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	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
5502	(166*10^120654+11)/3	120656	Robert Price	03/2021
5503	34066^3481+3481^34066	120652	Hans Havermann	02/2021
5504	8*10^120637-27	120638	Robert Price	10/2021
5505	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
5506	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
5507	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
5508	9*10^120617-61	120618	Robert Price	06/2021
5509	(29*10^120590-71)/3	120591	Robert Price	07/2021
5510	2^400571-15	120584	Lelio R Paula	10/2013
5511	(10^120574+359)/9	120574	Serge Batalov	12/2014
5512	(8*10^120552-17)/9	120552	Serge Batalov	11/2022
5513	27431^24810+24810^27431	120550	Hans Havermann	02/2021
5514	2^400424-216413	120540	Enzo Doria	04/2013
5515	29090^13911+13911^29090	120531	Hans Havermann	02/2021
5516	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
5517	27899^20868+20868^27899	120510	Hans Havermann	02/2021
5518	33740^3729+3729^33740	120506	Hans Havermann	02/2021
5519	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
5520	2^400166+1874899	120462	Enzo Doria	06/2016
5521	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
5522	37078^1771+1771^37078	120438	Hans Havermann	02/2021
5523	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
5524	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
5525	2^399999+54173	120412	Norman Luhn	08/2023
5526	(2^399974+2790)/2	120404	Stefano Morozzi	02/2021
5527	2^399966+73759	120402	Enzo Doria	04/2016
5528	(2^399961+2306)/2	120400	Stefano Morozzi	02/2021
5529	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
5530	2^399918-95	120388	Lelio R Paula	04/2013
5531	2^399918+214009	120388	Enzo Doria	10/2023
5532	(28*10^120381-67)/3	120382	Robert Price	10/2020
5533	(49*10^120380-139)/9	120381	Robert Price	03/2019
5534	(2^399874+2194)/2	120374	Stefano Morozzi	09/2020
5535	2^399792-1849259	120350	Enzo Doria	08/2015
5536	9*10^120342-7	120343	Robert Price	09/2015
5537	(2^399751+786)/2	120337	Stefano Morozzi	09/2020
5538	(331*10^120332-7)/9	120334	Robert Price	04/2022
5539	(13*10^120306-37)/3	120307	Robert Price	01/2019
5540	(23*10^120299+37)/3	120300	Robert Price	02/2022
5541	25935^27254-27254^25935	120297	Frank Doornink	03/2024
5542	(2^399604+3070)/2	120293	Stefano Morozzi	09/2020
5543	(2^399549+1062)/2	120276	Stefano Morozzi	09/2020
5544	2^399526-1861721	120270	Enzo Doria	11/2015
5545	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
5546	32016^5687+5687^32016	120217	Hans Havermann	01/2021
5547	(205*10^120212-1)/3	120214	Robert Price	11/2021
5548	2^399322-2798111	120208	Enzo Doria	04/2016
5549	30438^8867+8867^30438	120163	Hans Havermann	02/2021
5550	3^251841-5*2^251841	120159	Jon Grantham	08/2023
5552	72^64693-71^64693	120157	Robert Price	03/2014
5551	(17*10^120156-161)/9	120157	Robert Price	02/2021
5553	2^399111-28489	120145	Enzo Doria	08/2015
5554	(2^399014+1318)/2	120115	Stefano Morozzi	02/2021
5555	30254^9333+9333^30254	120110	Hans Havermann	02/2021
5556	2^398972+6561	120103	Henri Lifchitz	10/2024
5557	30882^7745+7745^30882	120101	Hans Havermann	02/2021
5559	2^398877+105	120074	Donovan Johnson	01/2006
5558	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
5560	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
5561	U(686581)/4280145953	120067	Serge Batalov	07/2024
5562	2^398710+57	120024	Lelio R Paula	04/2013
5563	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
5564	2^398691-115057	120018	Enzo Doria	06/2015
5565	L(574219)	120005	Renaud Lifchitz	03/2004
5566	2^398571+60413	119982	Yves Minet	03/2011
5567	28623^15538+15538^28623	119971	Hans Havermann	02/2021
5568	p(24179)#/2-64	119949	Robert Price	04/2017
5569	2^398448+1872001	119945	Enzo Doria	05/2016
5570	(10^119946*19-91)/6093	119944	Alfred Reich	10/2023
5571	(19*10^119946-91)/9/677	119944	Alfred Reich	11/2023
5572	(191*10^119941-17)/3	119943	Robert Price	11/2021
5573	634^42803+42803^634	119938	Norbert Schneider	07/2019
5574	31083^7220+7220^31083	119935	Hans Havermann	01/2021
5575	(68*10^119931-11)/3	119933	Robert Price	01/2020
5576	8*10^119930-3	119931	Ray Chandler	04/2011
5577	(2^398398+774)/2	119930	Stefano Morozzi	09/2020
5578	(10^119880+179)/9	119880	Serge Batalov	12/2014
5579	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
5580	(10^119836+77)/3	119836	Robert Price	01/2018
5581	26681^27074-27074^26681	119835	Frank Doornink	03/2024
5582	28179^17870+17870^28179	119821	Hans Havermann	02/2021
5583	2^398029+1872527	119819	Enzo Doria	05/2016
5584	33142^4119+4119^33142	119802	Hans Havermann	01/2021
5585	2^397897-113541	119779	Enzo Doria	08/2014
5586	28636^15171+15171^28636	119728	Hans Havermann	02/2021
5587	87^61730-61730^87	119727	Norman Luhn	09/2024
5588	(10556^29929-1)/(10556^173-1)	119724	Ryan Propper	11/2023
5589	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020
5591	(19*10^119716+101)/3	119717	Robert Price	09/2019
5590	29563^11208+11208^29563	119717	Hans Havermann	02/2021
5592	458^44991-44991^458	119715	Norman Luhn	09/2024
5593	2^397655-933075	119707	Paul Bourdelais	06/2021
5594	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
5595	28243^17308+17308^28243	119701	Hans Havermann	02/2021
5596	77*10^119688+3	119690	Robert Price	06/2020
5597	586*25^85601+3717	119668	Eric Chen	10/2023
5598	(2^397504+1698)/2	119661	Stefano Morozzi	09/2020
5599	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
5600	2^397426+73849	119638	Enzo Doria	04/2016
5601	8*10^119509+29	119510	Robert Price	11/2021
5602	2^396933-112723	119489	Enzo Doria	06/2014
5603	11^114738-150	119488	Enzo Doria	10/2012
5604	(4*10^119474+149)/9	119474	Robert Price	04/2018
5605	26964^26964-13^13	119472	Henri Lifchitz	08/2024
5606	2^396790-21	119446	Lelio R Paula	04/2013
5607	32061^5300+5300^32061	119405	Hans Havermann	01/2021
5608	(2^396633-7)/5	119398	Lelio R Paula	04/2014
5609	27382^22913+22913^27382	119388	Hans Havermann	03/2021
5610	(2^396577+2522)/2	119382	Stefano Morozzi	09/2020
5611	(2^396492+2230)/2	119356	Stefano Morozzi	01/2021
5612	(47*10^119354+259)/9	119355	Robert Price	03/2022
5614	105^59050+104	119352	Norbert Schneider	11/2016
5613	126^56824-125	119352	Norbert Schneider	12/2018
5615	2^396469+111546435	119350	Paul Bourdelais	10/2021
5616	139^55690-138	119345	Norbert Schneider	04/2019
5617	790^41179+41179^790	119322	Norbert Schneider	04/2019
5618	2^396374+73729	119321	Enzo Doria	04/2016
5619	88*10^119295+3	119297	Robert Price	05/2020
5620	2^396258-459491	119286	Enzo Doria	05/2015
5621	(2^396248+3126)/2	119283	Stefano Morozzi	09/2020
5622	2^396128-396128-1	119247	Karsten Bonath	06/2018
5623	(893*10^119228+7)/9	119230	Robert Price	06/2021
5624	(31*10^119229+257)/9	119230	Robert Price	12/2021
5625	(28*10^119206-67)/3	119207	Robert Price	10/2020
5626	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
5627	11^114458+6	119196	Paul Bourdelais	02/2021
5628	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
5629	(2^395902+202)/2	119179	Stefano Morozzi	09/2020
5630	(2^395825+582)/2	119155	Stefano Morozzi	09/2020
5631	(2^395733+1130)/2	119128	Stefano Morozzi	09/2020
5632	29548^10725+10725^29548	119091	Hans Havermann	02/2021
5633	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
5634	(30^80599+1)/31	119054	Robert Price	07/2013
5635	(232*10^119047+17)/3	119049	Robert Price	04/2021
5636	(43*10^119024-403)/9	119025	Robert Price	01/2019
5637	(4*10^119021+47)/3	119022	Robert Price	01/2022
5638	fibonacci(569433)+3	119005	Jon Grantham	08/2023
5639	26603^26888-26888^26603	118978	Norbert Schneider	07/2021
5640	912^40193-40193^912	118972	Norman Luhn	09/2024
5641	681^41992-41992^681	118970	Norman Luhn	09/2024
5642	6*10^118964+43	118965	Robert Price	07/2020
5643	(8*10^118960+49)/3	118961	Robert Price	05/2020
5644	31253^6402+6402^31253	118959	Hans Havermann	02/2021
5645	(194*10^118925-17)/3	118927	Robert Price	09/2020
5646	2^395062-109121	118926	Enzo Doria	04/2014
5647	2^395055-4627	118924	Yves Minet	05/2019
5648	(2^395054+702)/2	118923	Stefano Morozzi	09/2020
5649	2^395018-224141	118913	Harrison Mesh	06/2022
5650	(2^395011+2526)/2	118910	Stefano Morozzi	09/2020
5651	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
5652	25771^26948-26948^25771	118872	Frank Doornink	02/2024
5653	374^46201-46201^374	118870	Norman Luhn	09/2024
5654	(2^394858+1018)/2	118864	Stefano Morozzi	09/2020
5655	(77*10^118862-149)/9	118863	Robert Price	03/2022
5656	(16*10^118852+77)/3	118853	Robert Price	03/2019
5657	fibonacci(568658)-2	118843	Jon Grantham	08/2023
5658	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
5659	10^118772+163599	118773	Patrick De Geest	02/2021
5661	10^118772-40000000001	118772	Robert Price	09/2020
5660	10^118772-207603	118772	Patrick De Geest	02/2021
5662	26842^26577+26577^26842	118763	Hans Havermann	02/2021
5663	(2^394513+2034)/2	118760	Stefano Morozzi	09/2020
5664	(2^394473+2774)/2	118748	Stefano Morozzi	02/2021
5665	27949^17710+17710^27949	118734	Hans Havermann	02/2021
5666	2^394266+71389	118686	Enzo Doria	04/2016
5667	(10^118681-3^118681)/7	118681	Jon Grantham	08/2023
5668	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
5669	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
5670	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
5671	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
5672	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
5673	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
5674	29201^11568+11568^29201	118652	Hans Havermann	02/2021
5675	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
5676	(2^394131+2214)/2	118645	Stefano Morozzi	09/2020
5677	(17*10^118635+13)/3	118636	Robert Price	01/2019
5678	5^169727+2	118635	Lelio R Paula	08/2013
5679	2^394034-3	118617	M. Frind & P. Underwood	09/2002
5680	(7*10^118607+179)/3	118608	Robert Price	09/2018
5681	3^248572-6242	118599	Enzo Doria	05/2014
5682	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
5683	(49*10^118576-319)/9	118577	Robert Price	10/2021
5684	7^140303-6	118570	Robert Price	11/2014
5685	(2^393864+2686)/2	118565	Stefano Morozzi	09/2020
5686	(2^393862+3150)/2	118564	Stefano Morozzi	09/2020
5687	(2^393849+3762)/2	118561	Stefano Morozzi	01/2021
5688	(529*10^118554-7)/9	118556	Robert Price	08/2021
5689	26712^26777-26777^26712	118534	Norbert Schneider	07/2021
5690	(2^393661+2666)/2	118504	Stefano Morozzi	09/2020
5691	(2^393650+1614)/2	118501	Stefano Morozzi	09/2020
5692	27655^19264+19264^27655	118495	Hans Havermann	02/2021
5693	10^118485+469413	118486	Patrick De Geest	05/2021
5694	10^118485-50001	118485	Robert Price	08/2020
5695	(2^393528+1030)/2	118464	Stefano Morozzi	09/2020
5696	2^393427+75683	118434	Enzo Doria	04/2016
5697	2^393376-114749	118418	Enzo Doria	04/2015
5698	(65*10^118417+493)/9	118418	Robert Price	08/2021
5699	30960^6671+6671^30960	118397	Hans Havermann	02/2021
5700	(2^393234+2010)/2	118375	Stefano Morozzi	09/2020
5701	(2^393205+3030)/2	118367	Stefano Morozzi	09/2020
5702	(2^393191+2174)/2	118362	Stefano Morozzi	09/2020
5703	2^393180+73	118359	Lelio R Paula	04/2013
5704	3*2^393125+5	118343	Jon Grantham	07/2023
5705	27546^19771+19771^27546	118339	Hans Havermann	02/2021
5706	822^40595-40595^822	118330	Norman Luhn	09/2024
5707	p(23881)#/2+256	118328	Robert Price	05/2017
5708	(10^118324+359)/9	118324	Serge Batalov	12/2014
5709	(2^393048+570)/2	118319	Stefano Morozzi	09/2020
5710	p(23879)#/2+64	118317	Robert Price	03/2017
5711	2^393033+20147	118315	Enzo Doria	08/2023
5712	8*10^118308+59	118309	Robert Price	11/2021
5713	9*10^118282+29	118283	Robert Price	03/2022
5714	(238*10^118265-1)/3	118267	Robert Price	04/2020
5716	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
5715	(2^392707+1710)/2	118217	Stefano Morozzi	09/2020
5717	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
5718	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
5719	(2^392567+2750)/2	118175	Stefano Morozzi	01/2021
5720	55*10^118172+3	118174	Robert Price	07/2022
5721	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
5722	27185^22222+22222^27185	118168	Hans Havermann	01/2021
5723	2^392516-29219	118160	Enzo Doria	07/2015
5724	66*10^118155+7	118157	Robert Price	07/2020
5725	Phi(177231,10)	118152	Maksym Voznyy	09/2015
5726	2^392413-112123	118129	Enzo Doria	06/2014
5727	27491^19798+19798^27491	118119	Hans Havermann	02/2021
5728	(49*10^118109-319)/9	118110	Robert Price	10/2021
5729	(2^392342+5)/27	118106	Lelio R Paula	04/2014
5730	(2^392333+1782)/2	118104	Stefano Morozzi	01/2021
5731	2^392300-1841429	118095	Enzo Doria	06/2015
5732	3*2^392260-5	118083	Jon Grantham	07/2023
5733	2^392220+75241	118070	Enzo Doria	04/2016
5734	27836^17409+17409^27836	118047	Hans Havermann	02/2021
5735	10^118009+664447	118010	Patrick De Geest	07/2018
5736	10^118009-20001	118009	Robert Price	01/2018
5737	(14*10^117991+61)/3	117992	Robert Price	12/2018
5738	2^391933+5897	117984	Yves Minet	02/2011
5739	2^391912-1849259	117978	Enzo Doria	08/2015
5740	(2*34^77029+1043)/11	117968	Eric Chen	08/2023
5741	5*2^391836-3	117956	Jon Grantham	07/2023
5742	28357^14440+14440^28357	117953	Hans Havermann	02/2021
5743	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
5744	85^61124-61124^85	117934	Norman Luhn	09/2024
5745	(7*10^117930-79)/9	117930	Robert Price	01/2021
5746	27531^19168+19168^27531	117904	Hans Havermann	02/2021
5747	(46*10^117902+683)/9	117903	Robert Price	03/2019
5748	26349^26668-26668^26349	117893	Frank Doornink	03/2024
5749	27670^18189+18189^27670	117869	Hans Havermann	02/2021
5750	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014

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Probable Primes Top 10000

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