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	(316^48539+1)/317	121330	Eric Chen	10/2017
4502	(23*10^121320-71)/3	121321	Robert Price	07/2020
4503	2^403004+1866361	121317	Enzo Doria	03/2016
4504	2^402953+89	121301	Lelio R Paula	10/2013
4505	2^402944-2788319	121299	Enzo Doria	03/2016
4506	(44*10^121297-719)/9	121298	Robert Price	12/2018
4507	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
4508	2^402828-113183	121264	Enzo Doria	07/2014
4509	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
4510	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
4512	2^402715+1874223	121230	Enzo Doria	06/2016
4511	(35*10^121229-593)/9	121230	Robert Price	07/2018
4513	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
4514	28719^16568+16568^28719	121174	Hans Havermann	02/2021
4515	7*10^121144+9	121145	Robert Price	09/2015
4516	27490^25467+25467^27490	121121	Hans Havermann	02/2021
4517	34575^3182+3182^34575	121106	Hans Havermann	02/2021
4518	5*10^121100-37	121101	Robert Price	11/2021
4519	29954^10935+10935^29954	120979	Hans Havermann	02/2021
4520	33585^3992+3992^33585	120946	Hans Havermann	02/2021
4521	40296^1003+1003^40296	120941	Hans Havermann	02/2021
4522	2^401725-113251	120932	Enzo Doria	07/2014
4523	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
4524	2^401652+73711	120910	Enzo Doria	04/2016
4525	(2^401632+3)/79	120902	Lelio R Paula	04/2014
4526	40450^973+973^40450	120870	Hans Havermann	01/2021
4527	(8*10^120851-11)/3	120852	Robert Price	07/2023
4528	10^120841+88417	120842	Patrick De Geest	04/2020
4529	10^120841-123456789	120841	Robert Price	02/2020
4530	10^120841-176853	120841	Patrick De Geest	04/2020
4531	2^401406-2791331	120836	Enzo Doria	03/2016
4532	(28^83497+1)/29	120832	Robert Price	07/2013
4533	(22*10^120828+161)/3	120829	Robert Price	05/2019
4534	2^401369+1867367	120825	Enzo Doria	03/2016
4535	(5*10^120821+43)/3	120822	Robert Price	12/2021
4536	(10^120782+29)/3	120782	Serge Batalov	12/2014
4537	2^401215-1657	120778	Yves Minet	07/2014
4538	2^401159+53	120761	Lelio R Paula	10/2013
4539	27782^22179+22179^27782	120739	Hans Havermann	01/2021
4540	32974^4585+4585^32974	120730	Hans Havermann	02/2021
4541	2^401031-113047	120723	Enzo Doria	07/2014
4542	30598^8813+8813^30598	120713	Hans Havermann	02/2021
4543	(71*10^120703-287)/9	120704	Robert Price	09/2019
4544	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
4545	34793^2940+2940^34793	120675	Hans Havermann	02/2021
4546	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
4547	(166*10^120654+11)/3	120656	Robert Price	03/2021
4548	34066^3481+3481^34066	120652	Hans Havermann	02/2021
4549	8*10^120637-27	120638	Robert Price	10/2021
4550	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
4551	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
4552	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
4553	9*10^120617-61	120618	Robert Price	06/2021
4554	(29*10^120590-71)/3	120591	Robert Price	07/2021
4555	2^400571-15	120584	Lelio R Paula	10/2013
4556	(10^120574+359)/9	120574	Serge Batalov	12/2014
4557	(8*10^120552-17)/9	120552	Serge Batalov	11/2022
4558	27431^24810+24810^27431	120550	Hans Havermann	02/2021
4559	2^400424-216413	120540	Enzo Doria	04/2013
4560	29090^13911+13911^29090	120531	Hans Havermann	02/2021
4561	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
4562	27899^20868+20868^27899	120510	Hans Havermann	02/2021
4563	33740^3729+3729^33740	120506	Hans Havermann	02/2021
4564	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
4565	2^400166+1874899	120462	Enzo Doria	06/2016
4566	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
4567	37078^1771+1771^37078	120438	Hans Havermann	02/2021
4568	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
4569	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
4570	2^399999+54173	120412	Norman Luhn	08/2023
4571	(2^399974+2790)/2	120404	Stefano Morozzi	02/2021
4572	2^399966+73759	120402	Enzo Doria	04/2016
4573	(2^399961+2306)/2	120400	Stefano Morozzi	02/2021
4574	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
4575	2^399918-95	120388	Lelio R Paula	04/2013
4576	(28*10^120381-67)/3	120382	Robert Price	10/2020
4577	(49*10^120380-139)/9	120381	Robert Price	03/2019
4578	(2^399874+2194)/2	120374	Stefano Morozzi	09/2020
4579	2^399792-1849259	120350	Enzo Doria	08/2015
4580	9*10^120342-7	120343	Robert Price	09/2015
4581	(2^399751+786)/2	120337	Stefano Morozzi	09/2020
4582	(331*10^120332-7)/9	120334	Robert Price	04/2022
4583	(13*10^120306-37)/3	120307	Robert Price	01/2019
4584	(23*10^120299+37)/3	120300	Robert Price	02/2022
4585	(2^399604+3070)/2	120293	Stefano Morozzi	09/2020
4586	(2^399549+1062)/2	120276	Stefano Morozzi	09/2020
4587	2^399526-1861721	120270	Enzo Doria	11/2015
4588	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
4589	32016^5687+5687^32016	120217	Hans Havermann	01/2021
4590	(205*10^120212-1)/3	120214	Robert Price	11/2021
4591	2^399322-2798111	120208	Enzo Doria	04/2016
4592	30438^8867+8867^30438	120163	Hans Havermann	02/2021
4593	3^251841-5*2^251841	120159	Jon Grantham	08/2023
4595	72^64693-71^64693	120157	Robert Price	03/2014
4594	(17*10^120156-161)/9	120157	Robert Price	02/2021
4596	2^399111-28489	120145	Enzo Doria	08/2015
4597	(2^399014+1318)/2	120115	Stefano Morozzi	02/2021
4598	30254^9333+9333^30254	120110	Hans Havermann	02/2021
4599	30882^7745+7745^30882	120101	Hans Havermann	02/2021
4600	2^398877+105	120074	Donovan Johnson	01/2006
4601	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
4602	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
4603	2^398710+57	120024	Lelio R Paula	04/2013
4604	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
4605	2^398691-115057	120018	Enzo Doria	06/2015
4606	L(574219)	120005	Renaud Lifchitz	03/2004
4607	2^398571+60413	119982	Yves Minet	03/2011
4608	28623^15538+15538^28623	119971	Hans Havermann	02/2021
4609	p(24179)#/2-64	119949	Robert Price	04/2017
4610	2^398448+1872001	119945	Enzo Doria	05/2016
4611	(191*10^119941-17)/3	119943	Robert Price	11/2021
4612	634^42803+42803^634	119938	Norbert Schneider	07/2019
4613	31083^7220+7220^31083	119935	Hans Havermann	01/2021
4614	(68*10^119931-11)/3	119933	Robert Price	01/2020
4615	8*10^119930-3	119931	Ray Chandler	04/2011
4616	(2^398398+774)/2	119930	Stefano Morozzi	09/2020
4617	(10^119880+179)/9	119880	Serge Batalov	12/2014
4618	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
4619	(10^119836+77)/3	119836	Robert Price	01/2018
4620	28179^17870+17870^28179	119821	Hans Havermann	02/2021
4621	2^398029+1872527	119819	Enzo Doria	05/2016
4622	33142^4119+4119^33142	119802	Hans Havermann	01/2021
4623	2^397897-113541	119779	Enzo Doria	08/2014
4624	28636^15171+15171^28636	119728	Hans Havermann	02/2021
4625	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020
4627	(19*10^119716+101)/3	119717	Robert Price	09/2019
4626	29563^11208+11208^29563	119717	Hans Havermann	02/2021
4628	2^397655-933075	119707	Paul Bourdelais	06/2021
4629	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
4630	28243^17308+17308^28243	119701	Hans Havermann	02/2021
4631	77*10^119688+3	119690	Robert Price	06/2020
4632	(2^397504+1698)/2	119661	Stefano Morozzi	09/2020
4633	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
4634	2^397426+73849	119638	Enzo Doria	04/2016
4635	8*10^119509+29	119510	Robert Price	11/2021
4636	2^396933-112723	119489	Enzo Doria	06/2014
4637	11^114738-150	119488	Enzo Doria	10/2012
4638	(4*10^119474+149)/9	119474	Robert Price	04/2018
4639	2^396790-21	119446	Lelio R Paula	04/2013
4640	32061^5300+5300^32061	119405	Hans Havermann	01/2021
4641	(2^396633-7)/5	119398	Lelio R Paula	04/2014
4642	27382^22913+22913^27382	119388	Hans Havermann	03/2021
4643	(2^396577+2522)/2	119382	Stefano Morozzi	09/2020
4644	(2^396492+2230)/2	119356	Stefano Morozzi	01/2021
4645	(47*10^119354+259)/9	119355	Robert Price	03/2022
4647	105^59050+104	119352	Norbert Schneider	11/2016
4646	126^56824-125	119352	Norbert Schneider	12/2018
4648	2^396469+111546435	119350	Paul Bourdelais	10/2021
4649	139^55690-138	119345	Norbert Schneider	04/2019
4650	790^41179+41179^790	119322	Norbert Schneider	04/2019
4651	2^396374+73729	119321	Enzo Doria	04/2016
4652	88*10^119295+3	119297	Robert Price	05/2020
4653	2^396258-459491	119286	Enzo Doria	05/2015
4654	(2^396248+3126)/2	119283	Stefano Morozzi	09/2020
4655	2^396128-396128-1	119247	Karsten Bonath	06/2018
4656	(893*10^119228+7)/9	119230	Robert Price	06/2021
4657	(31*10^119229+257)/9	119230	Robert Price	12/2021
4658	(28*10^119206-67)/3	119207	Robert Price	10/2020
4659	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
4660	11^114458+6	119196	Paul Bourdelais	02/2021
4661	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
4662	(2^395902+202)/2	119179	Stefano Morozzi	09/2020
4663	(2^395825+582)/2	119155	Stefano Morozzi	09/2020
4664	(2^395733+1130)/2	119128	Stefano Morozzi	09/2020
4665	29548^10725+10725^29548	119091	Hans Havermann	02/2021
4666	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
4667	(30^80599+1)/31	119054	Robert Price	07/2013
4668	(232*10^119047+17)/3	119049	Robert Price	04/2021
4669	(43*10^119024-403)/9	119025	Robert Price	01/2019
4670	(4*10^119021+47)/3	119022	Robert Price	01/2022
4671	fibonacci(569433)+3	119005	Jon Grantham	08/2023
4672	26603^26888-26888^26603	118978	Norbert Schneider	07/2021
4673	6*10^118964+43	118965	Robert Price	07/2020
4674	(8*10^118960+49)/3	118961	Robert Price	05/2020
4675	31253^6402+6402^31253	118959	Hans Havermann	02/2021
4676	(194*10^118925-17)/3	118927	Robert Price	09/2020
4677	2^395062-109121	118926	Enzo Doria	04/2014
4678	2^395055-4627	118924	Yves Minet	05/2019
4679	(2^395054+702)/2	118923	Stefano Morozzi	09/2020
4680	2^395018-224141	118913	Harrison Mesh	06/2022
4681	(2^395011+2526)/2	118910	Stefano Morozzi	09/2020
4682	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
4683	(2^394858+1018)/2	118864	Stefano Morozzi	09/2020
4684	(77*10^118862-149)/9	118863	Robert Price	03/2022
4685	(16*10^118852+77)/3	118853	Robert Price	03/2019
4686	fibonacci(568658)-2	118843	Jon Grantham	08/2023
4687	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
4688	10^118772+163599	118773	Patrick De Geest	02/2021
4690	10^118772-40000000001	118772	Robert Price	09/2020
4689	10^118772-207603	118772	Patrick De Geest	02/2021
4691	26842^26577+26577^26842	118763	Hans Havermann	02/2021
4692	(2^394513+2034)/2	118760	Stefano Morozzi	09/2020
4693	(2^394473+2774)/2	118748	Stefano Morozzi	02/2021
4694	27949^17710+17710^27949	118734	Hans Havermann	02/2021
4695	2^394266+71389	118686	Enzo Doria	04/2016
4696	(10^118681-3^118681)/7	118681	Jon Grantham	08/2023
4697	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
4698	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
4699	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
4700	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
4701	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
4702	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
4703	29201^11568+11568^29201	118652	Hans Havermann	02/2021
4704	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
4705	(2^394131+2214)/2	118645	Stefano Morozzi	09/2020
4706	(17*10^118635+13)/3	118636	Robert Price	01/2019
4707	5^169727+2	118635	Lelio R Paula	08/2013
4708	2^394034-3	118617	M. Frind & P. Underwood	09/2002
4709	(7*10^118607+179)/3	118608	Robert Price	09/2018
4710	3^248572-6242	118599	Enzo Doria	05/2014
4711	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
4712	(49*10^118576-319)/9	118577	Robert Price	10/2021
4713	7^140303-6	118570	Robert Price	11/2014
4714	(2^393864+2686)/2	118565	Stefano Morozzi	09/2020
4715	(2^393862+3150)/2	118564	Stefano Morozzi	09/2020
4716	(2^393849+3762)/2	118561	Stefano Morozzi	01/2021
4717	(529*10^118554-7)/9	118556	Robert Price	08/2021
4718	26712^26777-26777^26712	118534	Norbert Schneider	07/2021
4719	(2^393661+2666)/2	118504	Stefano Morozzi	09/2020
4720	(2^393650+1614)/2	118501	Stefano Morozzi	09/2020
4721	27655^19264+19264^27655	118495	Hans Havermann	02/2021
4722	10^118485+469413	118486	Patrick De Geest	05/2021
4723	10^118485-50001	118485	Robert Price	08/2020
4724	(2^393528+1030)/2	118464	Stefano Morozzi	09/2020
4725	2^393427+75683	118434	Enzo Doria	04/2016
4726	2^393376-114749	118418	Enzo Doria	04/2015
4727	(65*10^118417+493)/9	118418	Robert Price	08/2021
4728	30960^6671+6671^30960	118397	Hans Havermann	02/2021
4729	(2^393234+2010)/2	118375	Stefano Morozzi	09/2020
4730	(2^393205+3030)/2	118367	Stefano Morozzi	09/2020
4731	(2^393191+2174)/2	118362	Stefano Morozzi	09/2020
4732	2^393180+73	118359	Lelio R Paula	04/2013
4733	3*2^393125+5	118343	Jon Grantham	07/2023
4734	27546^19771+19771^27546	118339	Hans Havermann	02/2021
4735	p(23881)#/2+256	118328	Robert Price	05/2017
4736	(10^118324+359)/9	118324	Serge Batalov	12/2014
4737	(2^393048+570)/2	118319	Stefano Morozzi	09/2020
4738	p(23879)#/2+64	118317	Robert Price	03/2017
4739	2^393033+20147	118315	Enzo Doria	08/2023
4740	8*10^118308+59	118309	Robert Price	11/2021
4741	9*10^118282+29	118283	Robert Price	03/2022
4742	(238*10^118265-1)/3	118267	Robert Price	04/2020
4744	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
4743	(2^392707+1710)/2	118217	Stefano Morozzi	09/2020
4745	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
4746	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
4747	(2^392567+2750)/2	118175	Stefano Morozzi	01/2021
4748	55*10^118172+3	118174	Robert Price	07/2022
4749	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
4750	27185^22222+22222^27185	118168	Hans Havermann	01/2021

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Probable Primes Top 10000

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