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	2^427807-21469	128783	Enzo Doria	07/2013
5502	29082^26783+26783^29082	128772	Hans Havermann	04/2021
5503	40055^1638+1638^40055	128750	Hans Havermann	04/2021
5504	(923^43411-1)/922	128720	Tom Wu	07/2024
5505	11^123594-240	128710	Enzo Doria	09/2012
5506	2^427504-21503	128692	Enzo Doria	07/2013
5507	37727^2574+2574^37727	128673	Hans Havermann	04/2021
5508	29686^21591+21591^29686	128668	Hans Havermann	04/2021
5509	10^128668-70000000001	128668	Robert Price	08/2021
5510	10^128668-350729	128668	Alfred Reich	08/2024
5511	2^427420+91	128667	Lelio R Paula	05/2017
5512	8*10^128651-37	128652	Robert Price	03/2022
5513	(68*10^128645-257)/9	128646	Robert Price	07/2019
5514	2^427269-113635	128621	Enzo Doria	08/2014
5515	2^427130+1877569	128579	Enzo Doria	08/2016
5516	2^427068+20011	128561	Enzo Doria	06/2023
5517	2^427016-115349	128545	Enzo Doria	07/2015
5518	2^427001+1334025	128541	Henri Lifchitz	11/2024
5519	(4*10^128510+137)/3	128511	Robert Price	03/2018
5520	2^426889-112879	128507	Enzo Doria	06/2014
5521	2^426804+1869931	128481	Enzo Doria	05/2016
5522	2^426750+77635	128465	Enzo Doria	05/2016
5523	27708^28913-28913^27708	128450	Frank Doornink	03/2024
5524	36988^2969+2969^36988	128445	Hans Havermann	03/2021
5525	36664^3185+3185^36664	128439	Hans Havermann	03/2021
5526	32618^8649+8649^32618	128416	Hans Havermann	04/2021
5527	28883^27874+27874^28883	128391	Hans Havermann	04/2021
5528	2^426425-91	128367	Lelio R Paula	05/2017
5529	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
5530	2^426352+74971	128345	Enzo Doria	04/2016
5531	(199*10^128343-7)/3	128345	Robert Price	05/2020
5532	4*10^128343-21	128344	Robert Price	09/2018
5533	(65*10^128338+493)/9	128339	Robert Price	08/2021
5534	35632^3997+3997^35632	128337	Hans Havermann	04/2021
5535	2^426300-1863689	128330	Enzo Doria	03/2016
5536	2^426293+1881017	128327	Enzo Doria	11/2016
5537	(88*10^128324-637)/9	128325	Robert Price	11/2020
5538	(491*10^128285+31)/9	128287	Robert Price	04/2022
5539	39103^1908+1908^39103	128281	Hans Havermann	04/2021
5540	2^426043+35	128252	Robert Price	11/2015
5541	(4*10^128244-19)/3	128245	Robert Price	03/2018
5542	26220^29021-29021^26220	128234	Frank Doornink	03/2024
5543	35489^4102+4102^35489	128222	Hans Havermann	04/2021
5544	34721^4926+4926^34721	128208	Hans Havermann	04/2021
5545	(305*10^128198+1)/9	128200	Robert Price	02/2020
5546	2^425808-459959	128181	Enzo Doria	06/2015
5547	30632^15291+15291^30632	128178	Hans Havermann	04/2021
5548	U(623603)	128177	Serge Batalov	07/2024
5549	35981^3648+3648^35981	128167	Hans Havermann	04/2021
5550	2^425627-113605	128127	Enzo Doria	08/2014
5551	(4*10^128109+119)/3	128110	Robert Price	12/2021
5552	(22*10^128094+53)/3	128095	Robert Price	07/2019
5553	(86*10^128086-221)/9	128087	Robert Price	09/2019
5554	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
5555	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
5556	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
5557	Phi(149401,10)/30037901719561	128003	Makoto Kamada	07/2022
5558	2^425205+4911	128000	Marek Hubal	02/2017
5559	29241^23836+23836^29241	127995	Hans Havermann	04/2021
5560	2^425118-113663	127974	Enzo Doria	08/2014
5561	(86*10^127967-329)/9	127968	Robert Price	01/2020
5562	2^425061+1869761	127957	Enzo Doria	05/2016
5563	746^44541+44541^746	127955	Norbert Schneider	07/2019
5564	30236^17043+17043^30236	127946	Hans Havermann	03/2021
5565	2^424938+212419	127920	Enzo Doria	08/2023
5566	2^424918-21141	127914	Enzo Doria	07/2013
5567	(62*10^127903+91)/9	127904	Robert Price	07/2021
5568	2^424864-29489	127897	Enzo Doria	08/2015
5569	30438^15893+15893^30438	127877	Hans Havermann	02/2021
5570	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
5571	28929^26258+26258^28929	127845	Hans Havermann	03/2021
5572	30563^15220+15220^30563	127828	Hans Havermann	03/2021
5573	2^424632-2786639	127827	Enzo Doria	03/2016
5574	10^127821-700001	127821	Robert Price	08/2021
5575	2^424577-113755	127811	Enzo Doria	09/2014
5576	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
5577	(56*10^127752+691)/9	127753	Robert Price	05/2019
5578	11^122629-720	127705	Enzo Doria	11/2012
5579	22*10^127645+3	127647	Robert Price	01/2020
5580	28715^27844+27844^28715	127631	Hans Havermann	03/2021
5581	(56*10^127612+187)/9	127613	Robert Price	10/2021
5582	(5*36^81995+821)/7	127609	Eric Chen	01/2021
5583	4*10^127562-39	127563	Robert Price	09/2020
5584	32595^8186+8186^32595	127547	Hans Havermann	03/2021
5585	2^423696-21429	127546	Enzo Doria	07/2013
5586	2^423664-1864559	127536	Enzo Doria	03/2016
5587	37889^2322+2322^37889	127530	Hans Havermann	03/2021
5588	37668^2429+2429^37668	127523	Hans Havermann	03/2021
5589	3^267267-4	127519	Henri Lifchitz	10/2014
5590	fibonacci(610144)-2	127513	Jon Grantham	08/2023
5591	26253^28852-28852^26253	127503	Frank Doornink	03/2024
5592	(103*10^127491+17)/3	127493	Robert Price	08/2020
5593	29376^21869+21869^29376	127487	Hans Havermann	03/2021
5594	31186^12241+12241^31186	127483	Hans Havermann	02/2021
5595	(19^99689+5^99689)/24	127477	Robert Price	09/2013
5596	27069^28754-28754^27069	127452	Frank Doornink	01/2024
5597	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
5598	30594^14645+14645^30594	127446	Hans Havermann	03/2021
5599	2^423328-21537	127435	Enzo Doria	07/2013
5600	(67*10^127413-7)/3	127415	Robert Price	01/2020
5601	(5*34^83193+700233)/11	127408	Eric Chen	08/2023
5602	(2*10^127407+73)/3	127407	Robert Price	09/2020
5603	(2^423165-7)/25	127384	Lelio R Paula	05/2015
5604	(7726^32768+1)/13917994151414876602369	127379	Kellen Shenton	04/2021
5605	(4*10^127349+17)/3	127350	Tyler Busby	01/2023
5606	29512^20647+20647^29512	127341	Hans Havermann	03/2021
5607	2^422987-3001935	127332	Paul Bourdelais	07/2023
5608	(112*10^127324+17)/3	127326	Robert Price	03/2020
5610	29565^20252+20252^29565	127321	Hans Havermann	03/2021
5609	232^232^232+1831^1831	127321	Henri Lifchitz	03/2025
5611	fibonacci(609165)-3	127308	Jon Grantham	08/2023
5613	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
5612	(5^182099-3^182099)/2	127282	Kellen Shenton	05/2022
5614	(16*10^127259+197)/3	127260	Robert Price	04/2019
5615	(26*10^127240+61)/3	127241	Robert Price	10/2019
5616	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
5617	2^422515-114997	127190	Enzo Doria	06/2015
5618	5*10^127179-3	127180	Robert Price	07/2015
5619	31678^10343+10343^31678	127176	Hans Havermann	03/2021
5620	(44*10^127169-233)/9	127170	Robert Price	01/2019
5621	34947^4352+4352^34947	127162	Hans Havermann	03/2021
5622	6*10^127158+19	127159	Robert Price	11/2021
5623	30469^14902+14902^30469	127155	Hans Havermann	03/2021
5624	5*10^127153+77	127154	Robert Price	12/2018
5625	29941^17620+17620^29941	127130	Hans Havermann	02/2021
5626	31607^10516+10516^31607	127119	Hans Havermann	03/2021
5627	(19*10^127118-97)/3	127119	Robert Price	10/2021
5628	(29*10^127111+691)/9	127112	Robert Price	08/2021
5629	736^44335+44335^736	127104	Norbert Schneider	07/2019
5630	33040^7023+7023^33040	127090	Hans Havermann	03/2021
5631	(4*10^127081+167)/9	127081	Robert Price	03/2022
5632	29748^18661+18661^29748	127052	Hans Havermann	03/2021
5633	27905^28578-28578^27905	127049	Frank Doornink	03/2024
5634	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
5635	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
5636	(14*10^127014-137)/3	127015	Robert Price	04/2021
5637	31436^10965+10965^31436	127002	Hans Havermann	03/2021
5638	28905^24758+24758^28905	127001	Hans Havermann	03/2021
5639	2^421860-113285	126993	Enzo Doria	07/2014
5640	(10^127030+7)/81234833/9230384921/6092460488946445358851	126991	Alfred Reich	07/2021
5641	(2^421827-7)/11	126982	Lelio R Paula	05/2015
5642	26268^28729-28729^26268	126966	Frank Doornink	03/2024
5643	11^121910-840	126957	Enzo Doria	12/2012
5644	(56*10^126935+187)/9	126936	Robert Price	10/2021
5645	28915^24538+24538^28915	126933	Hans Havermann	03/2021
5646	(29*10^126928-77)/3	126929	Robert Price	02/2020
5647	(259*10^126919-1)/3	126921	Robert Price	12/2020
5648	10^126919+204567	126920	Patrick De Geest	05/2021
5649	(2^421617+100280245065)	126920	Paul Bourdelais	05/2022
5650	10^126919-100001	126919	Robert Price	07/2020
5651	28340^28503+28503^28340	126907	Norbert Schneider	02/2021
5652	2^421534-3001935	126895	Paul Bourdelais	07/2023
5653	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
5654	(5*10^126871-119)/3	126872	Robert Price	03/2018
5655	331^50339-10004	126846	Enzo Doria	07/2012
5656	2^421363-2790757	126843	Enzo Doria	03/2016
5657	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
5658	37938^2203+2203^37938	126828	Hans Havermann	03/2021
5659	(13*10^126819+77)/9	126820	Robert Price	07/2022
5660	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
5662	(14*10^126784-83)/3	126785	Robert Price	12/2018
5661	2^421169-3001935	126785	Paul Bourdelais	07/2023
5663	2^421161-286183	126783	Enzo Doria	06/2015
5664	26733^28628-28628^26733	126738	Frank Doornink	03/2024
5665	(106*10^126726+17)/3	126728	Robert Price	04/2021
5666	30718^13347+13347^30718	126724	Hans Havermann	03/2021
5667	2^420939-113935	126716	Enzo Doria	10/2014
5668	11*23^93048+356	126708	Eric Chen	08/2023
5669	177^56363-2	126703	Lelio R Paula	10/2017
5670	2^420741-113659	126656	Enzo Doria	08/2014
5671	2^420694-21	126642	Lelio R Paula	05/2017
5672	(13*10^126638+437)/9	126639	Robert Price	04/2018
5673	(167*10^126637-17)/3	126639	Robert Price	03/2020
5674	4*10^126625+87	126626	Robert Price	08/2018
5675	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
5676	7*10^126600-99	126601	Robert Price	06/2019
5677	U(655247)/250330563881/206066063082749	126596	Serge Batalov	07/2024
5678	2^420424-59189	126561	Enzo Doria	10/2015
5679	28717^25534+25534^28717	126560	Hans Havermann	03/2021
5680	(86*10^126542+103)/9	126543	Robert Price	12/2021
5681	(19*10^126517-7)/3	126518	Robert Price	12/2023
5682	28922^23655+23655^28922	126503	Hans Havermann	03/2021
5683	2^420126+71893	126471	Enzo Doria	04/2016
5684	25982^28643-28643^25982	126450	Frank Doornink	03/2024
5685	(43*10^126441+47)/9	126442	Robert Price	12/2018
5686	8*10^126408+71	126409	Robert Price	05/2022
5687	2^419866+1877059	126393	Enzo Doria	07/2016
5688	29315^20484+20484^29315	126390	Hans Havermann	03/2021
5689	29433^19676+19676^29433	126384	Hans Havermann	03/2021
5690	F(604711)	126377	Henri Lifchitz	02/2005
5691	2^419757+72707	126360	Enzo Doria	04/2016
5692	2^419720-21569	126349	Enzo Doria	07/2013
5693	2^419637+29	126324	Henri Lifchitz	02/2006
5694	31004^11865+11865^31004	126319	Hans Havermann	03/2021
5695	2^419612+1876741	126316	Enzo Doria	07/2016
5696	2^419520+2793271	126289	Enzo Doria	03/2016
5697	(2^419447-5)/369	126264	Lelio R Paula	05/2014
5698	2^419328-1859939	126231	Enzo Doria	03/2016
5699	2^419282-1851507	126217	Enzo Doria	08/2015
5700	(133*10^126212+17)/3	126214	Robert Price	11/2021
5701	2^419251+1866143	126208	Enzo Doria	03/2016
5702	11^121185+2	126202	Robert Price	05/2014
5703	28203^28352+28352^28203	126175	Norbert Schneider	01/2021
5704	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
5705	2^418851+23	126087	Robert Price	09/2015
5706	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
5707	2^418829+167	126081	Lelio R Paula	01/2012
5708	31037^11530+11530^31037	126067	Hans Havermann	03/2021
5709	4*10^126064-69	126065	Robert Price	01/2022
5710	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
5711	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
5712	(35*10^126048-323)/9	126049	Robert Price	10/2021
5713	33016^6551+6551^33016	126000	Hans Havermann	03/2021
5714	2^418548-111546435	125996	Paul Bourdelais	10/2021
5715	25134^28625-28625^25134	125958	Frank Doornink	12/2023
5716	34736^4227+4227^34736	125954	Hans Havermann	03/2021
5717	(23*35^81566-144013)/34	125944	Eric Chen	05/2025
5718	26197^28502-28502^26197	125930	Frank Doornink	03/2024
5719	2^418319-109501	125927	Enzo Doria	04/2014
5720	2^418316-112373	125926	Enzo Doria	06/2014
5721	40398^1309+1309^40398	125919	Hans Havermann	03/2021
5722	(8*10^125894-29)/3	125895	Robert Price	07/2018
5723	(26*10^125886-413)/9	125887	Robert Price	05/2018
5724	10^(262938+1)-710^62938-1	125877	Robert Price	07/2023
5725	55*10^125847+9	125849	Robert Price	03/2022
5726	4*10^125832+57	125833	Robert Price	05/2022
5727	2^417968+1869811	125821	Enzo Doria	06/2016
5728	2^417902+63	125802	Lelio R Paula	09/2015
5729	(10^125792-91)/9	125792	Serge Batalov	12/2014
5730	30438^13573+13573^30438	125791	Hans Havermann	03/2021
5731	32867^6714+6714^32867	125782	Hans Havermann	03/2021
5732	31155^10892+10892^31155	125777	Hans Havermann	03/2021
5733	(35*10^125754-593)/9	125755	Robert Price	07/2018
5734	30455^13464+13464^30455	125754	Hans Havermann	03/2021
5735	(32*10^125751-77)/9	125752	Robert Price	06/2018
5736	2^417704+77011	125742	Enzo Doria	05/2016
5737	29755^16816+16816^29755	125737	Hans Havermann	03/2021
5738	(22*10^125734+203)/9	125735	Robert Price	10/2021
5739	29918^15915+15915^29918	125710	Hans Havermann	03/2021
5740	(10^125706+149)/3	125706	Serge Batalov	12/2014
5741	28531^25368+25368^28531	125659	Hans Havermann	03/2021
5742	2^417419-115309	125656	Enzo Doria	07/2015
5743	(46*10^125642+593)/9	125643	Robert Price	04/2022
5744	2^417315+213953	125625	Enzo Doria	10/2023
5745	2^417300+77281	125620	Enzo Doria	05/2016
5746	30638^12537+12537^30638	125561	Hans Havermann	03/2021
5747	2^417095-1657	125559	Yves Minet	07/2014
5748	30162^14525+14525^30162	125538	Hans Havermann	03/2021
5749	(56*10^125535+583)/9	125536	Robert Price	08/2021
5750	(23*10^125517-179)/3	125518	Robert Price	06/2022

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