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	2^409909-189	123395	Enzo Doria	05/2014
5502	135^57922-57922^135	123394	Norman Luhn	10/2024
5503	2^409896-109043	123391	Enzo Doria	04/2014
5504	2^409890+75409	123390	Enzo Doria	04/2016
5505	81254^33+33^81254	123386	Hans Havermann	03/2021
5506	33463^4854+4854^33463	123348	Hans Havermann	03/2021
5507	34061^4182+4182^34061	123348	Hans Havermann	03/2021
5508	133^58076-2	123345	Lelio R Paula	10/2017
5509	F(590041)	123311	Henri Lifchitz	01/2005
5510	(82*10^123299+377)/9	123300	Robert Price	03/2022
5511	2^409566-113501	123292	Enzo Doria	08/2014
5512	2^409533+77747	123282	Enzo Doria	05/2016
5513	2^409436-112799	123253	Enzo Doria	06/2014
5514	28212^23321+23321^28212	123223	Hans Havermann	03/2021
5515	2^409225+1873787	123189	Enzo Doria	06/2016
5516	2^409174+73009	123174	Enzo Doria	04/2016
5517	2^409058-112685	123139	Enzo Doria	06/2014
5518	(13*10^123137-61)/3	123138	Robert Price	11/2018
5519	4*10^123113+21	123114	Robert Price	12/2018
5520	2^408778+77689	123055	Enzo Doria	05/2016
5521	660^43643-43643^660	123054	Norman Luhn	10/2024
5522	2^408690-75	123028	Lelio R Paula	11/2013
5523	28327^22032+22032^28327	123026	Hans Havermann	03/2021
5524	(29*10^122996+673)/9	122997	Robert Price	12/2018
5525	(65*10^122994-101)/9	122995	Robert Price	01/2022
5526	2^408574-2787341	122994	Enzo Doria	03/2016
5527	3*10^122977+37	122978	Robert Price	08/2018
5528	(7*10^122976-67)/3	122977	Robert Price	10/2021
5529	Phi(157825,10)	122961	Maksym Voznyy	06/2015
5530	25493^27902-27902^25493	122948	Frank Doornink	02/2024
5531	26749^27768-27768^26749	122938	Frank Doornink	03/2024
5532	(68*10^122933-419)/9	122934	Robert Price	07/2019
5533	29712^13721+13721^29712	122931	Hans Havermann	03/2021
5534	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
5535	(266*10^122872-17)/3	122874	Robert Price	07/2020
5536	(16*10^122871+77)/3	122872	Robert Price	03/2019
5537	30395^11022+11022^30395	122865	Hans Havermann	03/2021
5538	4*10^122859-69	122860	Robert Price	01/2022
5539	(10^122857+167)/3	122857	Robert Price	05/2021
5540	33331^4852+4852^33331	122856	Hans Havermann	03/2021
5541	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
5542	(19*10^122836-43)/3	122837	Robert Price	05/2019
5543	315^49162-49162^315	122822	Norman Luhn	10/2024
5544	28420^20969+20969^28420	122820	Hans Havermann	03/2021
5545	(16*10^122818+179)/3	122819	Robert Price	11/2021
5546	29865^12934+12934^29865	122797	Hans Havermann	03/2021
5547	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
5548	17^99766+18	122757	Anonymous	09/2024
5549	(32*10^122733-77)/9	122734	Robert Price	06/2018
5550	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
5552	(22*10^122681+161)/3	122682	Robert Price	05/2019
5551	29513^14350+14350^29513	122682	Hans Havermann	03/2021
5553	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
5555	(26*10^122625-131)/3	122626	Robert Price	10/2019
5554	(643*33^80753+3709)/32	122626	Eric Chen	12/2023
5556	27925^24562+24562^27925	122599	Hans Havermann	03/2021
5557	(73*10^122592-1)/9	122593	Robert Price	01/2015
5558	(5*10^122592+91)/3	122593	Robert Price	04/2018
5559	36751^2166+2166^36751	122589	Hans Havermann	03/2021
5560	(85*10^122585-1)/3	122587	Robert Price	02/2020
5561	29368^14931+14931^29368	122585	Hans Havermann	03/2021
5562	2^407179-112075	122574	Enzo Doria	06/2014
5563	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
5564	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
5565	(646*10^122533+11)/9	122535	Robert Price	10/2021
5566	2^407008-1867919	122522	Enzo Doria	04/2016
5567	11^117642-300	122512	Enzo Doria	10/2012
5568	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
5569	2^406949+72197	122504	Enzo Doria	04/2016
5570	(19*10^122501+149)/3	122502	Robert Price	05/2019
5571	28632^18977+18977^28632	122495	Hans Havermann	03/2021
5572	31815^7076+7076^31815	122481	Hans Havermann	03/2021
5573	2^406826-65	122467	Lelio R Paula	11/2013
5574	2^406821-2797363	122466	Enzo Doria	04/2016
5575	(7*10^122456-331)/9	122456	Robert Price	03/2022
5576	2^406758-17	122447	Lelio R Paula	11/2013
5577	29941^12282+12282^29941	122437	Hans Havermann	03/2021
5578	(30^82883-1)/29	122427	Robert Price	12/2011
5579	27496^27577+27577^27496	122422	Norbert Schneider	12/2020
5580	28732^18215+18215^28732	122411	Hans Havermann	03/2021
5581	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
5582	4*10^122377+19	122378	Robert Price	10/2018
5583	28227^21634+21634^28227	122368	Hans Havermann	03/2021
5584	Phi(246362,10)	122365	Makoto Kamada	09/2019
5585	3*10^122345-97	122346	Robert Price	07/2018
5586	97^61575-2	122336	Lelio R Paula	12/2014
5587	2*10^122319+47	122320	Robert Price	12/2021
5588	208^52765+52765^208	122313	Norbert Schneider	11/2020
5590	2^406298+2799109	122308	Enzo Doria	04/2016
5589	2^406296+213691	122308	Enzo Doria	09/2023
5591	7*10^122294+57	122295	Robert Price	06/2019
5592	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
5593	2^406229-1849993	122288	Enzo Doria	08/2015
5594	3*10^122274+7	122275	Robert Price	07/2015
5595	2^406117+1876577	122254	Enzo Doria	07/2016
5596	29308^14835+14835^29308	122253	Hans Havermann	03/2021
5597	28119^22268+22268^28119	122253	Hans Havermann	03/2021
5598	32167^6312+6312^32167	122240	Hans Havermann	03/2021
5599	3^256199-2^256199	122238	Mike Oakes	06/2005
5600	27678^26053+26053^27678	122223	Hans Havermann	03/2021
5601	2^405992-78557	122216	Jorge Menendez	03/2018
5602	(8*10^122203+43)/3	122204	Robert Price	06/2018
5603	(58*10^122170+329)/9	122171	Robert Price	05/2019
5604	2^405774+179149	122151	Enzo Doria	06/2016
5605	2^405693+20417	122126	Enzo Doria	07/2023
5606	(218*10^122109+7)/9	122111	Robert Price	06/2022
5607	29189^15246+15246^29189	122103	Hans Havermann	03/2021
5609	34*10^122082-9	122084	Robert Price	06/2020
5608	33442^4473+4473^33442	122084	Hans Havermann	03/2021
5610	5*10^122082+41	122083	Robert Price	03/2019
5611	31849^6808+6808^31849	122078	Hans Havermann	03/2021
5613	2^405514-3311	122072	Yves Minet	12/2014
5614	2^405514-115511	122072	Enzo Doria	07/2015
5612	23*10^122070-7	122072	Robert Price	02/2020
5615	2^405422-113261	122045	Enzo Doria	07/2014
5616	95^61698-61698^95	122022	Norman Luhn	10/2024
5617	2^405173+71237	121970	Enzo Doria	04/2016
5618	fibonacci(583574)+2	121960	Jon Grantham	08/2023
5619	(154*10^121953+17)/9	121955	Robert Price	06/2022
5620	(34*10^121924+191)/9	121925	Robert Price	08/2021
5621	(2^405016+1)/257	121920	Lelio R Paula	04/2014
5622	28557^18590+18590^28557	121918	Hans Havermann	03/2021
5623	28641^18002+18002^28641	121877	Hans Havermann	03/2021
5624	2^404858+71329	121875	Enzo Doria	04/2016
5625	2^404813-114703	121861	Enzo Doria	04/2015
5626	2^404764+77791	121847	Enzo Doria	05/2016
5627	28830^16841+16841^28830	121847	Hans Havermann	03/2021
5628	(4*10^121825+89)/3	121826	Robert Price	08/2021
5629	317^48694+48694^317	121787	Norbert Schneider	08/2015
5630	2^404536-115259	121778	Enzo Doria	06/2015
5631	2^404501-631	121767	Yves Minet	07/2012
5632	5*10^121764-69	121765	Robert Price	02/2021
5633	28236^20485+20485^28236	121738	Hans Havermann	02/2021
5634	(382*10^121694-31)/9	121696	Robert Price	06/2022
5635	63^67620+2	121672	Lelio R Paula	08/2015
5636	(25*34^79445-28062367)/33	121669	Eric Chen	08/2023
5637	(13*33^80110-121453)/32	121648	Eric Chen	12/2023
5638	(16*10^121633+167)/3	121634	Robert Price	06/2019
5639	29955^11494+11494^29955	121632	Hans Havermann	02/2021
5640	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
5641	31088^8163+8163^31088	121612	Hans Havermann	02/2021
5642	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
5643	(211^52301-1)/210	121560	Anonymous	04/2024
5644	(10^121543-79)/3	121543	Robert Price	01/2018
5645	801^41852-41852^801	121523	Norman Luhn	10/2024
5646	2^403676+76831	121519	Enzo Doria	05/2016
5647	715^42564-42564^715	121491	Norman Luhn	10/2024
5648	(7*10^121487+143)/3	121488	Robert Price	03/2018
5649	27965^22086+22086^27965	121484	Hans Havermann	02/2021
5650	(893*10^121470+7)/9	121472	Robert Price	06/2021
5651	(206*10^121462-11)/3	121464	Robert Price	02/2022
5652	26282^27481-27481^26282	121457	Frank Doornink	03/2024
5653	(77*10^121455+67)/9	121456	Robert Price	12/2021
5654	2^403363-113635	121425	Enzo Doria	08/2014
5655	25531^27552-27552^25531	121424	Frank Doornink	02/2024
5656	(17*10^121418-113)/3	121419	Robert Price	06/2021
5657	2^403336-1861469	121417	Enzo Doria	03/2016
5658	27929^22186+22186^27929	121382	Hans Havermann	02/2021
5659	p(24442)#/2-64	121381	Robert Price	04/2017
5660	11^116555-720	121380	Enzo Doria	11/2012
5661	(873^41263+1)/874	121353	Jinyuan Wang	12/2024
5662	2^403100-461267	121346	Enzo Doria	07/2015
5663	2^403093-112213	121344	Enzo Doria	06/2014
5664	29404^13385+13385^29404	121340	Hans Havermann	02/2021
5665	28106^20745+20745^28106	121332	Hans Havermann	02/2021
5666	(316^48539+1)/317	121330	Eric Chen	10/2017
5667	(23*10^121320-71)/3	121321	Robert Price	07/2020
5668	2^403004+1866361	121317	Enzo Doria	03/2016
5669	2^402953+89	121301	Lelio R Paula	10/2013
5670	2^402944-2788319	121299	Enzo Doria	03/2016
5671	(44*10^121297-719)/9	121298	Robert Price	12/2018
5672	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
5673	2^402828-113183	121264	Enzo Doria	07/2014
5674	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
5675	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
5676	282^49477-49477^282	121231	Norman Luhn	10/2024
5678	2^402715+1874223	121230	Enzo Doria	06/2016
5677	(35*10^121229-593)/9	121230	Robert Price	07/2018
5679	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
5680	291^49190-49190^291	121199	Norman Luhn	10/2024
5681	28719^16568+16568^28719	121174	Hans Havermann	02/2021
5682	7*10^121144+9	121145	Robert Price	09/2015
5683	27490^25467+25467^27490	121121	Hans Havermann	02/2021
5684	34575^3182+3182^34575	121106	Hans Havermann	02/2021
5685	5*10^121100-37	121101	Robert Price	11/2021
5686	F(579521)/516247738177	121101	Serge Batalov	07/2024
5687	25592^27467-27467^25592	121078	Frank Doornink	02/2024
5688	29954^10935+10935^29954	120979	Hans Havermann	02/2021
5689	33585^3992+3992^33585	120946	Hans Havermann	02/2021
5690	40296^1003+1003^40296	120941	Hans Havermann	02/2021
5691	2^401725-113251	120932	Enzo Doria	07/2014
5692	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
5693	2^401652+73711	120910	Enzo Doria	04/2016
5694	(2^401632+3)/79	120902	Lelio R Paula	04/2014
5695	40450^973+973^40450	120870	Hans Havermann	01/2021
5696	(8*10^120851-11)/3	120852	Robert Price	07/2023
5697	10^120841+88417	120842	Patrick De Geest	04/2020
5698	10^120841-123456789	120841	Robert Price	02/2020
5699	10^120841-176853	120841	Patrick De Geest	04/2020
5700	2^401406-2791331	120836	Enzo Doria	03/2016
5701	(28^83497+1)/29	120832	Robert Price	07/2013
5702	(22*10^120828+161)/3	120829	Robert Price	05/2019
5703	2^401369+1867367	120825	Enzo Doria	03/2016
5704	(5*10^120821+43)/3	120822	Robert Price	12/2021
5705	26990^27263-27263^26990	120808	Frank Doornink	03/2024
5706	(10^120782+29)/3	120782	Serge Batalov	12/2014
5707	2^401215-1657	120778	Yves Minet	07/2014
5708	2^401159+53	120761	Lelio R Paula	10/2013
5709	27782^22179+22179^27782	120739	Hans Havermann	01/2021
5710	242^50649-50649^242	120738	Norman Luhn	09/2024
5711	32974^4585+4585^32974	120730	Hans Havermann	02/2021
5712	2^401031-113047	120723	Enzo Doria	07/2014
5713	30598^8813+8813^30598	120713	Hans Havermann	02/2021
5714	(71*10^120703-287)/9	120704	Robert Price	09/2019
5715	25671^27370-27370^25671	120687	Frank Doornink	02/2024
5716	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
5717	34793^2940+2940^34793	120675	Hans Havermann	02/2021
5718	26028^27329-27329^26028	120670	Frank Doornink	03/2024
5719	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
5720	(166*10^120654+11)/3	120656	Robert Price	03/2021
5721	34066^3481+3481^34066	120652	Hans Havermann	02/2021
5722	8*10^120637-27	120638	Robert Price	10/2021
5723	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
5724	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
5725	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
5726	9*10^120617-61	120618	Robert Price	06/2021
5727	(29*10^120590-71)/3	120591	Robert Price	07/2021
5728	2^400571-15	120584	Lelio R Paula	10/2013
5729	(10^120574+359)/9	120574	Serge Batalov	12/2014
5730	(8*10^120552-17)/9	120552	Serge Batalov	11/2022
5731	27431^24810+24810^27431	120550	Hans Havermann	02/2021
5732	2^400424-216413	120540	Enzo Doria	04/2013
5733	29090^13911+13911^29090	120531	Hans Havermann	02/2021
5734	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
5735	27899^20868+20868^27899	120510	Hans Havermann	02/2021
5736	33740^3729+3729^33740	120506	Hans Havermann	02/2021
5737	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
5738	2^400166+1874899	120462	Enzo Doria	06/2016
5739	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
5740	37078^1771+1771^37078	120438	Hans Havermann	02/2021
5741	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
5742	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
5743	2^399999+54173	120412	Norman Luhn	08/2023
5744	(2^399974+2790)/2	120404	Stefano Morozzi	02/2021
5745	2^399966+73759	120402	Enzo Doria	04/2016
5746	(2^399961+2306)/2	120400	Stefano Morozzi	02/2021
5747	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
5749	2^399918-95	120388	Lelio R Paula	04/2013
5748	2^399918+214009	120388	Enzo Doria	10/2023
5750	(28*10^120381-67)/3	120382	Robert Price	10/2020

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