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 ?
5501	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
5502	2^438079-1863877	131875	Enzo Doria	03/2016
5503	(16*10^131872-37)/3	131873	Robert Price	05/2021
5504	(2^438067+5)/329	131869	Lelio R Paula	06/2015
5505	2^437908-113855	131824	Enzo Doria	09/2014
5506	2^437884-286349	131817	Enzo Doria	07/2015
5507	15^112072+14	131807	Alfred Reich	10/2023
5508	5^188558+4	131797	Tyler NeSmith	05/2021
5509	(11*10^131784-17)/3	131785	Robert Price	06/2018
5510	(166^59357-1)/165	131777	Anonymous	06/2024
5511	4*10^131719-93	131720	Robert Price	07/2020
5512	31629^14606+14606^31629	131720	Hans Havermann	04/2021
5513	3^276062-112292	131716	Enzo Doria	07/2014
5514	2^437539+2025	131713	Henri Lifchitz	01/2025
5515	11*31^88313+322688	131708	Eric Chen	05/2024
5516	(7*10^131682+89)/3	131683	Robert Price	08/2020
5517	29512^28969+28969^29512	131681	Hans Havermann	03/2021
5518	2^437343+75953	131654	Enzo Doria	04/2016
5519	35^85243-34^85243	131621	Robert Price	05/2012
5520	(28*10^131586+59)/3	131587	Robert Price	05/2021
5521	(59*10^131575+391)/9	131576	Robert Price	03/2021
5522	Phi(51051,-17#)	131513	Henri Lifchitz	12/2025
5523	39984^1945+1945^39984	131505	Hans Havermann	03/2021
5524	25842^29801-29801^25842	131492	Frank Doornink	03/2024
5525	28592^29505-29505^28592	131482	Frank Doornink	05/2024
5526	25647^29818-29818^25647	131469	Frank Doornink	02/2024
5527	(203*10^131457+1)/3	131459	Robert Price	03/2020
5528	7*10^131421-41	131422	Robert Price	08/2021
5529	87309^32+32^87309	131414	Hans Havermann	03/2021
5530	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
5531	2^436521+224885	131406	Enzo Doria	07/2024
5532	(650*10^131391+43)/9	131393	Tyler Busby	01/2023
5533	2^436451+1884713	131385	Enzo Doria	03/2017
5534	2^436365+35	131359	Robert Price	11/2015
5536	2^436300+1866871	131340	Enzo Doria	03/2016
5535	(7*10^131339+179)/3	131340	Robert Price	09/2018
5537	14^114592-3	131338	Paul Bourdelais	12/2020
5538	36197^4236+4236^36197	131285	Hans Havermann	04/2021
5539	(37*10^131270+341)/9	131271	Robert Price	08/2018
5540	29863^24790+24790^29863	131227	Hans Havermann	03/2021
5541	(5*10^131223-29)/3	131224	Robert Price	03/2018
5542	29524^27825+27825^29524	131218	Hans Havermann	03/2021
5543	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
5544	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
5545	30639^19136+19136^30639	131192	Hans Havermann	04/2021
5546	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
5547	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
5548	2^435773+1875557	131181	Enzo Doria	06/2016
5550	(16*10^131180+167)/3	131181	Robert Price	06/2019
5549	(26*10^131180-77)/3	131181	Robert Price	11/2019
5551	(25*10^131144-7)/9	131145	Robert Price	05/2018
5552	29299^29358-29358^29299	131138	Norbert Schneider	03/2022
5553	2^435612-2789939	131133	Enzo Doria	12/2015
5554	33976^7231+7231^33976	131121	Hans Havermann	03/2021
5555	33715^7746+7746^33715	131121	Hans Havermann	03/2021
5556	66^72047-65^72047	131093	Robert Price	09/2013
5557	(5*10^131090+37)/3	131091	Robert Price	03/2018
5558	2^435468+75631	131089	Enzo Doria	04/2016
5559	37^83588-2	131083	Lelio R Paula	08/2015
5560	(4^217720+11)/3	131081	Robert Price	02/2017
5561	30407^20448+20448^30407	131074	Hans Havermann	04/2021
5562	(22*10^131070+179)/3	131071	Robert Price	02/2022
5563	28831^29388-29388^28831	131067	Frank Doornink	05/2024
5564	29487^27836+27836^29487	131059	Hans Havermann	04/2021
5565	29962^23615+23615^29962	131030	Hans Havermann	03/2021
5566	2^435202-113193	131009	Enzo Doria	07/2014
5567	41705^1384+1384^41705	131002	Hans Havermann	04/2021
5568	9*10^130998-19	130999	Robert Price	07/2019
5569	36243^4108+4108^36243	130969	Hans Havermann	04/2021
5570	(445^49433+1)/446	130914	Jinyuan Wang	05/2024
5571	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
5572	2^434835-111937	130899	Enzo Doria	05/2014
5573	(62*10^130895-629)/9	130896	Robert Price	07/2021
5574	2^434807+225	130890	Henri Lifchitz	11/2024
5575	2^434685+72257	130854	Enzo Doria	04/2016
5576	Phi(64497,-1105)	130853	Henri Lifchitz	12/2025
5577	(7*10^130825+113)/3	130826	Robert Price	02/2018
5578	2^434539-29317	130810	Enzo Doria	07/2015
5579	(74*10^130791+637)/9	130792	Robert Price	01/2022
5580	2^434469-114259	130789	Enzo Doria	01/2015
5581	(5*10^130763+103)/9	130763	Robert Price	04/2022
5582	2^434246+33	130722	Robert Price	11/2015
5583	30156^21599+21599^30156	130710	Hans Havermann	04/2021
5584	(41^81041-3^81041)/38	130701	Robert Price	09/2025
5585	(17*10^130695-161)/9	130696	Robert Price	02/2021
5586	30513^19148+19148^30513	130661	Hans Havermann	03/2021
5587	29736^24761+24761^29736	130654	Hans Havermann	04/2021
5588	9*10^130638+41	130639	Robert Price	08/2020
5589	2^433911-91	130621	Lelio R Paula	06/2017
5590	30786^17449+17449^30786	130588	Hans Havermann	03/2021
5591	2^433744-114419	130570	Enzo Doria	02/2015
5593	2^433708+1869451	130560	Enzo Doria	05/2016
5592	2^433710+93	130560	Lelio R Paula	06/2017
5594	7*10^130535-27	130536	Robert Price	11/2022
5595	(17^130533)%(10^130533)	130533	Henri Lifchitz	05/2025
5596	(9629^32768+1)/120501441265666	130520	Kellen Shenton	05/2021
5597	804*34^85220+713	130516	Eric Chen	08/2023
5598	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
5599	3^273521+10	130503	Tyler NeSmith	01/2021
5600	41659^1356+1356^41659	130487	Hans Havermann	03/2021
5601	4*10^130480+9	130481	Robert Price	05/2015
5602	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
5603	3*2^433422+5	130474	Jon Grantham	07/2023
5604	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
5605	(31*10^130414-49)/9	130415	Robert Price	11/2021
5606	26462^29485-29485^26462	130402	Frank Doornink	03/2024
5607	33481^7848+7848^33481	130401	Hans Havermann	03/2021
5608	(17*10^130393+7)/3	130394	Robert Price	06/2023
5609	(22*10^130392+203)/9	130393	Robert Price	10/2021
5610	29773^23950+23950^29773	130386	Hans Havermann	04/2021
5611	2^433023-113497	130353	Enzo Doria	08/2014
5612	31175^15178+15178^31175	130350	Hans Havermann	04/2021
5613	2^433002+1179379	130347	Enzo Doria	06/2016
5614	2^432974+19	130339	Robert Price	08/2015
5615	31903^12168+12168^31903	130331	Hans Havermann	04/2021
5616	2^432917+22217	130322	Enzo Doria	09/2023
5617	29387^27112+27112^29387	130278	Hans Havermann	04/2021
5618	2^432768+213181	130277	Enzo Doria	09/2023
5619	29577^25370+25370^29577	130267	Hans Havermann	04/2021
5620	31738^12685+12685^31738	130231	Hans Havermann	03/2021
5621	44235^878+878^44235	130206	Hans Havermann	04/2021
5622	32160^11171+11171^32160	130187	Hans Havermann	04/2021
5623	29489^25956+25956^29489	130172	Hans Havermann	04/2021
5624	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
5625	33005^8766+8766^33005	130133	Hans Havermann	04/2021
5626	(35*10^130132-611)/9	130133	Robert Price	02/2022
5627	(444^49408+1)/(444^256+1)	130125	Martin Hopf	12/2023
5628	2^432217+41	130111	Lelio R Paula	06/2017
5629	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
5630	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
5631	97^65480-2	130094	Lelio R Paula	05/2017
5632	36007^4102+4102^36007	130094	Hans Havermann	04/2021
5633	4*10^130088-89	130089	Robert Price	11/2018
5634	2^432117-113215	130081	Enzo Doria	07/2014
5635	(4*10^130080+41)/9	130080	Serge Batalov	11/2022
5636	9583*29^88890+736	129997	Eric Chen	06/2025
5637	2^431804+72511	129986	Enzo Doria	04/2016
5638	27902^29237-29237^27902	129978	Frank Doornink	03/2024
5639	33^85579+32	129953	Alfred Reich	10/2025
5640	(2313^38809-1)/(2313^197-1)	129898	Ryan Propper	11/2023
5641	(13*10^129896+137)/3	129897	Robert Price	06/2021
5642	(13*10^129890+71)/3	129891	Robert Price	06/2021
5643	29048^29101-29101^29048	129882	Norbert Schneider	03/2022
5644	37832^2709+2709^37832	129871	Hans Havermann	04/2021
5645	31055^15184+15184^31055	129853	Hans Havermann	04/2021
5647	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
5646	Phi(1632846L,3)	129844	Anonymous	03/2025
5648	31385^13702+13702^31385	129833	Hans Havermann	04/2021
5649	(13*10^129826+41)/9	129827	Tyler Busby	02/2023
5650	28901^29102-29102^28901	129822	Norbert Schneider	03/2022
5651	(47*10^129789-119)/9	129790	Robert Price	05/2019
5652	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
5653	25999^29384-29384^25999	129730	Frank Doornink	03/2024
5654	25771^29408-29408^25771	129723	Frank Doornink	02/2024
5655	(166*10^129712+17)/3	129714	Robert Price	07/2022
5656	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
5657	2^430807+1869563	129686	Enzo Doria	05/2016
5658	2^430721-21429	129660	Enzo Doria	07/2013
5659	Phi(326081,3)	129648	Henri Lifchitz	12/2025
5660	(4*10^129618+89)/3	129619	Robert Price	08/2021
5661	(142^60223-1)/141	129616	Anonymous	06/2024
5662	(10^129587-7^129587)/3	129587	Jon Grantham	07/2023
5663	2^430415-276271	129568	Enzo Doria	07/2015
5664	32282^10311+10311^32282	129558	Hans Havermann	04/2021
5665	29486^24741+24741^29486	129545	Hans Havermann	04/2021
5666	(29*10^129543+313)/9	129544	Robert Price	04/2021
5667	37095^3104+3104^37095	129533	Hans Havermann	04/2021
5668	31132^14459+14459^31132	129514	Hans Havermann	04/2021
5669	32582^9435+9435^32582	129506	Hans Havermann	03/2021
5670	30442^17953+17953^30442	129505	Hans Havermann	03/2021
5671	(199*10^129487-7)/3	129489	Robert Price	05/2020
5672	2^430142-2791721	129486	Enzo Doria	03/2016
5673	(7*10^129472-13)/3	129473	Robert Price	07/2018
5674	(8*10^129469+79)/3	129470	Robert Price	10/2020
5675	31678^12213+12213^31678	129463	Hans Havermann	04/2021
5676	10620^32143-10619^32143	129412	Norbert Schneider	08/2023
5677	(772*10^129406-7)/9	129408	Robert Price	06/2022
5678	(535^47431-1)/534	129406	Tom Wu	09/2024
5679	((320425-8193)F(618977)-(20425-8193)*L(618977))/2	129363	Yaroslav Berezhko	03/2025
5680	31100^14439+14439^31100	129362	Hans Havermann	04/2021
5681	33009^8288+8288^33009	129345	Hans Havermann	04/2021
5682	25895^29306-29306^25895	129334	Frank Doornink	03/2024
5683	(44^78697+43^78697)/87	129333	Aurel Gibier	11/2023
5684	29675^22804+22804^29675	129324	Hans Havermann	04/2021
5685	29068^28099+28099^29068	129315	Hans Havermann	04/2021
5686	2^429568-21017	129313	Enzo Doria	07/2013
5687	(10^129295+83)/3	129295	Robert Price	08/2021
5688	(853*10^129274-7)/9	129276	Robert Price	07/2021
5689	30958^14961+14961^30958	129249	Hans Havermann	04/2021
5690	(11*10^129239-179)/3	129240	Robert Price	09/2018
5691	28659^28988+28988^28659	129208	Norbert Schneider	02/2021
5692	29423^24616+24616^29423	129203	Hans Havermann	03/2021
5693	2^429194-112685	129201	Enzo Doria	06/2014
5694	31*35^83672+17398	129197	Eric Chen	05/2025
5695	2^429145-2780449	129186	Enzo Doria	04/2016
5696	32500^9427+9427^32500	129168	Hans Havermann	04/2021
5697	33577^7014+7014^33577	129136	Hans Havermann	03/2021
5698	2^428892-113453	129110	Enzo Doria	07/2014
5699	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
5700	2^428727-113959	129060	Enzo Doria	10/2014
5701	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
5702	(10^129051-31)/3	129051	Serge Batalov	12/2014
5703	(3^732836)/(2^732836)	129047	Henri Lifchitz	05/2025
5704	(134*10^129038+7)/3	129040	Robert Price	02/2020
5705	2^428564+71161	129011	Enzo Doria	04/2016
5706	28781^28930+28930^28781	129002	Norbert Schneider	02/2021
5707	29065^27424+27424^29065	128995	Hans Havermann	04/2021
5708	2^428502-113285	128992	Enzo Doria	07/2014
5709	2^428421-21373	128968	Enzo Doria	06/2013
5710	L(616787)	128901	Henri Lifchitz	09/2008
5711	(765^44701-1)/764	128900	Tom Wu	07/2024
5712	20^99055-3	128874	Paul Bourdelais	12/2020
5713	91^65772-2	128851	Lelio R Paula	05/2017
5714	2^428022+43	128848	Lelio R Paula	05/2017
5715	2^427999-459397	128841	Enzo Doria	05/2015
5716	2^427993+76847	128839	Enzo Doria	05/2016
5717	31059^14060+14060^31059	128833	Hans Havermann	03/2021
5718	10^128805+152871	128806	Patrick De Geest	05/2021
5719	10^128805-10001	128805	Robert Price	02/2021
5720	2^427824-1851507	128788	Enzo Doria	08/2015
5721	2^427807-21469	128783	Enzo Doria	07/2013
5722	29082^26783+26783^29082	128772	Hans Havermann	04/2021
5723	40055^1638+1638^40055	128750	Hans Havermann	04/2021
5724	(923^43411-1)/922	128720	Tom Wu	07/2024
5725	11^123594-240	128710	Enzo Doria	09/2012
5726	2^427504-21503	128692	Enzo Doria	07/2013
5727	37727^2574+2574^37727	128673	Hans Havermann	04/2021
5728	29686^21591+21591^29686	128668	Hans Havermann	04/2021
5729	10^128668-70000000001	128668	Robert Price	08/2021
5730	10^128668-350729	128668	Alfred Reich	08/2024
5731	Phi(57476,13#)	128668	Henri Lifchitz	12/2025
5732	2^427420+91	128667	Lelio R Paula	05/2017
5733	8*10^128651-37	128652	Robert Price	03/2022
5734	(68*10^128645-257)/9	128646	Robert Price	07/2019
5735	Phi(236553,7)	128631	Henri Lifchitz	12/2025
5736	2^427269-113635	128621	Enzo Doria	08/2014
5737	2^427130+1877569	128579	Enzo Doria	08/2016
5738	2^427068+20011	128561	Enzo Doria	06/2023
5739	2^427016-115349	128545	Enzo Doria	07/2015
5740	2^427001+1334025	128541	Henri Lifchitz	11/2024
5741	(4*10^128510+137)/3	128511	Robert Price	03/2018
5742	2^426889-112879	128507	Enzo Doria	06/2014
5743	2^426804+1869931	128481	Enzo Doria	05/2016
5744	2^426750+77635	128465	Enzo Doria	05/2016
5745	27708^28913-28913^27708	128450	Frank Doornink	03/2024
5746	36988^2969+2969^36988	128445	Hans Havermann	03/2021
5747	36664^3185+3185^36664	128439	Hans Havermann	03/2021
5748	32618^8649+8649^32618	128416	Hans Havermann	04/2021
5749	28883^27874+27874^28883	128391	Hans Havermann	04/2021
5750	2^426425-91	128367	Lelio R Paula	05/2017

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Probable Primes Top 10000

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