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	32950^10591+10591^32950	132622	Hans Havermann	04/2021
4502	33302^9597+9597^33302	132614	Hans Havermann	04/2021
4503	(19*10^132550+191)/3	132551	Robert Price	05/2019
4504	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
4505	(38^83891+1)/39	132529	Robert Price	09/2013
4506	2*10^132493-43	132494	Robert Price	04/2018
4507	31352^16809+16809^31352	132480	Hans Havermann	04/2021
4508	(418*10^132441+23)/9	132443	Robert Price	02/2020
4509	2^439931-21	132433	Lelio R Paula	08/2017
4510	47^79201-46^79201	132432	Robert Price	10/2012
4511	2^439897-113653	132423	Enzo Doria	08/2014
4512	35505^5362+5362^35505	132410	Hans Havermann	03/2021
4513	30079^25222+25222^30079	132402	Hans Havermann	04/2021
4514	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
4515	(695*10^132356+7)/9	132358	Robert Price	12/2021
4516	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
4517	2^439576-113247	132326	Enzo Doria	07/2014
4518	30059^25230+25230^30059	132318	Hans Havermann	04/2021
4519	2^439497-29143	132302	Enzo Doria	07/2015
4520	2^439409-114193	132276	Enzo Doria	12/2014
4521	(44*10^132233-233)/9	132234	Robert Price	01/2019
4522	25507^30000-30000^25507	132200	Frank Doornink	02/2024
4523	9*10^132148-7	132149	Robert Price	09/2015
4524	V(790390)	132144	Serge Batalov	07/2024
4525	(47*10^132125-119)/9	132126	Robert Price	05/2019
4526	2^438900+214051	132123	Enzo Doria	10/2023
4527	2^438845+1870217	132106	Enzo Doria	05/2016
4528	2^438789+87855	132089	Lelio R Paula	01/2016
4529	2^438774-2786411	132085	Enzo Doria	03/2016
4530	2^438755-1848205	132079	Enzo Doria	07/2015
4531	30502^21381+21381^30502	132075	Hans Havermann	04/2021
4532	2^438739-112087	132074	Enzo Doria	06/2014
4533	(2^438438+100280245065)	131983	Paul Bourdelais	05/2022
4534	35872^4777+4777^35872	131979	Hans Havermann	04/2021
4535	31198^16945+16945^31198	131938	Hans Havermann	03/2021
4536	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
4537	L(631181)	131910	Henri Lifchitz	09/2008
4538	(47*10^131886-119)/9	131887	Robert Price	05/2019
4539	5*2^438096-3	131881	Jon Grantham	07/2023
4540	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
4541	2^438079-1863877	131875	Enzo Doria	03/2016
4542	(16*10^131872-37)/3	131873	Robert Price	05/2021
4543	(2^438067+5)/329	131869	Lelio R Paula	06/2015
4544	2^437908-113855	131824	Enzo Doria	09/2014
4545	2^437884-286349	131817	Enzo Doria	07/2015
4546	15^112072+14	131807	Alfred Reich	10/2023
4547	5^188558+4	131797	Tyler NeSmith	05/2021
4548	(11*10^131784-17)/3	131785	Robert Price	06/2018
4549	(166^59357-1)/165	131777	Anonymous	06/2024
4551	4*10^131719-93	131720	Robert Price	07/2020
4550	31629^14606+14606^31629	131720	Hans Havermann	04/2021
4552	3^276062-112292	131716	Enzo Doria	07/2014
4553	11*31^88313+322688	131708	Eric Chen	05/2024
4554	(7*10^131682+89)/3	131683	Robert Price	08/2020
4555	29512^28969+28969^29512	131681	Hans Havermann	03/2021
4556	2^437343+75953	131654	Enzo Doria	04/2016
4557	35^85243-34^85243	131621	Robert Price	05/2012
4558	(28*10^131586+59)/3	131587	Robert Price	05/2021
4559	(59*10^131575+391)/9	131576	Robert Price	03/2021
4560	39984^1945+1945^39984	131505	Hans Havermann	03/2021
4561	25842^29801-29801^25842	131492	Frank Doornink	03/2024
4562	28592^29505-29505^28592	131482	Frank Doornink	05/2024
4563	25647^29818-29818^25647	131469	Frank Doornink	02/2024
4564	(203*10^131457+1)/3	131459	Robert Price	03/2020
4565	7*10^131421-41	131422	Robert Price	08/2021
4566	87309^32+32^87309	131414	Hans Havermann	03/2021
4567	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
4568	2^436521+224885	131406	Enzo Doria	07/2024
4569	(650*10^131391+43)/9	131393	Tyler Busby	01/2023
4570	2^436451+1884713	131385	Enzo Doria	03/2017
4571	2^436365+35	131359	Robert Price	11/2015
4573	2^436300+1866871	131340	Enzo Doria	03/2016
4572	(7*10^131339+179)/3	131340	Robert Price	09/2018
4574	14^114592-3	131338	Paul Bourdelais	12/2020
4575	36197^4236+4236^36197	131285	Hans Havermann	04/2021
4576	(37*10^131270+341)/9	131271	Robert Price	08/2018
4577	29863^24790+24790^29863	131227	Hans Havermann	03/2021
4578	(5*10^131223-29)/3	131224	Robert Price	03/2018
4579	29524^27825+27825^29524	131218	Hans Havermann	03/2021
4580	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
4581	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
4582	30639^19136+19136^30639	131192	Hans Havermann	04/2021
4583	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
4584	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
4585	2^435773+1875557	131181	Enzo Doria	06/2016
4586	(16*10^131180+167)/3	131181	Robert Price	06/2019
4587	(26*10^131180-77)/3	131181	Robert Price	11/2019
4588	(25*10^131144-7)/9	131145	Robert Price	05/2018
4589	29299^29358-29358^29299	131138	Norbert Schneider	03/2022
4590	2^435612-2789939	131133	Enzo Doria	12/2015
4591	33976^7231+7231^33976	131121	Hans Havermann	03/2021
4592	33715^7746+7746^33715	131121	Hans Havermann	03/2021
4593	66^72047-65^72047	131093	Robert Price	09/2013
4594	(5*10^131090+37)/3	131091	Robert Price	03/2018
4595	2^435468+75631	131089	Enzo Doria	04/2016
4596	37^83588-2	131083	Lelio R Paula	08/2015
4597	(4^217720+11)/3	131081	Robert Price	02/2017
4598	30407^20448+20448^30407	131074	Hans Havermann	04/2021
4599	(22*10^131070+179)/3	131071	Robert Price	02/2022
4600	28831^29388-29388^28831	131067	Frank Doornink	05/2024
4601	29487^27836+27836^29487	131059	Hans Havermann	04/2021
4602	29962^23615+23615^29962	131030	Hans Havermann	03/2021
4603	2^435202-113193	131009	Enzo Doria	07/2014
4604	41705^1384+1384^41705	131002	Hans Havermann	04/2021
4605	9*10^130998-19	130999	Robert Price	07/2019
4606	36243^4108+4108^36243	130969	Hans Havermann	04/2021
4607	(445^49433+1)/446	130914	Jinyuan Wang	05/2024
4608	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
4609	2^434835-111937	130899	Enzo Doria	05/2014
4610	(62*10^130895-629)/9	130896	Robert Price	07/2021
4611	2^434685+72257	130854	Enzo Doria	04/2016
4612	(7*10^130825+113)/3	130826	Robert Price	02/2018
4613	2^434539-29317	130810	Enzo Doria	07/2015
4614	(74*10^130791+637)/9	130792	Robert Price	01/2022
4615	2^434469-114259	130789	Enzo Doria	01/2015
4616	(5*10^130763+103)/9	130763	Robert Price	04/2022
4617	2^434246+33	130722	Robert Price	11/2015
4618	30156^21599+21599^30156	130710	Hans Havermann	04/2021
4619	(17*10^130695-161)/9	130696	Robert Price	02/2021
4620	30513^19148+19148^30513	130661	Hans Havermann	03/2021
4621	29736^24761+24761^29736	130654	Hans Havermann	04/2021
4622	9*10^130638+41	130639	Robert Price	08/2020
4623	2^433911-91	130621	Lelio R Paula	06/2017
4624	30786^17449+17449^30786	130588	Hans Havermann	03/2021
4625	2^433744-114419	130570	Enzo Doria	02/2015
4627	2^433708+1869451	130560	Enzo Doria	05/2016
4626	2^433710+93	130560	Lelio R Paula	06/2017
4628	7*10^130535-27	130536	Robert Price	11/2022
4629	(9629^32768+1)/120501441265666	130520	Kellen Shenton	05/2021
4630	804*34^85220+713	130516	Eric Chen	08/2023
4631	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
4632	3^273521+10	130503	Tyler NeSmith	01/2021
4633	41659^1356+1356^41659	130487	Hans Havermann	03/2021
4634	4*10^130480+9	130481	Robert Price	05/2015
4635	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
4636	3*2^433422+5	130474	Jon Grantham	07/2023
4637	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
4638	(31*10^130414-49)/9	130415	Robert Price	11/2021
4639	26462^29485-29485^26462	130402	Frank Doornink	03/2024
4640	33481^7848+7848^33481	130401	Hans Havermann	03/2021
4641	(17*10^130393+7)/3	130394	Robert Price	06/2023
4642	(22*10^130392+203)/9	130393	Robert Price	10/2021
4643	29773^23950+23950^29773	130386	Hans Havermann	04/2021
4644	2^433023-113497	130353	Enzo Doria	08/2014
4645	31175^15178+15178^31175	130350	Hans Havermann	04/2021
4646	2^433002+1179379	130347	Enzo Doria	06/2016
4647	2^432974+19	130339	Robert Price	08/2015
4648	31903^12168+12168^31903	130331	Hans Havermann	04/2021
4649	2^432917+22217	130322	Enzo Doria	09/2023
4650	29387^27112+27112^29387	130278	Hans Havermann	04/2021
4651	2^432768+213181	130277	Enzo Doria	09/2023
4652	29577^25370+25370^29577	130267	Hans Havermann	04/2021
4653	31738^12685+12685^31738	130231	Hans Havermann	03/2021
4654	44235^878+878^44235	130206	Hans Havermann	04/2021
4655	32160^11171+11171^32160	130187	Hans Havermann	04/2021
4656	29489^25956+25956^29489	130172	Hans Havermann	04/2021
4657	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
4658	33005^8766+8766^33005	130133	Hans Havermann	04/2021
4659	(35*10^130132-611)/9	130133	Robert Price	02/2022
4660	(444^49408+1)/(444^256+1)	130125	Martin Hopf	12/2023
4661	2^432217+41	130111	Lelio R Paula	06/2017
4662	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
4663	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
4664	97^65480-2	130094	Lelio R Paula	05/2017
4665	36007^4102+4102^36007	130094	Hans Havermann	04/2021
4666	4*10^130088-89	130089	Robert Price	11/2018
4667	2^432117-113215	130081	Enzo Doria	07/2014
4668	(4*10^130080+41)/9	130080	Serge Batalov	11/2022
4669	2^431804+72511	129986	Enzo Doria	04/2016
4670	27902^29237-29237^27902	129978	Frank Doornink	03/2024
4671	(2313^38809-1)/(2313^197-1)	129898	Ryan Propper	11/2023
4672	(13*10^129896+137)/3	129897	Robert Price	06/2021
4673	(13*10^129890+71)/3	129891	Robert Price	06/2021
4674	29048^29101-29101^29048	129882	Norbert Schneider	03/2022
4675	37832^2709+2709^37832	129871	Hans Havermann	04/2021
4676	31055^15184+15184^31055	129853	Hans Havermann	04/2021
4677	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
4678	31385^13702+13702^31385	129833	Hans Havermann	04/2021
4679	(13*10^129826+41)/9	129827	Tyler Busby	02/2023
4680	28901^29102-29102^28901	129822	Norbert Schneider	03/2022
4681	(47*10^129789-119)/9	129790	Robert Price	05/2019
4682	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
4683	25999^29384-29384^25999	129730	Frank Doornink	03/2024
4684	25771^29408-29408^25771	129723	Frank Doornink	02/2024
4685	(166*10^129712+17)/3	129714	Robert Price	07/2022
4686	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
4687	2^430807+1869563	129686	Enzo Doria	05/2016
4688	2^430721-21429	129660	Enzo Doria	07/2013
4689	(4*10^129618+89)/3	129619	Robert Price	08/2021
4690	(142^60223-1)/141	129616	Anonymous	06/2024
4691	(10^129587-7^129587)/3	129587	Jon Grantham	07/2023
4692	2^430415-276271	129568	Enzo Doria	07/2015
4693	32282^10311+10311^32282	129558	Hans Havermann	04/2021
4694	29486^24741+24741^29486	129545	Hans Havermann	04/2021
4695	(29*10^129543+313)/9	129544	Robert Price	04/2021
4696	37095^3104+3104^37095	129533	Hans Havermann	04/2021
4697	31132^14459+14459^31132	129514	Hans Havermann	04/2021
4698	32582^9435+9435^32582	129506	Hans Havermann	03/2021
4699	30442^17953+17953^30442	129505	Hans Havermann	03/2021
4700	(199*10^129487-7)/3	129489	Robert Price	05/2020
4701	2^430142-2791721	129486	Enzo Doria	03/2016
4702	(7*10^129472-13)/3	129473	Robert Price	07/2018
4703	(8*10^129469+79)/3	129470	Robert Price	10/2020
4704	31678^12213+12213^31678	129463	Hans Havermann	04/2021
4705	10620^32143-10619^32143	129412	Norbert Schneider	08/2023
4706	(772*10^129406-7)/9	129408	Robert Price	06/2022
4707	(535^47431-1)/534	129406	Tom Wu	09/2024
4708	31100^14439+14439^31100	129362	Hans Havermann	04/2021
4709	33009^8288+8288^33009	129345	Hans Havermann	04/2021
4710	25895^29306-29306^25895	129334	Frank Doornink	03/2024
4711	(44^78697+43^78697)/87	129333	Aurel Gibier	11/2023
4712	29675^22804+22804^29675	129324	Hans Havermann	04/2021
4713	29068^28099+28099^29068	129315	Hans Havermann	04/2021
4714	2^429568-21017	129313	Enzo Doria	07/2013
4715	(10^129295+83)/3	129295	Robert Price	08/2021
4716	(853*10^129274-7)/9	129276	Robert Price	07/2021
4717	30958^14961+14961^30958	129249	Hans Havermann	04/2021
4718	(11*10^129239-179)/3	129240	Robert Price	09/2018
4719	28659^28988+28988^28659	129208	Norbert Schneider	02/2021
4720	29423^24616+24616^29423	129203	Hans Havermann	03/2021
4721	2^429194-112685	129201	Enzo Doria	06/2014
4722	2^429145-2780449	129186	Enzo Doria	04/2016
4723	32500^9427+9427^32500	129168	Hans Havermann	04/2021
4724	33577^7014+7014^33577	129136	Hans Havermann	03/2021
4725	2^428892-113453	129110	Enzo Doria	07/2014
4726	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
4727	2^428727-113959	129060	Enzo Doria	10/2014
4728	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
4729	(10^129051-31)/3	129051	Serge Batalov	12/2014
4730	(134*10^129038+7)/3	129040	Robert Price	02/2020
4731	2^428564+71161	129011	Enzo Doria	04/2016
4732	28781^28930+28930^28781	129002	Norbert Schneider	02/2021
4733	29065^27424+27424^29065	128995	Hans Havermann	04/2021
4734	2^428502-113285	128992	Enzo Doria	07/2014
4735	2^428421-21373	128968	Enzo Doria	06/2013
4736	L(616787)	128901	Henri Lifchitz	09/2008
4737	(765^44701-1)/764	128900	Tom Wu	07/2024
4738	20^99055-3	128874	Paul Bourdelais	12/2020
4739	91^65772-2	128851	Lelio R Paula	05/2017
4740	2^428022+43	128848	Lelio R Paula	05/2017
4741	2^427999-459397	128841	Enzo Doria	05/2015
4742	2^427993+76847	128839	Enzo Doria	05/2016
4743	31059^14060+14060^31059	128833	Hans Havermann	03/2021
4744	10^128805+152871	128806	Patrick De Geest	05/2021
4745	10^128805-10001	128805	Robert Price	02/2021
4746	2^427824-1851507	128788	Enzo Doria	08/2015
4747	2^427807-21469	128783	Enzo Doria	07/2013
4748	29082^26783+26783^29082	128772	Hans Havermann	04/2021
4749	40055^1638+1638^40055	128750	Hans Havermann	04/2021
4750	(923^43411-1)/922	128720	Tom Wu	07/2024

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