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 ?
4251	2^321971-112747	96923	Enzo Doria	06/2014
4252	11^93062-92	96915	Lelio R Paula	06/2016
4253	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
4254	3^203051+34	96880	Lelio R Paula	05/2016
4255	2*10^96867-51	96868	Robert Price	11/2017
4256	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
4257	2^321716-2786939	96847	Enzo Doria	03/2016
4259	2^321701-113053	96842	Enzo Doria	07/2014
4258	2^321700-28635	96842	Lelio R Paula	06/2016
4260	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
4261	6^124433-124433	96828	Robert Price	01/2014
4262	2^321631+69	96821	Lelio R Paula	12/2012
4263	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
4264	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
4265	(59*10^96798+31)/9	96799	Robert Price	09/2015
4266	223319#+231223	96790	Makoto Morimoto	02/2016
4267	2^321519-28635	96787	Lelio R Paula	06/2016
4268	2^321487-1867237	96778	Enzo Doria	03/2016
4269	2^321461-63	96770	Lelio R Paula	12/2012
4270	2^321439+123	96763	Lelio R Paula	12/2012
4271	2^321434+709	96762	Lelio R Paula	02/2013
4272	14^84413+89	96749	Lelio R Paula	07/2016
4273	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
4274	13^86847+96	96743	Lelio R Paula	06/2016
4275	9*2^321336-7	96733	Lelio R Paula	08/2014
4276	(209*10^96722-17)/3	96724	Robert Price	05/2017
4277	2^321237-4615	96702	Yves Minet	05/2019
4278	2^321187-1159	96687	Yves Minet	11/2012
4279	2^321182-1850081	96686	Enzo Doria	08/2015
4280	2^321116-112829	96666	Enzo Doria	06/2014
4281	2^321108-109499	96664	Enzo Doria	04/2014
4282	2^321098+2793859	96661	Enzo Doria	03/2016
4283	2^321057+4097	96648	Lelio R Paula	06/2016
4284	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
4285	p(19849)#/2-64	96581	Robert Price	04/2017
4287	2^320817+189	96576	Lelio R Paula	12/2012
4286	2^320816-4685	96576	Yves Minet	05/2019
4288	(361*10^96567-163)/9	96569	Robert Price	10/2017
4289	2^320788-110327	96567	Enzo Doria	05/2014
4290	2^320764+793	96560	Lelio R Paula	02/2013
4291	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
4292	2^320616-78795	96516	Lelio R Paula	03/2016
4293	2^320612-461939	96514	Enzo Doria	07/2015
4294	5*2^320431+7	96461	Lelio R Paula	08/2014
4295	19^75431-90	96458	Lelio R Paula	06/2016
4296	(2^320370+3)/67	96440	Lelio R Paula	10/2013
4297	2^320309+1871477	96423	Enzo Doria	05/2016
4298	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
4299	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
4300	2^320232-173	96400	Lelio R Paula	12/2012
4301	175^42975-2	96395	Lelio R Paula	10/2017
4302	10^96377+199911	96378	Patrick De Geest	12/2016
4303	10^96377-20001	96377	Robert Price	11/2016
4304	2^320124-2790449	96367	Enzo Doria	03/2016
4306	2^320043-108775	96343	Enzo Doria	04/2014
4305	24989^7168+7168^24989	96343	Hans Havermann	11/2019
4307	10^96338+424939	96339	Patrick De Geest	03/2016
4308	10^96338-9281	96338	Robert Price	09/2015
4309	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
4310	2^319838+4257	96281	Lelio R Paula	03/2016
4311	2^319830-16995	96279	Lelio R Paula	03/2016
4312	6^123713+143	96268	Lelio R Paula	05/2016
4313	(28*10^96265-97)/3	96266	Robert Price	07/2016
4314	103^47825-102	96264	Norbert Schneider	10/2016
4315	2^319713-81	96244	Lelio R Paula	11/2012
4316	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
4317	12^89153-43	96213	Lelio R Paula	06/2016
4318	(2*10^96195-59)/3	96195	Robert Price	05/2017
4319	2^319545+147	96193	Lelio R Paula	11/2012
4320	(50^56597+1)/51	96155	Robert Price	03/2014
4321	(41*10^96137-59)/9	96138	Robert Price	10/2017
4322	2^319353-110343	96135	Enzo Doria	05/2014
4323	11^92309-42	96130	Lelio R Paula	05/2016
4324	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
4325	(7*10^96112+143)/3	96113	Robert Price	04/2016
4326	2^319237+65835	96100	Lelio R Paula	03/2016
4327	2^319194-1841	96087	Yves Minet	03/2013
4328	20^73847-31	96078	Lelio R Paula	05/2016
4329	50^56543-49	96065	Norbert Schneider	09/2018
4330	2^319107-109555	96061	Enzo Doria	04/2014
4331	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
4332	2^319098-112157	96059	Enzo Doria	06/2014
4333	15^81673+94	96055	Lelio R Paula	07/2016
4334	2^319074+1871749	96051	Enzo Doria	05/2016
4335	2^319007-112111	96031	Enzo Doria	06/2014
4336	2^318946-1421	96013	Yves Minet	01/2013
4337	2^318834-110411	95979	Enzo Doria	05/2014
4338	2^318831-1965	95978	Lelio R Paula	03/2016
4339	(5*10^95976+7)/3	95977	Erik Branger	03/2014
4340	5*3^201089-8	95945	Lelio R Paula	08/2014
4341	2^318711-139	95942	Lelio R Paula	11/2012
4342	2^318635-1167	95919	Lelio R Paula	03/2016
4343	15^81555+16	95917	Lelio R Paula	07/2016
4344	(37*10^95895+377)/9	95896	Robert Price	10/2017
4345	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
4346	2^318496-97305	95877	Lelio R Paula	03/2016
4347	2^318466+15015	95868	Lelio R Paula	03/2016
4348	6^123187-173129	95859	Mike Oakes	04/2011
4349	2^318423-487	95855	Yves Minet	03/2012
4350	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
4351	45369!2+1024	95787	Robert Price	02/2015
4352	3^200758-86	95786	Lelio R Paula	05/2016
4353	(2^318271+1)/(346031404238891654090604244843)	95781	Gord Palameta	12/2018
4354	3*10^95776-59	95777	Robert Price	10/2017
4355	193^41901-2	95768	Lelio R Paula	10/2017
4356	4*10^95752-71	95753	Robert Price	11/2017
4357	((10^47850-1)10000/9+6421)10^47850+(10^47850-1)/9	95704	Hans Havermann	05/2019
4358	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
4359	4*10^95672+91	95673	Robert Price	11/2017
4360	(11*10^95641-113)/3	95642	Robert Price	01/2017
4361	(13*10^95588+11)/3	95589	Robert Price	05/2015
4362	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
4363	3^200325+70	95580	Lelio R Paula	05/2016
4364	(25*10^95574-7)/9	95575	Robert Price	12/2014
4365	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
4366	2^317464+31	95567	Lelio R Paula	11/2012
4367	7^113073+82	95558	Lelio R Paula	04/2016
4368	2^317251+465	95503	Lelio R Paula	03/2016
4369	19^74684+58	95503	Lelio R Paula	06/2016
4370	(2^317250-7)/339	95500	Lelio R Paula	07/2013
4371	6^122718-79	95494	Lelio R Paula	05/2016
4372	22168^20291+20291^22168	95485	Hans Havermann	10/2019
4373	2^317141-110491	95469	Enzo Doria	05/2014
4374	2^317094+76309	95455	Enzo Doria	05/2016
4375	2^317085+95	95453	Lelio R Paula	11/2012
4376	(17*10^95451-377)/9	95452	Robert Price	11/2017
4377	2^317057-109551	95444	Enzo Doria	04/2014
4378	3^200026+28	95437	Lelio R Paula	05/2016
4379	2^317024+93	95434	Donovan Johnson	06/2008
4380	2^316999+1605	95427	Lelio R Paula	03/2016
4381	2^316995-110427	95426	Enzo Doria	05/2014
4383	2^316937+177	95408	Lelio R Paula	11/2012
4382	4*10^95407+91	95408	Robert Price	11/2017
4384	2^316908+1915	95399	Lelio R Paula	03/2016
4385	2^316894+99	95395	Lelio R Paula	11/2012
4386	6^122547+11	95361	Lelio R Paula	05/2016
4387	2^316771+82875	95358	Lelio R Paula	03/2016
4388	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
4389	1*10^95326+57	95327	Robert Price	03/2011
4390	10^95326-393687	95326	Patrick De Geest	09/2013
4391	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
4392	2^316654-109481	95323	Enzo Doria	04/2014
4393	8*10^95316+51	95317	Robert Price	05/2017
4394	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
4395	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
4396	(71*10^95277-539)/9	95278	Robert Price	11/2017
4397	23422^11691+11691^23422	95278	Hans Havermann	10/2019
4398	19^74503-56	95271	Lelio R Paula	06/2016
4399	11^91475-4380	95262	Enzo Doria	01/2013
4400	(62*10^95251-611)/9	95252	Robert Price	05/2017
4401	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
4402	(79*10^95214-43)/9	95215	Erik Branger	11/2013
4403	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
4404	5*2^316213+9	95191	Lelio R Paula	08/2014
4405	2^316205-1848163	95188	Enzo Doria	07/2015
4406	2^316185-2787913	95182	Enzo Doria	04/2016
4407	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
4408	2^316140-5	95168	Henri Lifchitz	02/2006
4409	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
4410	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
4411	2^316069+76817	95147	Enzo Doria	05/2016
4412	(199*10^95134-7)/3	95136	Robert Price	02/2017
4413	2^316027-97305	95134	Lelio R Paula	03/2016
4414	2^316006-2798051	95128	Enzo Doria	04/2016
4415	2^315921-2797603	95102	Enzo Doria	04/2016
4416	2*10^95095+63	95096	Robert Price	10/2017
4417	2^315857+1299	95083	Lelio R Paula	03/2016
4418	14^82955-43	95078	Lelio R Paula	06/2016
4419	(2*10^95072-17)/3	95072	Robert Price	08/2014
4420	2^315727+65	95044	Lelio R Paula	11/2012
4421	2^315725+1885757	95043	Enzo Doria	03/2017
4422	1*10^94983+21	94984	Robert Price	03/2011
4423	10^94983-717	94983	Patrick De Geest	08/2013
4424	17^77187-82	94975	Lelio R Paula	07/2016
4425	3*10^94964+37	94965	Robert Price	10/2017
4426	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
4427	2^315423-110329	94952	Enzo Doria	05/2014
4428	11^91169-7230	94943	Enzo Doria	02/2013
4429	7*10^94938+61	94939	Robert Price	02/2017
4430	2^315351+1025	94931	Lelio R Paula	03/2016
4431	2^315350-112253	94930	Enzo Doria	06/2014
4434	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
4433	2^315268+7	94906	Lelio R Paula	10/2012
4432	11^91133+62	94906	Lelio R Paula	05/2016
4435	30^64244+41	94897	Lelio R Paula	08/2012
4436	(151*10^94885-7)/9	94887	Robert Price	07/2017
4437	4^157583+22147	94875	Mike Oakes	01/2011
4438	2^315098+123	94854	Lelio R Paula	11/2012
4439	3^198791-34	94848	Robert Price	11/2013
4440	3*2^315067+7	94846	Lelio R Paula	08/2014
4441	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
4442	(16*10^94822+53)/3	94823	Robert Price	12/2016
4443	8*6^121849-7	94818	Lelio R Paula	10/2014
4444	(85*10^94802+473)/9	94803	Robert Price	03/2017
4445	2^314870-108761	94786	Enzo Doria	03/2014
4446	5*2^314841-3	94778	Lelio R Paula	08/2014
4447	6^121772+113	94758	Lelio R Paula	05/2016
4448	6^121756-16253	94745	Enzo Doria	02/2013
4449	2^314718-112793	94740	Enzo Doria	06/2014
4450	2^314697-1847293	94734	Enzo Doria	07/2015
4452	2^314548-249	94689	Yves Minet	02/2012
4451	5^135469+42	94689	Lelio R Paula	04/2016
4453	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
4454	(2*10^94604+547)/9	94604	Robert Price	10/2017
4455	3*2^314152+5	94570	Lelio R Paula	08/2014
4456	2*6^121530-5	94570	Lelio R Paula	10/2014
4457	7*10^94563+87	94564	Robert Price	11/2016
4458	2^314114-109677	94558	Enzo Doria	04/2014
4459	(218389#+240867)/(311811)	94557	Makoto Morimoto	10/2017
4460	2^314059+76583	94542	Enzo Doria	05/2016
4461	2^314041-4035	94536	Lelio R Paula	03/2016
4462	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
4463	11^90760-4710	94517	Enzo Doria	01/2013
4464	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
4465	94*10^94493-3	94495	Robert Price	11/2016
4466	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
4467	(F(375345)^2+L(375345)^2)/4	94477	Henri Lifchitz	10/2017
4468	7^111792-32	94476	Lelio R Paula	04/2016
4469	11^90680-5850	94434	Enzo Doria	01/2013
4470	2^313675-110125	94426	Enzo Doria	04/2014
4471	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
4472	2^313609-112225	94406	Enzo Doria	06/2014
4473	2^313584+72901	94399	Enzo Doria	04/2016
4474	2^313510-112865	94376	Enzo Doria	06/2014
4475	7*10^94373+87	94374	Robert Price	11/2016
4476	(9^98897+8^98897)/17	94371	Robert Price	12/2012
4477	2^313453-114703	94359	Enzo Doria	04/2015
4478	8*10^94357-51	94358	Robert Price	10/2017
4479	(379*10^94337-1)/9	94339	Robert Price	08/2017
4480	2^313344-313344+1	94326	Robert Price	10/2014
4481	20^72481-49	94300	Lelio R Paula	05/2016
4482	44725!2+128	94289	Robert Price	03/2015
4483	4*10^94286+9	94287	Robert Price	05/2015
4484	17^76621+24	94279	Lelio R Paula	07/2016
4485	2^313156-112859	94270	Enzo Doria	06/2014
4486	6^121130-59	94258	Lelio R Paula	05/2016
4487	3^197542+28	94252	Robert Price	11/2013
4488	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
4489	2^313045-5955	94236	Lelio R Paula	03/2016
4490	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
4491	2^312909-1865203	94195	Enzo Doria	03/2016
4492	2^312848-149	94177	Lelio R Paula	11/2012
4493	4^156403-77597	94164	Mike Oakes	04/2011
4494	18^75004-85	94151	Lelio R Paula	06/2016
4495	19^73622-48	94145	Lelio R Paula	06/2016
4496	(11^90397-3^90397)/8	94138	Robert Price	04/2011
4497	(3^197287+5)/16	94129	Lelio R Paula	04/2013
4498	12^87212-37	94118	Lelio R Paula	06/2016
4499	11^90376+76	94117	Lelio R Paula	05/2016
4500	(6^120946-11)/5	94114	Paul Bourdelais	11/2011

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PRP Records

Probable Primes Top 10000

(255244 PRPs in the top)