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 ?
4501	(10^94096+191)/3	94096	Robert Price	11/2017
4502	2^312562-112685	94091	Enzo Doria	06/2014
4503	137^44026-2	94072	Lelio R Paula	10/2017
4504	2^312404-869688105	94043	Lelio R Paula	09/2016
4505	2^312387+2793533	94038	Enzo Doria	03/2016
4507	10^94016+91	94017	Robert Price	04/2011
4506	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
4508	10^94016-188963	94016	Patrick De Geest	08/2013
4509	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
4510	6^120802+7661	94003	Mike Oakes	04/2011
4511	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
4512	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
4513	2^312201+51	93982	Lelio R Paula	11/2012
4514	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
4515	3^196892+58	93942	Lelio R Paula	05/2016
4516	2^312060+18915	93940	Lelio R Paula	03/2016
4517	42^57867-41	93933	Norbert Schneider	08/2018
4518	2^311992-16209	93919	Enzo Doria	04/2013
4519	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
4520	2^311965-39	93911	Lelio R Paula	11/2012
4521	2^311920-111689	93898	Enzo Doria	05/2014
4522	130^44414+129	93889	Norbert Schneider	01/2019
4523	7*10^93887-47	93888	Robert Price	02/2017
4524	12^86965-13	93851	Lelio R Paula	06/2016
4525	2^311705+16095	93833	Lelio R Paula	03/2016
4526	2^311665-81	93821	Lelio R Paula	11/2012
4527	730^32761+32761^730	93806	Norbert Schneider	09/2017
4528	11^90073+92	93802	Lelio R Paula	05/2016
4529	6*10^93792+41	93793	Robert Price	01/2017
4530	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
4531	12^86900-77	93781	Lelio R Paula	06/2016
4532	2^311508-109769	93774	Enzo Doria	04/2014
4533	2^311486-1859621	93767	Enzo Doria	03/2016
4534	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
4535	(10^93811-1)/(996812952121099970133280113810431639637782545831)	93765	Gord Palameta	10/2018
4536	2^311471+311469	93763	Renaud Lifchitz	01/2003
4537	(88*10^93760-1)/3	93762	Robert Price	10/2017
4538	2^311426+79459	93749	Enzo Doria	06/2016
4539	2^311294+5775	93709	Lelio R Paula	03/2016
4540	2^311252-1017	93697	Lelio R Paula	03/2016
4541	2^311247-112041	93695	Enzo Doria	06/2014
4542	7*10^93692-83	93693	Robert Price	09/2017
4543	2^311205-109645	93683	Enzo Doria	04/2014
4544	5^134027-84	93681	Lelio R Paula	04/2016
4545	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
4546	(2^311027-2^155514+1)/5	93628		11/2006
4547	3^196192-28	93608	Robert Price	12/2013
4548	216091#+261433	93606	Makoto Morimoto	12/2015
4549	5^133917+68	93604	Lelio R Paula	04/2016
4550	2^310924-1709	93598	Yves Minet	03/2013
4551	(266*10^93577-11)/3	93579	Robert Price	09/2016
4552	(16*10^93577+161)/3	93578	Robert Price	05/2016
4553	3^196113-56	93570	Lelio R Paula	04/2016
4554	2^310806-110345	93562	Enzo Doria	05/2014
4555	3^196093+86	93561	Lelio R Paula	04/2016
4556	2^310780-2327	93555	Yves Minet	10/2013
4557	30^63332+41	93550	Lelio R Paula	08/2012
4558	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
4559	8*5^133807+7	93528	Lelio R Paula	10/2014
4560	2^310686+8193	93526	Lelio R Paula	03/2016
4561	2^310646+63	93514	Lelio R Paula	11/2012
4562	(77*10^93508+31)/9	93509	Robert Price	10/2015
4563	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
4564	(2*10^93497+7)/9	93497	Erik Branger	03/2011
4565	3^195958-112852	93496	Enzo Doria	07/2014
4566	2^310583+16385	93495	Lelio R Paula	03/2016
4567	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
4568	9*7^110614+2	93481	Lelio R Paula	11/2014
4569	2^310469-8295	93461	Lelio R Paula	03/2016
4570	2^310459-1159	93458	Yves Minet	11/2012
4571	6^120075-95	93437	Lelio R Paula	05/2016
4572	148^43041-147	93411	Norbert Schneider	05/2019
4573	2^310289+98327	93407	Yves Minet	11/2010
4574	2^310217-113143	93385	Enzo Doria	07/2014
4575	7^110494-68	93379	Lelio R Paula	04/2016
4576	2^310184-113093	93375	Enzo Doria	07/2014
4577	2^310180-110417	93374	Enzo Doria	05/2014
4578	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
4579	3^195669+68	93358	Lelio R Paula	04/2016
4580	10^93356+91	93357	Robert Price	04/2011
4581	10^93356-28313	93356	Patrick De Geest	08/2013
4582	(85*10^93346+23)/9	93347	Robert Price	11/2015
4583	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
4584	3^195556+8680	93304	Lelio R Paula	04/2016
4585	2^309942-109991	93302	Enzo Doria	04/2014
4586	2^309926-1867301	93298	Enzo Doria	03/2016
4587	2^309924+85951	93297	Yves Minet	03/2011
4588	2^309896-4229	93288	Yves Minet	08/2018
4589	(86*10^93263-77)/9	93264	Robert Price	05/2016
4590	6^119836-125	93251	Lelio R Paula	05/2016
4591	(77*10^93249-257)/9	93250	Robert Price	10/2017
4592	3^195430-2	93244	Theodore Burton	02/2007
4593	(13*10^93236+47)/3	93237	Robert Price	01/2017
4594	(67*10^93226-7)/3	93228	Robert Price	10/2017
4595	(86*10^93217-221)/9	93218	Robert Price	06/2017
4596	2^309637-16329	93211	Enzo Doria	04/2013
4597	(41*10^93207+49)/9	93208	Robert Price	04/2016
4598	14^81312-57	93194	Lelio R Paula	06/2016
4599	41^57783-40	93192	Theodore Burton	02/2007
4600	3*10^93179-97	93180	Robert Price	08/2017
4601	5*7^110252-4	93175	Lelio R Paula	11/2014
4602	83061!4-512	93137	Robert Price	11/2019
4603	2^309380-27	93133	Lelio R Paula	11/2012
4604	23*10^93116-7	93118	Robert Price	03/2016
4605	(29*10^93082+1)/3	93083	Robert Price	11/2015
4606	(58*10^93062-13)/9	93063	Robert Price	09/2015
4607	2^309131+1869383	93058	Enzo Doria	05/2016
4608	2^309066-93	93039	Lelio R Paula	11/2012
4609	2^309063-113269	93038	Enzo Doria	07/2014
4610	3^194965+16	93022	Robert Price	10/2013
4611	2^308979+1869143	93012	Enzo Doria	05/2016
4612	5^133064+54	93008	Lelio R Paula	04/2016
4613	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
4614	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
4615	(2*10^92976-17)/3	92976	Robert Price	08/2014
4616	2^308809+37967	92961	Phil Moore	03/2008
4617	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
4618	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
4619	2^308650+513	92913	Lelio R Paula	02/2016
4620	5*7^109936+6	92908	Lelio R Paula	10/2014
4621	2*10^92897+89	92898	Robert Price	07/2016
4622	12^86073-29	92889	Lelio R Paula	06/2016
4623	2^308566-117	92888	Lelio R Paula	11/2012
4624	(17*10^92869-11)/3	92870	Robert Price	07/2015
4625	2^308459+75431	92856	Enzo Doria	04/2016
4626	2^308426-1866377	92846	Enzo Doria	03/2016
4627	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
4628	2^308349-112111	92823	Enzo Doria	06/2014
4629	9*10^92821+19	92822	Robert Price	05/2016
4630	2^308337-75	92819	Lelio R Paula	11/2012
4631	4*3^194508+7	92805	Lelio R Paula	08/2014
4632	22*25^66379-113	92796	Curtis Bright	05/2015
4633	11^89101-1080	92790	Enzo Doria	12/2012
4634	2^308236-1867859	92789	Enzo Doria	04/2016
4635	12^85963+25	92770	Lelio R Paula	06/2016
4636	7^109750-66	92750	Lelio R Paula	04/2016
4637	9*10^92742+11	92743	Robert Kinser	01/2017
4638	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
4639	2^307997-110655	92717	Enzo Doria	05/2014
4640	L(443609)	92709	Renaud Lifchitz	11/2003
4641	10^92691+9	92692	Robert Price	03/2011
4642	10^92691-252291	92691	Patrick De Geest	08/2013
4643	2^307879-2521	92681	Yves Minet	07/2014
4644	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
4645	14^80831+47	92643	Lelio R Paula	06/2016
4646	15^78744+92	92611	Lelio R Paula	07/2016
4647	65^51083-64	92610	Norbert Schneider	11/2014
4648	131^43737-130	92604	Norbert Schneider	02/2019
4649	6^118996-16943	92597	Enzo Doria	02/2013
4650	(16*10^92591+41)/3	92592	Robert Price	10/2017
4651	(3^194014-7)/2	92568	Lelio R Paula	04/2013
4652	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
4653	(26*10^92546-77)/3	92547	Robert Price	02/2017
4654	3^193954+340	92540	Lelio R Paula	04/2016
4655	2^307407-307407^2	92539	Henri Lifchitz	05/2005
4656	(17*10^92513-11)/3	92514	Robert Price	07/2015
4657	2^307318-4211	92512	Yves Minet	06/2011
4658	2^307280+193	92501	Lelio R Paula	11/2012
4659	20^71075-33	92471	Lelio R Paula	05/2016
4660	2^307126-78795	92455	Lelio R Paula	02/2016
4661	2^307125-49789	92454	Henri Lifchitz	08/2005
4662	2^307099+23	92447	Lelio R Paula	11/2012
4663	129^43798+128	92440	Norbert Schneider	01/2019
4664	Phi(277314,10)/3327769	92430	Makoto Kamada	05/2019
4665	7*10^92414-69	92415	Robert Price	01/2017
4666	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
4667	2^306915+1873373	92391	Enzo Doria	06/2016
4668	2^306908+12915	92389	Lelio R Paula	02/2016
4669	19^72244-80	92383	Lelio R Paula	06/2016
4671	2^306849+75	92371	Lelio R Paula	11/2012
4670	(397*10^92369+53)/9	92371	Robert Price	11/2017
4672	2^306813-869688105	92360	Lelio R Paula	08/2016
4673	2^306672-109059	92318	Enzo Doria	04/2014
4674	6^118604-17063	92292	Enzo Doria	02/2013
4675	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
4676	2^306467-1835611	92256	Enzo Doria	04/2015
4677	2^306433+76427	92246	Enzo Doria	05/2016
4679	2^306430-113313	92245	Enzo Doria	07/2014
4678	(23*10^92244-59)/9	92245	Robert Price	03/2017
4680	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
4681	(25*10^92186+59)/3	92187	Robert Price	05/2016
4682	2^306213-286183	92180	Enzo Doria	06/2015
4683	10^92178+61	92179	Robert Price	04/2011
4684	10^92178-175509	92178	Patrick De Geest	07/2013
4685	2^306200+1185	92176	Lelio R Paula	02/2016
4686	2^306153+11	92162	Lelio R Paula	11/2012
4687	(2^306141-7)/5	92157	Lelio R Paula	06/2013
4688	(26*10^92152-23)/3	92153	Robert Price	08/2016
4689	(2*10^92152+67)/3	92152	Robert Price	04/2017
4690	410^92099+37^92099	92100	Mike Oakes	12/2010
4691	115^44684+114	92081	Norbert Schneider	07/2018
4692	(2^305867-2^152934+1)/5	92075		11/2006
4693	2^305851-109495	92071	Enzo Doria	04/2014
4695	12^85300+35	92055	Lelio R Paula	06/2016
4694	((10^46026-1)1000/9+739)10^46026+(10^46026-1)/9	92055	Hans Havermann	05/2019
4696	3^192911+92	92042	Lelio R Paula	04/2016
4697	2^305723-276271	92032	Enzo Doria	07/2015
4698	2^305676+93	92018	Donovan Johnson	06/2008
4699	3^192819+4	91999	Lelio R Paula	04/2013
4700	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
4701	2^305539+72911	91977	Enzo Doria	04/2016
4702	Phi(212014,10)	91960	Makoto Kamada	04/2019
4703	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
4704	82077!4-128	91928	Robert Price	11/2019
4705	85^47642+84	91922	Norbert Schneider	10/2015
4706	10^91920+187651	91921	Patrick De Geest	07/2013
4707	10^91920-39	91920	Robert Price	05/2011
4708	(22*10^91903+41)/9	91904	Robert Price	02/2015
4710	2^305275-27	91897	Lelio R Paula	11/2012
4709	3^192607-7726	91897	Enzo Doria	05/2014
4711	(7*10^91856-61)/9	91856	Erik Branger	12/2009
4712	(89*10^91839-53)/9	91840	Robert Price	11/2015
4713	8*5^131351+7	91812	Lelio R Paula	10/2014
4714	3^192426-68	91811	Lelio R Paula	04/2016
4715	2^304973+117	91807	Lelio R Paula	11/2012
4716	2^304939-1863727	91796	Enzo Doria	03/2016
4717	2^304902+8415	91785	Lelio R Paula	02/2016
4718	18^73119+61	91785	Lelio R Paula	06/2016
4719	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
4720	2^304747+71355	91738	Lelio R Paula	02/2016
4721	8*3^192251+5	91728	Lelio R Paula	08/2014
4722	2^304674-87	91717	Lelio R Paula	11/2012
4723	(28*10^91715+701)/9	91716	Robert Price	11/2017
4724	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
4725	(5*10^91707-119)/3	91708	Robert Price	04/2016
4726	2^304633-112771	91704	Enzo Doria	06/2014
4727	9*10^91693+23	91694	Robert Price	11/2017
4728	2^304578-16713	91688	Enzo Doria	05/2013
4729	6^117824-18713	91685	Enzo Doria	03/2013
4730	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
4731	(2^304551-7)/8912231	91673	Lelio R Paula	06/2013
4732	(2^304532-3)/3013	91670	Lelio R Paula	06/2013
4733	2^304507-16645	91666	Enzo Doria	04/2013
4734	(29*2^304489+1)/31	91661	Lelio R Paula	09/2013
4735	2^304471-1836127	91655	Enzo Doria	04/2015
4736	2^304433+32769	91644	Lelio R Paula	02/2016
4737	2^304410-16625	91637	Enzo Doria	04/2013
4738	183^40500-2	91630	Lelio R Paula	10/2017
4739	(203*10^91613+1)/3	91615	Robert Price	09/2017
4740	4*5^131052+7	91603	Lelio R Paula	10/2014
4741	2^304278-4001	91597	Yves Minet	04/2017
4742	2^304272-1866377	91595	Enzo Doria	03/2016
4743	2^304268+19683	91594	Lelio R Paula	02/2016
4744	2^304162-161	91562	Lelio R Paula	11/2012
4745	5*7^108331+6	91552	Lelio R Paula	10/2014
4746	2^304082-2787821	91538	Enzo Doria	03/2016
4747	2^304015+64133	91518	David Broadhurst	06/2002
4748	(7*2^303963+1)/3	91503	Lelio R Paula	09/2013
4749	(2^303945-9)/3617	91494	Lelio R Paula	06/2013
4750	2^303930+1880527	91493	Enzo Doria	10/2016

Find by discoverer :

PRP Records

Probable Primes Top 10000

(255244 PRPs in the top)