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	(55*10^106222+377)/9	106223	Robert Price	02/2019
4502	2^352814-131	106208	Lelio R Paula	10/2011
4503	2^352752+73951	106189	Enzo Doria	04/2016
4504	6^136434+5	106167	Lelio R Paula	11/2014
4505	25296^15737+15737^25296	106166	Hans Havermann	09/2020
4506	8*10^106157-13	106158	Robert Price	08/2019
4507	7*5^151872-8	106155	Lelio R Paula	11/2014
4508	105^52520-2	106153	Lelio R Paula	10/2017
4509	2^352601-1604809	106144	Enzo Doria	05/2015
4510	12^98353-43	106141	Lelio R Paula	02/2017
4511	2^352585-18901	106139	Enzo Doria	05/2013
4512	26363^10614+10614^26363	106135	Hans Havermann	09/2020
4513	(2^352554-3)/193	106128	Lelio R Paula	12/2013
4514	2^352540+15015	106126	Lelio R Paula	01/2017
4515	25068^17119+17119^25068	106125	Hans Havermann	09/2020
4516	2^352524-3149	106121	Yves Minet	10/2014
4517	2^352486-1858781	106109	Enzo Doria	04/2016
4518	2^352444+12705	106097	Lelio R Paula	01/2017
4519	28561^5182+5182^28561	106090	Hans Havermann	10/2020
4520	(182*10^106083+43)/9	106085	Robert Price	02/2020
4521	(266*10^106066+1)/3	106068	Robert Price	04/2020
4522	2^352228-18953	106032	Enzo Doria	05/2013
4523	(2^352223+1118)/2	106030	Stefano Morozzi	09/2020
4524	(2^352212+2250)/2	106027	Stefano Morozzi	01/2021
4525	(2^352136+2638)/2	106004	Stefano Morozzi	09/2020
4526	2^352107+1872533	105995	Enzo Doria	05/2016
4527	(2^352096+2086)/2	105992	Stefano Morozzi	09/2020
4528	2^352066-2591	105983	Yves Minet	07/2014
4529	2^352030+715	105972	Lelio R Paula	10/2011
4530	9*6^136176-5	105967	Lelio R Paula	11/2014
4531	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
4532	28582^5097+5097^28582	105963	Hans Havermann	09/2020
4533	155^48377+2	105962	Lelio R Paula	08/2013
4534	2^351865+1869707	105922	Enzo Doria	05/2016
4535	24974^17427+17427^24974	105921	Hans Havermann	09/2020
4536	25163^16194+16194^25163	105920	Hans Havermann	09/2020
4537	2^351831+23	105912	Lelio R Paula	10/2011
4538	(2^351818+3798)/2	105908	Stefano Morozzi	02/2021
4539	9*2^351784-5	105899	Lelio R Paula	09/2014
4540	(2^351776+2766)/2	105895	Stefano Morozzi	01/2021
4541	(85*10^105881+203)/9	105882	Robert Price	09/2020
4542	2^351671-112387	105864	Enzo Doria	06/2014
4543	2^351669-109501	105863	Enzo Doria	04/2014
4544	2^351644+74731	105856	Enzo Doria	04/2016
4545	13^95025-42	105853	Lelio R Paula	12/2016
4546	2^351599+15015	105842	Lelio R Paula	01/2017
4547	19^82763+90	105834	Lelio R Paula	01/2017
4548	26050^11551+11551^26050	105832	Hans Havermann	09/2020
4549	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
4550	20^81329-51	105812	Lelio R Paula	01/2017
4551	(5*10^105811+211)/9	105811	Robert Price	02/2018
4552	2^351483+28425	105807	Lelio R Paula	01/2017
4553	25231^15610+15610^25231	105804	Hans Havermann	09/2020
4554	15^89960+86	105802	Lelio R Paula	02/2017
4555	2^351460-17289	105801	Enzo Doria	05/2013
4556	19^82735+22	105798	Lelio R Paula	01/2017
4557	2^351435-109077	105793	Enzo Doria	04/2014
4558	2^351393+1089	105780	Lelio R Paula	01/2017
4559	2^351364+72631	105772	Enzo Doria	04/2016
4560	(2^351333+3626)/2	105762	Stefano Morozzi	09/2020
4561	26818^8783+8783^26818	105761	Hans Havermann	09/2020
4564	2^351305+1872467	105754	Enzo Doria	05/2016
4563	3^221649+16	105754	Lelio R Paula	11/2016
4562	32511^1790+1790^32511	105754	Hans Havermann	09/2020
4565	8*3^221637-5	105749	Lelio R Paula	09/2014
4566	2^351279-2780449	105746	Enzo Doria	03/2016
4567	(2^351263+3198)/2	105741	Stefano Morozzi	09/2020
4568	15^89903-26	105735	Lelio R Paula	02/2017
4570	2^351213-73	105726	Lelio R Paula	10/2011
4569	(2^351214+1210)/2	105726	Stefano Morozzi	09/2020
4571	2^351192-4589	105720	Yves Minet	07/2011
4572	20^81250-33	105709	Lelio R Paula	12/2016
4573	(2^351133+3530)/2	105702	Stefano Morozzi	09/2020
4574	(2^351103+534)/2	105693	Stefano Morozzi	09/2020
4575	2^351076-113159	105685	Enzo Doria	07/2014
4576	93^53688-2	105684	Lelio R Paula	09/2013
4577	2^351060-4559	105680	Yves Minet	07/2011
4578	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
4579	11^101473-750	105674	Enzo Doria	11/2012
4580	3*5^151181-8	105672	Lelio R Paula	11/2014
4581	15^89831-34	105650	Lelio R Paula	02/2017
4583	11^101448-360	105648	Enzo Doria	08/2012
4582	3*7^125011+4	105648	Lelio R Paula	11/2014
4584	2^350943-113269	105645	Enzo Doria	07/2014
4585	2*10^105636-91	105637	Robert Price	04/2020
4586	24231^22880+22880^24231	105634	Hans Havermann	09/2020
4587	35296^983+983^35296	105626	Hans Havermann	09/2020
4588	2^350868-19725	105622	Enzo Doria	06/2013
4589	2^350858-59291	105619	Enzo Doria	10/2015
4590	2^350851+135	105617	Lelio R Paula	10/2011
4591	2^350841-741	105614	Lelio R Paula	01/2017
4592	3*10^105582+77	105583	Robert Price	09/2018
4593	24915^17284+17284^24915	105581	Hans Havermann	09/2020
4594	(5*10^105576-53)/3	105577	Robert Price	09/2020
4595	8*10^105571+3	105572	Robert Price	08/2015
4596	2^350674-78557	105564	Jorge Menendez	03/2018
4597	2*5^151026-3	105563	Lelio R Paula	11/2014
4598	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
4599	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
4600	3^221211+236	105545	Lelio R Paula	11/2016
4601	(32*10^105530-77)/9	105531	Robert Price	06/2018
4603	10^105515+33	105516	Lelio R Paula	11/2016
4602	24644^19125+19125^24644	105516	Hans Havermann	10/2020
4604	10^105515-41033	105515	Patrick De Geest	12/2016
4605	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
4606	17^85732-72	105489	Lelio R Paula	01/2017
4607	(2^350399+3618)/2	105481	Stefano Morozzi	09/2020
4608	(2^350379+1010)/2	105475	Stefano Morozzi	09/2020
4609	25233^15118+15118^25233	105462	Hans Havermann	09/2020
4610	26261^10366+10366^26261	105454	Hans Havermann	09/2020
4611	2^350307-110329	105453	Enzo Doria	05/2014
4612	2^350253-20365	105437	Enzo Doria	06/2013
4613	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
4614	(2^350187+2658)/2	105417	Stefano Morozzi	09/2020
4615	2^350139-109009	105403	Enzo Doria	04/2014
4616	(2^350129+3026)/2	105400	Stefano Morozzi	09/2020
4617	(2^350097+2070)/2	105390	Stefano Morozzi	09/2020
4618	3*5^150763+4	105380	Lelio R Paula	11/2014
4619	12^97643+91	105375	Lelio R Paula	02/2017
4620	6*5^150744-7	105367	Lelio R Paula	11/2014
4621	(2^350018+2074)/2	105366	Stefano Morozzi	09/2020
4622	4*10^105364-39	105365	Robert Price	09/2020
4623	2^349996-112169	105360	Enzo Doria	06/2014
4624	(2^349997+3702)/2	105360	Stefano Morozzi	09/2020
4625	(418*10^105343+23)/9	105345	Robert Price	02/2020
4626	25490^13563+13563^25490	105334	Hans Havermann	10/2020
4627	11^101142-1080	105329	Enzo Doria	12/2012
4628	(68*10^105320-41)/9	105321	Robert Price	10/2013
4629	24800^17649+17649^24800	105319	Hans Havermann	09/2020
4630	3^220712-9934	105307	Enzo Doria	05/2014
4631	7*10^105296+9	105297	Robert Price	09/2015
4632	89*10^105284-7	105286	Robert Price	04/2020
4633	2^349739+1873373	105282	Enzo Doria	06/2016
4634	7^124574+24	105278	Lelio R Paula	11/2016
4635	2^349708-20957	105273	Enzo Doria	06/2013
4636	34115^1218+1218^34115	105267	Hans Havermann	09/2020
4637	2^349649-20469	105255	Enzo Doria	06/2013
4638	2^349607-20109	105243	Enzo Doria	06/2013
4639	(85*10^105242+473)/9	105243	Robert Price	01/2020
4640	2^349594-19085	105239	Enzo Doria	05/2013
4641	2^349530+1874479	105220	Enzo Doria	06/2016
4642	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
4643	(2^349452+3570)/2	105196	Stefano Morozzi	09/2020
4644	3^220464-112852	105189	Enzo Doria	07/2014
4645	2^349419-17349	105186	Enzo Doria	05/2013
4646	2^349400-2579	105180	Yves Minet	07/2014
4647	8*5^150471+3	105176	Lelio R Paula	11/2014
4648	(2^349359+2298)/2	105168	Stefano Morozzi	02/2021
4649	655^37342+37342^655	105165	Norbert Schneider	08/2018
4650	13^94403+94	105160	Lelio R Paula	12/2016
4651	2^349301-112309	105151	Enzo Doria	06/2014
4652	30291^2960+2960^30291	105149	Hans Havermann	09/2020
4653	27350^6981+6981^27350	105132	Hans Havermann	09/2020
4655	9*2^349220+5	105127	Lelio R Paula	09/2014
4654	(2^349225+3122)/2	105127	Stefano Morozzi	09/2020
4656	7*3^220317+8	105119	Lelio R Paula	09/2014
4658	7^124386+88	105119	Lelio R Paula	11/2016
4657	(2^349197+570)/2	105119	Stefano Morozzi	09/2020
4659	2^349171-19657	105111	Enzo Doria	06/2013
4660	(2^349115+590)/2	105094	Stefano Morozzi	09/2020
4661	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
4662	(2^349111-5)/3	105093	Lelio R Paula	12/2013
4663	675^37142+37142^675	105087	Norbert Schneider	08/2018
4664	2^348981-2797573	105054	Enzo Doria	04/2016
4665	2^348869-6555	105021	Lelio R Paula	01/2017
4666	5^150217+78	104998	Lelio R Paula	11/2016
4667	(88*10^104989-1)/3	104991	Robert Price	04/2020
4668	(28*10^104972+149)/3	104973	Robert Price	12/2019
4669	24927^16262+16262^24927	104972	Hans Havermann	10/2020
4670	2^348703-113005	104971	Enzo Doria	06/2014
4672	2^348612-809	104943	Yves Minet	05/2013
4671	(73*10^104942-1)/9	104943	Robert Price	01/2015
4673	2^348583-350407	104934	Enzo Doria	06/2015
4674	2^348531-949	104919	Yves Minet	05/2012
4675	20^80636-59	104910	Lelio R Paula	12/2016
4676	8*10^104893-13	104894	Robert Price	08/2019
4678	2^348437+35	104890	Lelio R Paula	09/2011
4677	25208^14487+14487^25208	104890	Hans Havermann	09/2020
4679	2^348348+135	104864	Lelio R Paula	09/2011
4680	6*10^104852-31	104853	Robert Price	07/2020
4682	(2^348284+9)/25	104843	Lelio R Paula	12/2013
4681	75^55914-74	104843	Norbert Schneider	01/2015
4683	2^348268+255255	104840	Lelio R Paula	01/2017
4684	35540^891+891^35540	104839	Hans Havermann	09/2020
4685	5^149985-52	104836	Lelio R Paula	11/2016
4686	2^348224-20249	104826	Enzo Doria	06/2013
4687	(2^348217+2522)/2	104824	Stefano Morozzi	09/2020
4688	2^348212-20105	104823	Enzo Doria	06/2013
4689	24647^17898+17898^24647	104819	Hans Havermann	10/2020
4690	20^80562+19	104814	Lelio R Paula	12/2016
4691	2*10^104811-87	104812	Robert Price	04/2018
4692	2^348149-20053	104804	Enzo Doria	06/2013
4693	2^348095-171	104788	Lelio R Paula	09/2011
4694	25383^13412+13412^25383	104769	Hans Havermann	09/2020
4695	2^348003-20377	104760	Enzo Doria	06/2013
4697	2^347994-741	104757	Lelio R Paula	12/2016
4696	(2^347993+2234)/2	104757	Stefano Morozzi	01/2021
4698	(2^347990+790)/2	104756	Stefano Morozzi	09/2020
4699	25137^14702+14702^25137	104756	Hans Havermann	09/2020
4700	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
4701	2^347910-109937	104732	Enzo Doria	04/2014
4702	(88*10^104709-637)/9	104710	Robert Price	11/2020
4703	5^149794+28	104702	Lelio R Paula	11/2016
4704	105^51800-2	104698	Lelio R Paula	10/2017
4705	(16^86939+3^86939)/19	104684	Robert Price	06/2013
4706	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
4707	2^347731-18609	104678	Enzo Doria	05/2013
4708	4*6^134519+7	104677	Lelio R Paula	11/2014
4709	25321^13588+13588^25321	104656	Hans Havermann	09/2020
4710	2^347612-18545	104642	Enzo Doria	05/2013
4713	6^134465+95	104635	Lelio R Paula	11/2016
4711	(2^347588+3718)/2	104635	Stefano Morozzi	09/2020
4712	(166*10^104633-7)/3	104635	Robert Price	11/2020
4714	2^347517-17301	104614	Enzo Doria	05/2013
4715	(2^347493+3186)/2	104606	Stefano Morozzi	09/2020
4716	(2^347490+2574)/2	104605	Stefano Morozzi	09/2020
4717	3^219222-310	104596	Lelio R Paula	11/2016
4718	25993^10554+10554^25993	104581	Hans Havermann	09/2020
4719	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
4720	2^347372-17853	104570	Enzo Doria	05/2013
4721	2^347314+99	104552	Lelio R Paula	09/2011
4722	2^347300-22233	104548	Enzo Doria	06/2013
4723	2^347287-19845	104544	Enzo Doria	06/2013
4724	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
4725	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
4726	7*2^347239-3	104531	Lelio R Paula	09/2014
4727	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
4728	5*3^219047+8	104513	Lelio R Paula	09/2014
4729	2^347148-109073	104502	Enzo Doria	04/2014
4730	2^347129-20145	104497	Enzo Doria	06/2013
4731	4*10^104461-57	104462	Robert Price	10/2018
4732	(2^346989+590)/2	104454	Stefano Morozzi	09/2020
4733	2^346923-19585	104435	Enzo Doria	05/2013
4734	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
4735	2^346854+346854^2+1	104414	Robert Price	06/2014
4736	2^346834+11715	104408	Lelio R Paula	04/2015
4737	24276^19961+19961^24276	104392	Hans Havermann	09/2020
4738	79^55009+78	104387	Norbert Schneider	02/2015
4739	3^218744+58	104368	Lelio R Paula	11/2016
4740	9*10^104361+89	104362	Robert Price	11/2019
4741	25048^14665+14665^25048	104358	Hans Havermann	09/2020
4742	2^346649+65	104352	Lelio R Paula	09/2011
4743	2^346638-17265	104349	Enzo Doria	05/2013
4744	(2^346606+2082)/2	104339	Stefano Morozzi	09/2020
4745	(2^346607+2070)/2	104339	Stefano Morozzi	09/2020
4746	(2^346582+3202)/2	104332	Stefano Morozzi	09/2020
4747	26092^9967+9967^26092	104331	Hans Havermann	09/2020
4748	5*10^104326+77	104327	Robert Price	12/2018
4749	(2^346564+2026)/2	104326	Stefano Morozzi	09/2020
4750	6^134055+101	104316	Lelio R Paula	11/2016

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