2^183340+19683	55191	Lelio R Paula	02/2012
9747	6^70923+35	55189	Lelio R Paula	10/2012
9748	2^183317-4035	55184	Lelio R Paula	01/2011
9749	2^183284-15	55174	Lelio R Paula	03/2011
9750	2^183255+149	55166	Lelio R Paula	02/2011

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PRP Records

Probable Primes Top 10000

(252932 PRPs in the top)