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 ?
8751	3*10^97205-61	97206	Robert Price	04/2021
8752	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
8753	(35*10^97194-341)/9	97195	Robert Price	08/2021
8754	(4872^26357-1)/4871	97194	Serge Batalov	06/2022
8755	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
8756	(796*10^97183-31)/9	97185	Robert Price	07/2022
8757	(2^322789+2214)/2	97169	Stefano Morozzi	09/2020
8758	2^322725+75761	97150	Enzo Doria	04/2016
8759	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
8760	(2175^29101-1)/2174	97121	Serge Batalov	06/2022
8761	22402^21639+21639^22402	97118	Hans Havermann	07/2020
8762	23399^14128+14128^23399	97108	Hans Havermann	06/2020
8763	(2892^28057-1)/2891	97108	Serge Batalov	06/2022
8764	(9578^24391-1)/9577	97104	Serge Batalov	06/2022
8765	(2^322525+2606)/2	97090	Stefano Morozzi	09/2020
8766	(9563^24391-1)/9562	97087	Serge Batalov	06/2022
8767	(41*10^97085+373)/9	97086	Robert Price	04/2017
8768	(2^322473+854)/2	97074	Stefano Morozzi	02/2021
8769	2^322413+77	97056	Lelio R Paula	12/2012
8770	2^322406+177	97054	Lelio R Paula	12/2012
8771	(349^38167-1)/348	97050	Serge Batalov	06/2022
8772	(14*10^97044+31)/9	97045	Robert Price	02/2015
8773	2^322302+255255	97023	Lelio R Paula	07/2016
8774	(1302^31147-1)/1301	97008	Serge Batalov	06/2022
8775	2^322196-113093	96991	Enzo Doria	07/2014
8776	(2^322169+2690)/2	96983	Stefano Morozzi	09/2020
8777	(49*10^96980+221)/9	96981	Robert Price	02/2022
8778	9*10^96968-47	96969	Robert Price	11/2021
8779	(5895^25717-1)/5894	96962	Serge Batalov	06/2022
8780	(27473^21841-1)/27472	96946	Serge Batalov	06/2022
8781	23109^15668+15668^23109	96943	Hans Havermann	07/2020
8782	2^322000-1861469	96932	Enzo Doria	03/2016
8783	2^321971-112747	96923	Enzo Doria	06/2014
8784	23754^12023+12023^23754	96917	Hans Havermann	07/2020
8785	11^93062-92	96915	Lelio R Paula	06/2016
8786	(37871^21169-1)/37870	96914	Serge Batalov	06/2022
8787	(2^321922+2214)/2	96908	Stefano Morozzi	09/2020
8788	(2^321900+2086)/2	96902	Stefano Morozzi	09/2020
8789	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
8790	3^203051+34	96880	Lelio R Paula	05/2016
8791	2*10^96867-51	96868	Robert Price	11/2017
8792	(2^321779+2618)/2	96865	Stefano Morozzi	09/2020
8793	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
8794	2^321716-2786939	96847	Enzo Doria	03/2016
8795	22496^20181+20181^22496	96844	Hans Havermann	03/2020
8796	2^321701-113053	96842	Enzo Doria	07/2014
8797	2^321700-28635	96842	Lelio R Paula	06/2016
8798	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
8799	6*10^96835+13	96836	Robert Price	10/2021
8800	6^124433-124433	96828	Robert Price	01/2014
8801	2^321631+69	96821	Lelio R Paula	12/2012
8802	(27109^21841-1)/27108	96820	Serge Batalov	06/2022
8803	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
8804	(5052^26141-1)/5051	96809	Serge Batalov	06/2022
8805	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
8806	(59*10^96798+31)/9	96799	Robert Price	09/2015
8807	(2^321536+2062)/2	96792	Stefano Morozzi	09/2020
8808	223319#+231223	96790	Makoto Morimoto	02/2016
8809	2^321519-28635	96787	Lelio R Paula	06/2016
8810	2^321487-1867237	96778	Enzo Doria	03/2016
8811	2^321461-63	96770	Lelio R Paula	12/2012
8812	(16053^23011-1)/16052	96770	Serge Batalov	06/2022
8813	2^321439+123	96763	Lelio R Paula	12/2012
8814	2^321434+709	96762	Lelio R Paula	02/2013
8815	(2^321415+554)/2	96756	Stefano Morozzi	09/2020
8816	14^84413+89	96749	Lelio R Paula	07/2016
8817	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
8818	13^86847+96	96743	Lelio R Paula	06/2016
8819	9*2^321336-7	96733	Lelio R Paula	08/2014
8820	(209*10^96722-17)/3	96724	Robert Price	05/2017
8821	(54163^20431-1)/54162	96710	Serge Batalov	06/2022
8822	2^321237-4615	96702	Yves Minet	05/2019
8823	(27273^21799-1)/27272	96691	Serge Batalov	06/2022
8824	2^321187-1159	96687	Yves Minet	11/2012
8825	2^321182-1850081	96686	Enzo Doria	08/2015
8827	23359^13768+13768^23359	96680	Hans Havermann	06/2020
8826	(65630^20071-1)/65629	96680	Serge Batalov	06/2022
8828	2^321116-112829	96666	Enzo Doria	06/2014
8829	2^321108-109499	96664	Enzo Doria	04/2014
8830	2^321098+2793859	96661	Enzo Doria	03/2016
8831	(2^321100+1170)/2	96661	Stefano Morozzi	09/2020
8832	2^321057+4097	96648	Lelio R Paula	06/2016
8833	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
8834	22743^17750+17750^22743	96640	Hans Havermann	04/2020
8835	22882^16679+16679^22882	96612	Hans Havermann	02/2020
8836	23452^13163+13163^23452	96608	Hans Havermann	02/2020
8837	(1042^32009-1)/1041	96596	Serge Batalov	06/2022
8838	(85*10^96594-373)/9	96595	Robert Price	05/2021
8839	(2^320863+666)/2	96590	Stefano Morozzi	09/2020
8840	p(19849)#/2-64	96581	Robert Price	04/2017
8841	2^320817+189	96576	Lelio R Paula	12/2012
8842	2^320816-4685	96576	Yves Minet	05/2019
8844	(361*10^96567-163)/9	96569	Robert Price	10/2017
8843	(19*10^96568+137)/3	96569	Robert Price	03/2022
8845	2^320788-110327	96567	Enzo Doria	05/2014
8846	(3065^27697-1)/3064	96561	Serge Batalov	06/2022
8847	2^320764+793	96560	Lelio R Paula	02/2013
8848	(2^320752+1842)/2	96556	Stefano Morozzi	02/2021
8849	(48331^20611-1)/48330	96542	Serge Batalov	06/2022
8850	(50595^20521-1)/50594	96529	Serge Batalov	06/2022
8851	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
8852	23288^13947+13947^23288	96517	Hans Havermann	07/2020
8854	2^320616-78795	96516	Lelio R Paula	03/2016
8853	(19*10^96520+287)/9/109/409	96516	Alfred Reich	11/2022
8855	2^320612-461939	96514	Enzo Doria	07/2015
8856	(21245^22303-1)/21244	96507	Serge Batalov	06/2022
8857	10^96504+987654321	96505	Robert Price	12/2019
8858	10^96504+71887	96505	Patrick De Geest	02/2020
8859	22654^18195+18195^22654	96505	Hans Havermann	07/2020
8860	10^96504-139277	96504	Patrick De Geest	02/2020
8861	(218^41263-1)/217	96490	Serge Batalov	06/2022
8862	(47220^20641-1)/47219	96474	Serge Batalov	06/2022
8863	5*2^320431+7	96461	Lelio R Paula	08/2014
8864	19^75431-90	96458	Lelio R Paula	06/2016
8865	(11853^23677-1)/11852	96452	Serge Batalov	06/2022
8866	(2^320386+2814)/2	96446	Stefano Morozzi	02/2021
8867	(2^320370+3)/67	96440	Lelio R Paula	10/2013
8868	3*10^96431-17	96432	Robert Price	03/2021
8869	2^320309+1871477	96423	Enzo Doria	05/2016
8870	(10412^24001-1)/10411	96421	Serge Batalov	06/2022
8871	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
8872	(29*10^96407-23)/3	96408	Robert Price	03/2022
8873	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
8874	2^320232-173	96400	Lelio R Paula	12/2012
8875	175^42975-2	96395	Lelio R Paula	10/2017
8876	(2^320170+2718)/2	96381	Stefano Morozzi	09/2020
8877	10^96377+199911	96378	Patrick De Geest	12/2016
8878	10^96377-20001	96377	Robert Price	11/2016
8879	(18079^22639-1)/18078	96374	Serge Batalov	06/2022
8881	2^320124-2790449	96367	Enzo Doria	03/2016
8880	10^96366+19197	96367	Patrick De Geest	08/2021
8883	10^96366-10000000001	96366	Robert Price	04/2021
8882	10^96366-287367	96366	Patrick De Geest	08/2021
8884	(26351^21799-1)/26350	96365	Serge Batalov	06/2022
8885	22488^19255+19255^22488	96351	Hans Havermann	11/2019
8886	23248^13939+13939^23248	96346	Hans Havermann	11/2019
8887	(5928^25537-1)/5927	96345	Serge Batalov	06/2022
8889	2^320043-108775	96343	Enzo Doria	04/2014
8888	24989^7168+7168^24989	96343	Hans Havermann	11/2019
8890	10^96338+424939	96339	Patrick De Geest	03/2016
8891	10^96338-9281	96338	Robert Price	09/2015
8892	(8527^24509-1)/8526	96336	Serge Batalov	06/2022
8893	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
8894	(2444^28433-1)/2443	96331	Serge Batalov	06/2022
8895	(48690^20551-1)/48689	96327	Serge Batalov	06/2022
8896	(61935^20101-1)/61934	96318	Serge Batalov	06/2022
8897	25699^5596+5596^25699	96317	Hans Havermann	07/2020
8898	(7*10^96312+83)/9	96312	Tyler Busby	01/2023
8899	(11*10^96298+529)/9	96299	Robert Price	09/2021
8901	26502^4297+4297^26502	96287	Hans Havermann	07/2020
8900	(54180^20341-1)/54179	96287	Serge Batalov	06/2022
8902	2^319838+4257	96281	Lelio R Paula	03/2016
8903	2^319830-16995	96279	Lelio R Paula	03/2016
8904	6^123713+143	96268	Lelio R Paula	05/2016
8905	(28*10^96265-97)/3	96266	Robert Price	07/2016
8906	(3799^26893-1)/3798	96265	Serge Batalov	06/2022
8908	103^47825-102	96264	Norbert Schneider	10/2016
8907	(54041^20341-1)/54040	96264	Serge Batalov	06/2022
8909	(2^319777+2082)/2	96263	Stefano Morozzi	09/2020
8910	(2^319771+3686)/2	96261	Stefano Morozzi	09/2020
8911	2^319713-81	96244	Lelio R Paula	11/2012
8912	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
8913	22834^16393+16393^22834	96238	Hans Havermann	05/2020
8914	8*10^96236+27	96237	Robert Price	09/2021
8915	12^89153-43	96213	Lelio R Paula	06/2016
8916	(25048^21871-1)/25047	96202	Serge Batalov	06/2022
8918	(2*10^96195-59)/3	96195	Robert Price	05/2017
8917	9*10^96194-77	96195	Robert Price	08/2020
8919	2^319545+147	96193	Lelio R Paula	11/2012
8920	23357^13128+13128^23357	96189	Hans Havermann	02/2020
8921	(19838^22381-1)/19837	96179	Serge Batalov	06/2022
8922	(221^41023-1)/220	96172	Serge Batalov	06/2022
8923	25952^5073+5073^25952	96160	Hans Havermann	12/2019
8924	(50891^20431-1)/50890	96157	Serge Batalov	06/2022
8925	(50^56597+1)/51	96155	Robert Price	03/2014
8926	22313^20374+20374^22313	96149	Hans Havermann	12/2019
8927	22279^20668+20668^22279	96141	Hans Havermann	11/2019
8928	(41*10^96137-59)/9	96138	Robert Price	10/2017
8929	2^319353-110343	96135	Enzo Doria	05/2014
8930	11^92309-42	96130	Lelio R Paula	05/2016
8931	(21675^22171-1)/21674	96129	Serge Batalov	06/2022
8932	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
8933	(7*10^96112+143)/3	96113	Robert Price	04/2016
8934	26731^3940+3940^26731	96112	Hans Havermann	07/2020
8935	22640^17583+17583^22640	96109	Hans Havermann	07/2020
8936	(19178^22441-1)/19177	96107	Serge Batalov	06/2022
8937	2^319237+65835	96100	Lelio R Paula	03/2016
8938	2^319194-1841	96087	Yves Minet	03/2013
8939	23949^10280+10280^23949	96084	Hans Havermann	07/2020
8940	(1927^29251-1)/1926	96083	Serge Batalov	06/2022
8941	20^73847-31	96078	Lelio R Paula	05/2016
8942	(60229^20101-1)/60228	96075	Serge Batalov	06/2022
8943	(28044^21601-1)/28043	96074	Serge Batalov	06/2022
8944	50^56543-49	96065	Norbert Schneider	09/2018
8945	2^319107-109555	96061	Enzo Doria	04/2014
8946	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
8947	2^319098-112157	96059	Enzo Doria	06/2014
8948	15^81673+94	96055	Lelio R Paula	07/2016
8949	(85761^19471-1)/85760	96052	Serge Batalov	06/2022
8950	2^319074+1871749	96051	Enzo Doria	05/2016
8951	25670^5517+5517^25670	96050	Hans Havermann	06/2020
8952	6*10^96037+19	96038	Robert Price	11/2021
8953	2^319007-112111	96031	Enzo Doria	06/2014
8954	(57987^20161-1)/57986	96029	Serge Batalov	06/2022
8956	2^318946-1421	96013	Yves Minet	01/2013
8955	(68310^19861-1)/68309	96013	Serge Batalov	06/2022
8957	(20294^22291-1)/20293	96012	Serge Batalov	06/2022
8958	(304^38669-1)/303	96008	Serge Batalov	06/2022
8959	(1840^29401-1)/1839	95986	Serge Batalov	06/2022
8960	22830^16003+16003^22830	95982	Hans Havermann	02/2020
8961	2^318834-110411	95979	Enzo Doria	05/2014
8962	2^318831-1965	95978	Lelio R Paula	03/2016
8963	(5*10^95976+7)/3	95977	Erik Branger	03/2014
8964	(12797^23369-1)/12796	95975	Serge Batalov	06/2022
8965	(10534^23857-1)/10533	95963	Serge Batalov	06/2022
8966	22871^15696+15696^22871	95962	Hans Havermann	01/2020
8967	(2^318760+858)/2	95957	Stefano Morozzi	02/2021
8968	23167^13860+13860^23167	95953	Hans Havermann	01/2020
8969	(823^32911-1)/822	95946	Serge Batalov	06/2022
8971	5*3^201089-8	95945	Lelio R Paula	08/2014
8970	(81783^19531-1)/81782	95945	Serge Batalov	06/2022
8972	2^318711-139	95942	Lelio R Paula	11/2012
8973	2^318635-1167	95919	Lelio R Paula	03/2016
8974	15^81555+16	95917	Lelio R Paula	07/2016
8975	(37*10^95895+377)/9	95896	Robert Price	10/2017
8976	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
8977	2^318496-97305	95877	Lelio R Paula	03/2016
8978	22129^21496+21496^22129	95871	Hans Havermann	07/2020
8980	2^318466+15015	95868	Lelio R Paula	03/2016
8979	24847^7216+7216^24847	95868	Hans Havermann	07/2020
8981	23706^11065+11065^23706	95866	Hans Havermann	07/2020
8982	(2863^27733-1)/2862	95865	Serge Batalov	06/2022
8983	6^123187-173129	95859	Mike Oakes	04/2011
8984	2^318423-487	95855	Yves Minet	03/2012
8985	10^95848+443709	95849	Patrick De Geest	10/2022
8986	10^95848-5000000001	95848	Robert Price	09/2022
8987	10^95848-61971	95848	Patrick De Geest	10/2022
8988	(2^318359+678)/2	95836	Stefano Morozzi	09/2020
8989	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
8990	(8060^24533-1)/8059	95831	Serge Batalov	06/2022
8991	(9853^23993-1)/9852	95814	Serge Batalov	06/2022
8993	(2^318267+2550)/2	95808	Stefano Morozzi	09/2020
8992	(5048^25873-1)/5047	95808	Serge Batalov	06/2022
8995	4*10^95799+13	95800	Robert Price	02/2021
8994	(65533^19891-1)/65532	95800	Serge Batalov	06/2022
8996	45369!2+1024	95787	Robert Price	02/2015
8997	3^200758-86	95786	Lelio R Paula	05/2016
8998	(2^318271+1)/(346031404238891654090604244843)	95781	Gord Palameta	12/2018
8999	(2^318171+2030)/2	95779	Stefano Morozzi	09/2020
9000	3*10^95776-59	95777	Robert Price	10/2017

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