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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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 ?
9001	23277^12058+12058^23277	95000	Hans Havermann	09/2020
9002	1*10^94983+21	94984	Robert Price	03/2011
9003	10^94983-717	94983	Patrick De Geest	08/2013
9004	17^77187-82	94975	Lelio R Paula	07/2016
9005	3*10^94964+37	94965	Robert Price	10/2017
9006	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
9007	2^315423-110329	94952	Enzo Doria	05/2014
9008	11^91169-7230	94943	Enzo Doria	02/2013
9009	7*10^94938+61	94939	Robert Price	02/2017
9010	2^315351+1025	94931	Lelio R Paula	03/2016
9011	2^315350-112253	94930	Enzo Doria	06/2014
9012	(2^315343+1766)/2	94928	Stefano Morozzi	09/2020
9013	(2^315343+3066)/2	94928	Stefano Morozzi	09/2020
9016	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
9015	2^315268+7	94906	Lelio R Paula	10/2012
9014	11^91133+62	94906	Lelio R Paula	05/2016
9017	(2^315264+1558)/2	94904	Stefano Morozzi	09/2020
9018	30^64244+41	94897	Lelio R Paula	08/2012
9019	(151*10^94885-7)/9	94887	Robert Price	07/2017
9020	4^157583+22147	94875	Mike Oakes	01/2011
9021	2^315098+123	94854	Lelio R Paula	11/2012
9022	3^198791-34	94848	Robert Price	11/2013
9023	3*2^315067+7	94846	Lelio R Paula	08/2014
9024	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
9025	22576^15875+15875^22576	94836	Hans Havermann	09/2020
9026	(16*10^94822+53)/3	94823	Robert Price	12/2016
9027	8*6^121849-7	94818	Lelio R Paula	10/2014
9028	(85*10^94802+473)/9	94803	Robert Price	03/2017
9029	21767^21852-21852^21767	94790	Norbert Schneider	06/2020
9030	2^314870-108761	94786	Enzo Doria	03/2014
9031	5*2^314841-3	94778	Lelio R Paula	08/2014
9032	(2^314842+550)/2	94777	Stefano Morozzi	09/2020
9033	11738^23289-23289^11738	94777	Norbert Schneider	05/2022
9034	(2^314787+2630)/2	94761	Stefano Morozzi	09/2020
9035	6^121772+113	94758	Lelio R Paula	05/2016
9036	(2^314740+3642)/2	94746	Stefano Morozzi	09/2020
9037	6^121756-16253	94745	Enzo Doria	02/2013
9038	2^314718-112793	94740	Enzo Doria	06/2014
9039	2^314697-1847293	94734	Enzo Doria	07/2015
9040	22836^14065+14065^22836	94727	Hans Havermann	09/2020
9042	2^314548-249	94689	Yves Minet	02/2012
9041	5^135469+42	94689	Lelio R Paula	04/2016
9043	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
9044	25773^4712+4712^25773	94670	Hans Havermann	08/2020
9045	(2^314485+3614)/2	94670	Stefano Morozzi	09/2020
9046	(2*10^94604+547)/9	94604	Robert Price	10/2017
9047	(2^314164+2562)/2	94573	Stefano Morozzi	09/2020
9048	3*2^314152+5	94570	Lelio R Paula	08/2014
9049	2*6^121530-5	94570	Lelio R Paula	10/2014
9050	7*10^94563+87	94564	Robert Price	11/2016
9051	2^314114-109677	94558	Enzo Doria	04/2014
9052	(218389#+240867)/(311811)	94557	Makoto Morimoto	10/2017
9053	2^314059+76583	94542	Enzo Doria	05/2016
9054	2^314041-4035	94536	Lelio R Paula	03/2016
9055	(2^314028+3102)/2	94532	Stefano Morozzi	09/2020
9056	(2^314012+618)/2	94527	Stefano Morozzi	09/2020
9057	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
9058	11^90760-4710	94517	Enzo Doria	01/2013
9059	21675^21796+21796^21675	94507	Norbert Schneider	04/2020
9060	2^313942+100280245065	94506	Paul Bourdelais	10/2021
9061	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
9062	94*10^94493-3	94495	Robert Price	11/2016
9063	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
9064	(2^313859+2706)/2	94481	Stefano Morozzi	09/2020
9065	(F(375345)^2+L(375345)^2)/4	94477	Henri Lifchitz	10/2017
9066	7^111792-32	94476	Lelio R Paula	04/2016
9067	(2^313800+822)/2	94463	Stefano Morozzi	01/2021
9068	9*10^94462-47	94463	Robert Price	11/2021
9069	11*10^94460+3	94462	Robert Price	07/2021
9070	(202*10^94441-1)/3	94443	Robert Price	05/2020
9071	11^90680-5850	94434	Enzo Doria	01/2013
9072	(752^32833-1)/751	94432	Michael Stocker	05/2020
9073	2^313675-110125	94426	Enzo Doria	04/2014
9074	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
9075	2^313609-112225	94406	Enzo Doria	06/2014
9076	2^313584+72901	94399	Enzo Doria	04/2016
9077	(2^313567+1310)/2	94393	Stefano Morozzi	02/2021
9078	(2^313562+730)/2	94392	Stefano Morozzi	09/2020
9079	2^313510-112865	94376	Enzo Doria	06/2014
9080	7*10^94373+87	94374	Robert Price	11/2016
9081	(9^98897+8^98897)/17	94371	Robert Price	12/2012
9082	2^313453-114703	94359	Enzo Doria	04/2015
9083	8*10^94357-51	94358	Robert Price	10/2017
9084	25903^4392+4392^25903	94356	Hans Havermann	09/2020
9085	31706^945+945^31706	94340	Hans Havermann	09/2020
9086	(379*10^94337-1)/9	94339	Robert Price	08/2017
9087	2^313344-313344+1	94326	Robert Price	10/2014
9088	(2^313313+3662)/2	94317	Stefano Morozzi	09/2020
9089	20^72481-49	94300	Lelio R Paula	05/2016
9090	(34*10^94293-259)/9	94294	Robert Price	12/2021
9091	44725!2+128	94289	Robert Price	03/2015
9092	4*10^94286+9	94287	Robert Price	05/2015
9093	17^76621+24	94279	Lelio R Paula	07/2016
9094	26274^3875+3875^26274	94279	Hans Havermann	09/2020
9095	4*10^94270-33	94271	Robert Price	04/2021
9096	2^313156-112859	94270	Enzo Doria	06/2014
9097	(49*10^94262-211)/9	94263	Robert Price	06/2022
9098	6^121130-59	94258	Lelio R Paula	05/2016
9099	3^197542+28	94252	Robert Price	11/2013
9100	(2^313076+3550)/2	94245	Stefano Morozzi	09/2020
9101	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
9102	2^313045-5955	94236	Lelio R Paula	03/2016
9103	22099^18358+18358^22099	94227	Hans Havermann	08/2020
9104	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
9105	2^312909-1865203	94195	Enzo Doria	03/2016
9106	25013^5830+5830^25013	94191	Hans Havermann	09/2020
9107	2^312848-149	94177	Lelio R Paula	11/2012
9108	(2^312819+3278)/2	94168	Stefano Morozzi	02/2021
9109	4^156403-77597	94164	Mike Oakes	04/2011
9110	18^75004-85	94151	Lelio R Paula	06/2016
9111	19^73622-48	94145	Lelio R Paula	06/2016
9112	(11^90397-3^90397)/8	94138	Robert Price	04/2011
9113	(3^197287+5)/16	94129	Lelio R Paula	04/2013
9114	(23*10^94123-29)/3	94124	Robert Price	03/2022
9115	24220^7691+7691^24220	94119	Hans Havermann	09/2020
9116	12^87212-37	94118	Lelio R Paula	06/2016
9117	11^90376+76	94117	Lelio R Paula	05/2016
9118	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
9119	(2^312622+534)/2	94109	Stefano Morozzi	09/2020
9120	(10^94096+191)/3	94096	Robert Price	11/2017
9121	23794^9005+9005^23794	94093	Hans Havermann	09/2020
9122	2^312562-112685	94091	Enzo Doria	06/2014
9123	137^44026-2	94072	Lelio R Paula	10/2017
9124	s(164441)	94052	Robert Price	05/2020
9125	2^312404-869688105	94043	Lelio R Paula	09/2016
9126	2^312387+2793533	94038	Enzo Doria	03/2016
9128	10^94016+91	94017	Robert Price	04/2011
9127	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
9129	10^94016-188963	94016	Patrick De Geest	08/2013
9130	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
9131	(401*10^94010+13)/9	94012	Robert Price	09/2021
9132	23866^8691+8691^23866	94010	Hans Havermann	08/2020
9133	6^120802+7661	94003	Mike Oakes	04/2011
9134	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
9135	(2^312245+702)/2	93995	Stefano Morozzi	09/2020
9136	(56*10^93993+493)/9	93994	Robert Price	10/2021
9137	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
9138	2^312201+51	93982	Lelio R Paula	11/2012
9139	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
9140	(781*10^93942-7)/9	93944	Robert Price	12/2021
9141	3^196892+58	93942	Lelio R Paula	05/2016
9142	2^312060+18915	93940	Lelio R Paula	03/2016
9143	42^57867-41	93933	Norbert Schneider	08/2018
9144	8*10^93921+83	93922	Robert Price	11/2021
9145	2^311992-16209	93919	Enzo Doria	04/2013
9146	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
9147	2^311965-39	93911	Lelio R Paula	11/2012
9148	2^311920-111689	93898	Enzo Doria	05/2014
9149	130^44414+129	93889	Norbert Schneider	01/2019
9150	(2^311892+2730)/2	93889	Stefano Morozzi	09/2020
9151	7*10^93887-47	93888	Robert Price	02/2017
9152	9*10^93878-37	93879	Robert Price	06/2021
9153	(28*10^93874+323)/9	93875	Robert Price	10/2021
9154	(2^311778+1530)/2	93855	Stefano Morozzi	09/2020
9155	12^86965-13	93851	Lelio R Paula	06/2016
9156	24862^5953+5953^24862	93848	Hans Havermann	09/2020
9157	22299^16148+16148^22299	93837	Hans Havermann	08/2020
9158	2^311705+16095	93833	Lelio R Paula	03/2016
9159	(2^311701+3002)/2	93832	Stefano Morozzi	09/2020
9160	norm(Mod(x,x^3-x-1)^768329-1)	93831	Paul Vanderveen	09/2022
9162	2^311665-81	93821	Lelio R Paula	11/2012
9161	(2^311665+2654)/2	93821	Stefano Morozzi	09/2020
9163	(2^311648+3058)/2	93816	Stefano Morozzi	09/2020
9164	(2^311639+2738)/2	93813	Stefano Morozzi	01/2021
9165	730^32761+32761^730	93806	Norbert Schneider	09/2017
9166	11^90073+92	93802	Lelio R Paula	05/2016
9167	6*10^93792+41	93793	Robert Price	01/2017
9168	10^93790+64611	93791	Patrick De Geest	04/2020
9171	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
9169	10^93790-123456789	93790	Robert Price	02/2020
9170	10^93790-157517	93790	Patrick De Geest	04/2020
9172	(49*10^93782+293)/9	93783	Robert Price	03/2021
9173	12^86900-77	93781	Lelio R Paula	06/2016
9174	2^311508-109769	93774	Enzo Doria	04/2014
9175	2^311486-1859621	93767	Enzo Doria	03/2016
9176	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
9177	(10^93811-1)/(996812952121099970133280113810431639637782545831)	93765	Gord Palameta	10/2018
9178	2^311471+311469	93763	Renaud Lifchitz	01/2003
9179	(88*10^93760-1)/3	93762	Robert Price	10/2017
9180	2^311426+79459	93749	Enzo Doria	06/2016
9181	21537^21634+21634^21537	93745	Norbert Schneider	04/2020
9182	2^311409+111546435	93744	Paul Bourdelais	10/2021
9183	(2^311360+3078)/2	93729	Stefano Morozzi	09/2020
9184	(2^311341+2186)/2	93723	Stefano Morozzi	09/2020
9185	(2^311313+774)/2	93715	Stefano Morozzi	09/2020
9187	2^311294+5775	93709	Lelio R Paula	03/2016
9186	25155^5312+5312^25155	93709	Hans Havermann	09/2020
9188	2^311252-1017	93697	Lelio R Paula	03/2016
9189	2^311247-112041	93695	Enzo Doria	06/2014
9190	7*10^93692-83	93693	Robert Price	09/2017
9191	2^311205-109645	93683	Enzo Doria	04/2014
9192	5^134027-84	93681	Lelio R Paula	04/2016
9193	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
9194	(2^311027-2^155514+1)/5	93628		11/2006
9195	26748^3161+3161^26748	93614	Hans Havermann	08/2020
9196	3^196192-28	93608	Robert Price	12/2013
9197	216091#+261433	93606	Makoto Morimoto	12/2015
9198	5^133917+68	93604	Lelio R Paula	04/2016
9199	2^310924-1709	93598	Yves Minet	03/2013
9200	24555^6476+6476^24555	93587	Hans Havermann	08/2020
9201	(2^310867+734)/2	93580	Stefano Morozzi	09/2020
9202	(266*10^93577-11)/3	93579	Robert Price	09/2016
9203	(16*10^93577+161)/3	93578	Robert Price	05/2016
9204	3^196113-56	93570	Lelio R Paula	04/2016
9205	2^310806-110345	93562	Enzo Doria	05/2014
9206	3^196093+86	93561	Lelio R Paula	04/2016
9207	2^310780-2327	93555	Yves Minet	10/2013
9208	30^63332+41	93550	Lelio R Paula	08/2012
9209	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
9210	8*5^133807+7	93528	Lelio R Paula	10/2014
9211	2^310686+8193	93526	Lelio R Paula	03/2016
9212	22681^13282+13282^22681	93520	Hans Havermann	09/2020
9213	2^310646+63	93514	Lelio R Paula	11/2012
9214	(77*10^93508+31)/9	93509	Robert Price	10/2015
9215	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
9216	(2*10^93497+7)/9	93497	Erik Branger	03/2011
9217	3^195958-112852	93496	Enzo Doria	07/2014
9218	2^310583+16385	93495	Lelio R Paula	03/2016
9219	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
9220	9*7^110614+2	93481	Lelio R Paula	11/2014
9221	(19*10^93467+83)/3	93468	Robert Price	08/2020
9222	2^310469-8295	93461	Lelio R Paula	03/2016
9223	2^310459-1159	93458	Yves Minet	11/2012
9224	6^120075-95	93437	Lelio R Paula	05/2016
9225	(2^310362+1758)/2	93428	Stefano Morozzi	09/2020
9226	256*19^73047+9	93412	Eric Chen	12/2022
9227	148^43041-147	93411	Norbert Schneider	05/2019
9228	2^310289+98327	93407	Yves Minet	11/2010
9229	21769^19510+19510^21769	93395	Hans Havermann	08/2020
9230	2^310217-113143	93385	Enzo Doria	07/2014
9231	7^110494-68	93379	Lelio R Paula	04/2016
9232	2^310184-113093	93375	Enzo Doria	07/2014
9233	2^310180-110417	93374	Enzo Doria	05/2014
9234	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
9235	(2^310173+3150)/2	93372	Stefano Morozzi	09/2020
9236	3^195669+68	93358	Lelio R Paula	04/2016
9237	10^93356+91	93357	Robert Price	04/2011
9238	10^93356-28313	93356	Patrick De Geest	08/2013
9239	(85*10^93346+23)/9	93347	Robert Price	11/2015
9240	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
9241	10^93333+191061	93334	Patrick De Geest	09/2022
9243	10^93333-4000001	93333	Robert Price	07/2021
9242	10^93333-44807	93333	Patrick De Geest	09/2022
9244	3^195556+8680	93304	Lelio R Paula	04/2016
9245	2^309942-109991	93302	Enzo Doria	04/2014
9246	2^309926-1867301	93298	Enzo Doria	03/2016
9247	2^309924+85951	93297	Yves Minet	03/2011
9248	2^309896-4229	93288	Yves Minet	08/2018
9249	(86*10^93263-77)/9	93264	Robert Price	05/2016
9250	6^119836-125	93251	Lelio R Paula	05/2016

Find by discoverer :

PRP Records

Probable Primes Top 10000

(291910 PRPs in the top)