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 ?
4501	11^92309-42	96130	Lelio R Paula	05/2016
4502	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
4503	(7*10^96112+143)/3	96113	Robert Price	04/2016
4504	2^319237+65835	96100	Lelio R Paula	03/2016
4505	2^319194-1841	96087	Yves Minet	03/2013
4506	20^73847-31	96078	Lelio R Paula	05/2016
4507	50^56543-49	96065	Norbert Schneider	09/2018
4508	2^319107-109555	96061	Enzo Doria	04/2014
4509	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
4510	2^319098-112157	96059	Enzo Doria	06/2014
4511	15^81673+94	96055	Lelio R Paula	07/2016
4512	2^319074+1871749	96051	Enzo Doria	05/2016
4513	2^319007-112111	96031	Enzo Doria	06/2014
4514	2^318946-1421	96013	Yves Minet	01/2013
4515	22830^16003+16003^22830	95982	Hans Havermann	02/2020
4516	2^318834-110411	95979	Enzo Doria	05/2014
4517	2^318831-1965	95978	Lelio R Paula	03/2016
4518	(5*10^95976+7)/3	95977	Erik Branger	03/2014
4519	22871^15696+15696^22871	95962	Hans Havermann	01/2020
4520	23167^13860+13860^23167	95953	Hans Havermann	01/2020
4521	5*3^201089-8	95945	Lelio R Paula	08/2014
4522	2^318711-139	95942	Lelio R Paula	11/2012
4523	2^318635-1167	95919	Lelio R Paula	03/2016
4524	15^81555+16	95917	Lelio R Paula	07/2016
4525	(37*10^95895+377)/9	95896	Robert Price	10/2017
4526	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
4527	2^318496-97305	95877	Lelio R Paula	03/2016
4528	2^318466+15015	95868	Lelio R Paula	03/2016
4529	6^123187-173129	95859	Mike Oakes	04/2011
4530	2^318423-487	95855	Yves Minet	03/2012
4531	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
4532	45369!2+1024	95787	Robert Price	02/2015
4533	3^200758-86	95786	Lelio R Paula	05/2016
4534	(2^318271+1)/(346031404238891654090604244843)	95781	Gord Palameta	12/2018
4535	3*10^95776-59	95777	Robert Price	10/2017
4536	193^41901-2	95768	Lelio R Paula	10/2017
4537	4*10^95752-71	95753	Robert Price	11/2017
4538	23640^11197+11197^23640	95721	Hans Havermann	12/2019
4539	((10^47850-1)10000/9+6421)10^47850+(10^47850-1)/9	95704	Hans Havermann	05/2019
4540	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
4541	4*10^95672+91	95673	Robert Price	11/2017
4542	(11*10^95641-113)/3	95642	Robert Price	01/2017
4543	(13*10^95588+11)/3	95589	Robert Price	05/2015
4544	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
4545	3^200325+70	95580	Lelio R Paula	05/2016
4546	(25*10^95574-7)/9	95575	Robert Price	12/2014
4547	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
4548	2^317464+31	95567	Lelio R Paula	11/2012
4549	7^113073+82	95558	Lelio R Paula	04/2016
4550	2^317251+465	95503	Lelio R Paula	03/2016
4551	19^74684+58	95503	Lelio R Paula	06/2016
4552	(2^317250-7)/339	95500	Lelio R Paula	07/2013
4553	6^122718-79	95494	Lelio R Paula	05/2016
4554	22168^20291+20291^22168	95485	Hans Havermann	10/2019
4555	2^317141-110491	95469	Enzo Doria	05/2014
4556	2^317094+76309	95455	Enzo Doria	05/2016
4557	2^317085+95	95453	Lelio R Paula	11/2012
4558	(17*10^95451-377)/9	95452	Robert Price	11/2017
4559	2^317057-109551	95444	Enzo Doria	04/2014
4560	3^200026+28	95437	Lelio R Paula	05/2016
4561	2^317024+93	95434	Donovan Johnson	06/2008
4562	2^316999+1605	95427	Lelio R Paula	03/2016
4563	2^316995-110427	95426	Enzo Doria	05/2014
4565	2^316937+177	95408	Lelio R Paula	11/2012
4564	4*10^95407+91	95408	Robert Price	11/2017
4566	2^316908+1915	95399	Lelio R Paula	03/2016
4567	2^316894+99	95395	Lelio R Paula	11/2012
4568	6^122547+11	95361	Lelio R Paula	05/2016
4569	2^316771+82875	95358	Lelio R Paula	03/2016
4570	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
4571	1*10^95326+57	95327	Robert Price	03/2011
4572	10^95326-393687	95326	Patrick De Geest	09/2013
4573	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
4574	2^316654-109481	95323	Enzo Doria	04/2014
4575	8*10^95316+51	95317	Robert Price	05/2017
4576	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
4577	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
4578	(71*10^95277-539)/9	95278	Robert Price	11/2017
4579	23422^11691+11691^23422	95278	Hans Havermann	10/2019
4580	19^74503-56	95271	Lelio R Paula	06/2016
4581	11^91475-4380	95262	Enzo Doria	01/2013
4582	(62*10^95251-611)/9	95252	Robert Price	05/2017
4583	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
4584	(79*10^95214-43)/9	95215	Erik Branger	11/2013
4585	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
4586	5*2^316213+9	95191	Lelio R Paula	08/2014
4587	2^316205-1848163	95188	Enzo Doria	07/2015
4588	2^316185-2787913	95182	Enzo Doria	04/2016
4589	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
4590	2^316140-5	95168	Henri Lifchitz	02/2006
4591	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
4592	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
4593	2^316069+76817	95147	Enzo Doria	05/2016
4594	(199*10^95134-7)/3	95136	Robert Price	02/2017
4595	2^316027-97305	95134	Lelio R Paula	03/2016
4596	2^316006-2798051	95128	Enzo Doria	04/2016
4597	24994^6397+6397^24994	95127	Hans Havermann	02/2020
4598	2^315921-2797603	95102	Enzo Doria	04/2016
4599	2*10^95095+63	95096	Robert Price	10/2017
4600	2^315857+1299	95083	Lelio R Paula	03/2016
4601	14^82955-43	95078	Lelio R Paula	06/2016
4602	(2*10^95072-17)/3	95072	Robert Price	08/2014
4603	2^315727+65	95044	Lelio R Paula	11/2012
4604	2^315725+1885757	95043	Enzo Doria	03/2017
4605	1*10^94983+21	94984	Robert Price	03/2011
4606	10^94983-717	94983	Patrick De Geest	08/2013
4607	17^77187-82	94975	Lelio R Paula	07/2016
4608	3*10^94964+37	94965	Robert Price	10/2017
4609	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
4610	2^315423-110329	94952	Enzo Doria	05/2014
4611	11^91169-7230	94943	Enzo Doria	02/2013
4612	7*10^94938+61	94939	Robert Price	02/2017
4613	2^315351+1025	94931	Lelio R Paula	03/2016
4614	2^315350-112253	94930	Enzo Doria	06/2014
4617	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
4616	2^315268+7	94906	Lelio R Paula	10/2012
4615	11^91133+62	94906	Lelio R Paula	05/2016
4618	30^64244+41	94897	Lelio R Paula	08/2012
4619	(151*10^94885-7)/9	94887	Robert Price	07/2017
4620	4^157583+22147	94875	Mike Oakes	01/2011
4621	2^315098+123	94854	Lelio R Paula	11/2012
4622	3^198791-34	94848	Robert Price	11/2013
4623	3*2^315067+7	94846	Lelio R Paula	08/2014
4624	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
4625	(16*10^94822+53)/3	94823	Robert Price	12/2016
4626	8*6^121849-7	94818	Lelio R Paula	10/2014
4627	(85*10^94802+473)/9	94803	Robert Price	03/2017
4628	2^314870-108761	94786	Enzo Doria	03/2014
4629	5*2^314841-3	94778	Lelio R Paula	08/2014
4630	6^121772+113	94758	Lelio R Paula	05/2016
4631	6^121756-16253	94745	Enzo Doria	02/2013
4632	2^314718-112793	94740	Enzo Doria	06/2014
4633	2^314697-1847293	94734	Enzo Doria	07/2015
4635	2^314548-249	94689	Yves Minet	02/2012
4634	5^135469+42	94689	Lelio R Paula	04/2016
4636	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
4637	(2*10^94604+547)/9	94604	Robert Price	10/2017
4638	3*2^314152+5	94570	Lelio R Paula	08/2014
4639	2*6^121530-5	94570	Lelio R Paula	10/2014
4640	7*10^94563+87	94564	Robert Price	11/2016
4641	2^314114-109677	94558	Enzo Doria	04/2014
4642	(218389#+240867)/(311811)	94557	Makoto Morimoto	10/2017
4643	2^314059+76583	94542	Enzo Doria	05/2016
4644	2^314041-4035	94536	Lelio R Paula	03/2016
4645	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
4646	11^90760-4710	94517	Enzo Doria	01/2013
4647	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
4648	94*10^94493-3	94495	Robert Price	11/2016
4649	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
4650	(F(375345)^2+L(375345)^2)/4	94477	Henri Lifchitz	10/2017
4651	7^111792-32	94476	Lelio R Paula	04/2016
4652	11^90680-5850	94434	Enzo Doria	01/2013
4653	2^313675-110125	94426	Enzo Doria	04/2014
4654	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
4655	2^313609-112225	94406	Enzo Doria	06/2014
4656	2^313584+72901	94399	Enzo Doria	04/2016
4657	2^313510-112865	94376	Enzo Doria	06/2014
4658	7*10^94373+87	94374	Robert Price	11/2016
4659	(9^98897+8^98897)/17	94371	Robert Price	12/2012
4660	2^313453-114703	94359	Enzo Doria	04/2015
4661	8*10^94357-51	94358	Robert Price	10/2017
4662	(379*10^94337-1)/9	94339	Robert Price	08/2017
4663	2^313344-313344+1	94326	Robert Price	10/2014
4664	20^72481-49	94300	Lelio R Paula	05/2016
4665	44725!2+128	94289	Robert Price	03/2015
4666	4*10^94286+9	94287	Robert Price	05/2015
4667	17^76621+24	94279	Lelio R Paula	07/2016
4668	2^313156-112859	94270	Enzo Doria	06/2014
4669	6^121130-59	94258	Lelio R Paula	05/2016
4670	3^197542+28	94252	Robert Price	11/2013
4671	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
4672	2^313045-5955	94236	Lelio R Paula	03/2016
4673	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
4674	2^312909-1865203	94195	Enzo Doria	03/2016
4675	2^312848-149	94177	Lelio R Paula	11/2012
4676	4^156403-77597	94164	Mike Oakes	04/2011
4677	18^75004-85	94151	Lelio R Paula	06/2016
4678	19^73622-48	94145	Lelio R Paula	06/2016
4679	(11^90397-3^90397)/8	94138	Robert Price	04/2011
4680	(3^197287+5)/16	94129	Lelio R Paula	04/2013
4681	12^87212-37	94118	Lelio R Paula	06/2016
4682	11^90376+76	94117	Lelio R Paula	05/2016
4683	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
4684	(10^94096+191)/3	94096	Robert Price	11/2017
4685	2^312562-112685	94091	Enzo Doria	06/2014
4686	137^44026-2	94072	Lelio R Paula	10/2017
4687	2^312404-869688105	94043	Lelio R Paula	09/2016
4688	2^312387+2793533	94038	Enzo Doria	03/2016
4690	10^94016+91	94017	Robert Price	04/2011
4689	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
4691	10^94016-188963	94016	Patrick De Geest	08/2013
4692	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
4693	6^120802+7661	94003	Mike Oakes	04/2011
4694	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
4695	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
4696	2^312201+51	93982	Lelio R Paula	11/2012
4697	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
4698	3^196892+58	93942	Lelio R Paula	05/2016
4699	2^312060+18915	93940	Lelio R Paula	03/2016
4700	42^57867-41	93933	Norbert Schneider	08/2018
4701	2^311992-16209	93919	Enzo Doria	04/2013
4702	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
4703	2^311965-39	93911	Lelio R Paula	11/2012
4704	2^311920-111689	93898	Enzo Doria	05/2014
4705	130^44414+129	93889	Norbert Schneider	01/2019
4706	7*10^93887-47	93888	Robert Price	02/2017
4707	12^86965-13	93851	Lelio R Paula	06/2016
4708	2^311705+16095	93833	Lelio R Paula	03/2016
4709	2^311665-81	93821	Lelio R Paula	11/2012
4710	730^32761+32761^730	93806	Norbert Schneider	09/2017
4711	11^90073+92	93802	Lelio R Paula	05/2016
4712	6*10^93792+41	93793	Robert Price	01/2017
4714	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
4713	10^93790-123456789	93790	Robert Price	02/2020
4715	12^86900-77	93781	Lelio R Paula	06/2016
4716	2^311508-109769	93774	Enzo Doria	04/2014
4717	2^311486-1859621	93767	Enzo Doria	03/2016
4718	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
4719	(10^93811-1)/(996812952121099970133280113810431639637782545831)	93765	Gord Palameta	10/2018
4720	2^311471+311469	93763	Renaud Lifchitz	01/2003
4721	(88*10^93760-1)/3	93762	Robert Price	10/2017
4722	2^311426+79459	93749	Enzo Doria	06/2016
4723	2^311294+5775	93709	Lelio R Paula	03/2016
4724	2^311252-1017	93697	Lelio R Paula	03/2016
4725	2^311247-112041	93695	Enzo Doria	06/2014
4726	7*10^93692-83	93693	Robert Price	09/2017
4727	2^311205-109645	93683	Enzo Doria	04/2014
4728	5^134027-84	93681	Lelio R Paula	04/2016
4729	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
4730	(2^311027-2^155514+1)/5	93628		11/2006
4731	3^196192-28	93608	Robert Price	12/2013
4732	216091#+261433	93606	Makoto Morimoto	12/2015
4733	5^133917+68	93604	Lelio R Paula	04/2016
4734	2^310924-1709	93598	Yves Minet	03/2013
4735	(266*10^93577-11)/3	93579	Robert Price	09/2016
4736	(16*10^93577+161)/3	93578	Robert Price	05/2016
4737	3^196113-56	93570	Lelio R Paula	04/2016
4738	2^310806-110345	93562	Enzo Doria	05/2014
4739	3^196093+86	93561	Lelio R Paula	04/2016
4740	2^310780-2327	93555	Yves Minet	10/2013
4741	30^63332+41	93550	Lelio R Paula	08/2012
4742	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
4743	8*5^133807+7	93528	Lelio R Paula	10/2014
4744	2^310686+8193	93526	Lelio R Paula	03/2016
4745	2^310646+63	93514	Lelio R Paula	11/2012
4746	(77*10^93508+31)/9	93509	Robert Price	10/2015
4747	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
4748	(2*10^93497+7)/9	93497	Erik Branger	03/2011
4749	3^195958-112852	93496	Enzo Doria	07/2014
4750	2^310583+16385	93495	Lelio R Paula	03/2016

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PRP Records

Probable Primes Top 10000

(259919 PRPs in the top)