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 ?
8251	12^87212-37	94118	Lelio R Paula	06/2016
8252	11^90376+76	94117	Lelio R Paula	05/2016
8253	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
8254	(2^312622+534)/2	94109	Stefano Morozzi	09/2020
8255	(10^94096+191)/3	94096	Robert Price	11/2017
8256	23794^9005+9005^23794	94093	Hans Havermann	09/2020
8257	2^312562-112685	94091	Enzo Doria	06/2014
8258	137^44026-2	94072	Lelio R Paula	10/2017
8259	s(164441)	94052	Robert Price	05/2020
8260	2^312404-869688105	94043	Lelio R Paula	09/2016
8261	2^312387+2793533	94038	Enzo Doria	03/2016
8263	10^94016+91	94017	Robert Price	04/2011
8262	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
8264	10^94016-188963	94016	Patrick De Geest	08/2013
8265	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
8266	(401*10^94010+13)/9	94012	Robert Price	09/2021
8267	23866^8691+8691^23866	94010	Hans Havermann	08/2020
8268	6^120802+7661	94003	Mike Oakes	04/2011
8269	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
8270	(2^312245+702)/2	93995	Stefano Morozzi	09/2020
8271	(56*10^93993+493)/9	93994	Robert Price	10/2021
8272	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
8273	2^312201+51	93982	Lelio R Paula	11/2012
8274	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
8275	(781*10^93942-7)/9	93944	Robert Price	12/2021
8276	3^196892+58	93942	Lelio R Paula	05/2016
8277	2^312060+18915	93940	Lelio R Paula	03/2016
8278	42^57867-41	93933	Norbert Schneider	08/2018
8279	8*10^93921+83	93922	Robert Price	11/2021
8280	2^311992-16209	93919	Enzo Doria	04/2013
8281	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
8282	2^311965-39	93911	Lelio R Paula	11/2012
8283	2^311920-111689	93898	Enzo Doria	05/2014
8284	130^44414+129	93889	Norbert Schneider	01/2019
8285	(2^311892+2730)/2	93889	Stefano Morozzi	09/2020
8286	7*10^93887-47	93888	Robert Price	02/2017
8287	9*10^93878-37	93879	Robert Price	06/2021
8288	(28*10^93874+323)/9	93875	Robert Price	10/2021
8289	(2^311778+1530)/2	93855	Stefano Morozzi	09/2020
8290	12^86965-13	93851	Lelio R Paula	06/2016
8291	24862^5953+5953^24862	93848	Hans Havermann	09/2020
8292	22299^16148+16148^22299	93837	Hans Havermann	08/2020
8293	2^311705+16095	93833	Lelio R Paula	03/2016
8294	(2^311701+3002)/2	93832	Stefano Morozzi	09/2020
8296	2^311665-81	93821	Lelio R Paula	11/2012
8295	(2^311665+2654)/2	93821	Stefano Morozzi	09/2020
8297	(2^311648+3058)/2	93816	Stefano Morozzi	09/2020
8298	(2^311639+2738)/2	93813	Stefano Morozzi	01/2021
8299	730^32761+32761^730	93806	Norbert Schneider	09/2017
8300	11^90073+92	93802	Lelio R Paula	05/2016
8301	6*10^93792+41	93793	Robert Price	01/2017
8302	10^93790+64611	93791	Patrick De Geest	04/2020
8305	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
8303	10^93790-123456789	93790	Robert Price	02/2020
8304	10^93790-157517	93790	Patrick De Geest	04/2020
8306	(49*10^93782+293)/9	93783	Robert Price	03/2021
8307	12^86900-77	93781	Lelio R Paula	06/2016
8308	2^311508-109769	93774	Enzo Doria	04/2014
8309	2^311486-1859621	93767	Enzo Doria	03/2016
8310	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
8311	(10^93811-1)/(996812952121099970133280113810431639637782545831)	93765	Gord Palameta	10/2018
8312	2^311471+311469	93763	Renaud Lifchitz	01/2003
8313	(88*10^93760-1)/3	93762	Robert Price	10/2017
8314	2^311426+79459	93749	Enzo Doria	06/2016
8315	21537^21634+21634^21537	93745	Norbert Schneider	04/2020
8316	2^311409+111546435	93744	Paul Bourdelais	10/2021
8317	(2^311360+3078)/2	93729	Stefano Morozzi	09/2020
8318	(2^311341+2186)/2	93723	Stefano Morozzi	09/2020
8319	(2^311313+774)/2	93715	Stefano Morozzi	09/2020
8321	2^311294+5775	93709	Lelio R Paula	03/2016
8320	25155^5312+5312^25155	93709	Hans Havermann	09/2020
8322	2^311252-1017	93697	Lelio R Paula	03/2016
8323	2^311247-112041	93695	Enzo Doria	06/2014
8324	7*10^93692-83	93693	Robert Price	09/2017
8325	2^311205-109645	93683	Enzo Doria	04/2014
8326	5^134027-84	93681	Lelio R Paula	04/2016
8327	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
8328	(2^311027-2^155514+1)/5	93628		11/2006
8329	26748^3161+3161^26748	93614	Hans Havermann	08/2020
8330	3^196192-28	93608	Robert Price	12/2013
8331	216091#+261433	93606	Makoto Morimoto	12/2015
8332	5^133917+68	93604	Lelio R Paula	04/2016
8333	2^310924-1709	93598	Yves Minet	03/2013
8334	24555^6476+6476^24555	93587	Hans Havermann	08/2020
8335	(2^310867+734)/2	93580	Stefano Morozzi	09/2020
8336	(266*10^93577-11)/3	93579	Robert Price	09/2016
8337	(16*10^93577+161)/3	93578	Robert Price	05/2016
8338	3^196113-56	93570	Lelio R Paula	04/2016
8339	2^310806-110345	93562	Enzo Doria	05/2014
8340	3^196093+86	93561	Lelio R Paula	04/2016
8341	2^310780-2327	93555	Yves Minet	10/2013
8342	30^63332+41	93550	Lelio R Paula	08/2012
8343	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
8344	8*5^133807+7	93528	Lelio R Paula	10/2014
8345	2^310686+8193	93526	Lelio R Paula	03/2016
8346	22681^13282+13282^22681	93520	Hans Havermann	09/2020
8347	2^310646+63	93514	Lelio R Paula	11/2012
8348	(77*10^93508+31)/9	93509	Robert Price	10/2015
8349	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
8350	(2*10^93497+7)/9	93497	Erik Branger	03/2011
8351	3^195958-112852	93496	Enzo Doria	07/2014
8352	2^310583+16385	93495	Lelio R Paula	03/2016
8353	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
8354	9*7^110614+2	93481	Lelio R Paula	11/2014
8355	(19*10^93467+83)/3	93468	Robert Price	08/2020
8356	2^310469-8295	93461	Lelio R Paula	03/2016
8357	2^310459-1159	93458	Yves Minet	11/2012
8358	6^120075-95	93437	Lelio R Paula	05/2016
8359	(2^310362+1758)/2	93428	Stefano Morozzi	09/2020
8360	148^43041-147	93411	Norbert Schneider	05/2019
8361	2^310289+98327	93407	Yves Minet	11/2010
8362	21769^19510+19510^21769	93395	Hans Havermann	08/2020
8363	2^310217-113143	93385	Enzo Doria	07/2014
8364	7^110494-68	93379	Lelio R Paula	04/2016
8365	2^310184-113093	93375	Enzo Doria	07/2014
8366	2^310180-110417	93374	Enzo Doria	05/2014
8367	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
8368	(2^310173+3150)/2	93372	Stefano Morozzi	09/2020
8369	3^195669+68	93358	Lelio R Paula	04/2016
8370	10^93356+91	93357	Robert Price	04/2011
8371	10^93356-28313	93356	Patrick De Geest	08/2013
8372	(85*10^93346+23)/9	93347	Robert Price	11/2015
8373	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
8374	10^93333-4000001	93333	Robert Price	07/2021
8375	3^195556+8680	93304	Lelio R Paula	04/2016
8376	2^309942-109991	93302	Enzo Doria	04/2014
8377	2^309926-1867301	93298	Enzo Doria	03/2016
8378	2^309924+85951	93297	Yves Minet	03/2011
8379	2^309896-4229	93288	Yves Minet	08/2018
8380	(86*10^93263-77)/9	93264	Robert Price	05/2016
8381	6^119836-125	93251	Lelio R Paula	05/2016
8382	(77*10^93249-257)/9	93250	Robert Price	10/2017
8383	21822^18749+18749^21822	93245	Hans Havermann	09/2020
8384	3^195430-2	93244	Theodore Burton	02/2007
8385	(13*10^93236+47)/3	93237	Robert Price	01/2017
8386	(67*10^93226-7)/3	93228	Robert Price	10/2017
8387	(86*10^93217-221)/9	93218	Robert Price	06/2017
8388	2^309637-16329	93211	Enzo Doria	04/2013
8389	(41*10^93207+49)/9	93208	Robert Price	04/2016
8390	14^81312-57	93194	Lelio R Paula	06/2016
8391	41^57783-40	93192	Theodore Burton	02/2007
8392	3*10^93179-97	93180	Robert Price	08/2017
8393	5*7^110252-4	93175	Lelio R Paula	11/2014
8394	22022^16959+16959^22022	93140	Hans Havermann	08/2020
8395	83061!4-512	93137	Robert Price	11/2019
8396	25169^5016+5016^25169	93135	Hans Havermann	08/2020
8397	(483641^16384+1)/2	93135	Richard Fischer	02/2021
8398	2^309380-27	93133	Lelio R Paula	11/2012
8399	25653^4268+4268^25653	93127	Hans Havermann	08/2020
8400	(2^309355+1826)/2	93125	Stefano Morozzi	02/2021
8401	(2^309334+2710)/2	93119	Stefano Morozzi	09/2020
8402	23*10^93116-7	93118	Robert Price	03/2016
8403	(2^309270+3214)/2	93100	Stefano Morozzi	09/2020
8404	(29*10^93082+1)/3	93083	Robert Price	11/2015
8405	(2^309198+3738)/2	93078	Stefano Morozzi	09/2020
8406	(58*10^93062-13)/9	93063	Robert Price	09/2015
8407	(2^309138+1794)/2	93060	Stefano Morozzi	01/2021
8408	2^309131+1869383	93058	Enzo Doria	05/2016
8409	(2^309114+3610)/2	93053	Stefano Morozzi	09/2020
8410	2^309066-93	93039	Lelio R Paula	11/2012
8411	2^309063-113269	93038	Enzo Doria	07/2014
8412	3^194965+16	93022	Robert Price	10/2013
8413	(89*10^93019-737)/9	93020	Robert Price	01/2022
8414	2^308979+1869143	93012	Enzo Doria	05/2016
8415	5^133064+54	93008	Lelio R Paula	04/2016
8416	(2^308947+2750)/2	93003	Stefano Morozzi	01/2021
8417	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
8418	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
8419	(2*10^92976-17)/3	92976	Robert Price	08/2014
8420	24783^5642+5642^24783	92972	Hans Havermann	08/2020
8421	(472489^16384+1)/2	92969	Richard Fischer	01/2021
8422	2^308809+37967	92961	Phil Moore	03/2008
8423	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
8424	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
8425	2^308650+513	92913	Lelio R Paula	02/2016
8426	5*7^109936+6	92908	Lelio R Paula	10/2014
8427	2*10^92897+89	92898	Robert Price	07/2016
8428	(2^308585+3182)/2	92894	Stefano Morozzi	09/2020
8429	(467307^16384+1)/2	92891	Richard Fischer	01/2021
8430	12^86073-29	92889	Lelio R Paula	06/2016
8431	2^308566-117	92888	Lelio R Paula	11/2012
8432	11594^22851-22851^11594	92872	Norbert Schneider	03/2022
8433	(17*10^92869-11)/3	92870	Robert Price	07/2015
8434	2^308459+75431	92856	Enzo Doria	04/2016
8435	2^308426-1866377	92846	Enzo Doria	03/2016
8436	24810^5521+5521^24810	92840	Hans Havermann	09/2020
8437	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
8438	2^308349-112111	92823	Enzo Doria	06/2014
8439	9*10^92821+19	92822	Robert Price	05/2016
8440	2^308337-75	92819	Lelio R Paula	11/2012
8441	4*3^194508+7	92805	Lelio R Paula	08/2014
8442	22*25^66379-113	92796	Curtis Bright	05/2015
8443	24538^6047+6047^24538	92792	Hans Havermann	09/2020
8444	11^89101-1080	92790	Enzo Doria	12/2012
8445	2^308236-1867859	92789	Enzo Doria	04/2016
8446	12^85963+25	92770	Lelio R Paula	06/2016
8447	23692^8221+8221^23692	92753	Hans Havermann	08/2020
8448	7^109750-66	92750	Lelio R Paula	04/2016
8449	9*10^92742+11	92743	Robert Kinser	01/2017
8450	(2^308054+778)/2	92734	Stefano Morozzi	09/2020
8451	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
8452	2^307997-110655	92717	Enzo Doria	05/2014
8453	L(443609)	92709	Renaud Lifchitz	11/2003
8454	10^92691+9	92692	Robert Price	03/2011
8455	10^92691-252291	92691	Patrick De Geest	08/2013
8456	(2^307883+3506)/2	92682	Stefano Morozzi	09/2020
8457	2^307879-2521	92681	Yves Minet	07/2014
8458	21269^21412+21412^21269	92666	Norbert Schneider	04/2020
8459	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
8460	14^80831+47	92643	Lelio R Paula	06/2016
8461	15^78744+92	92611	Lelio R Paula	07/2016
8462	65^51083-64	92610	Norbert Schneider	11/2014
8463	(2^307639+506)/2	92609	Stefano Morozzi	09/2020
8464	131^43737-130	92604	Norbert Schneider	02/2019
8465	6^118996-16943	92597	Enzo Doria	02/2013
8466	(16*10^92591+41)/3	92592	Robert Price	10/2017
8467	(2^307566+3094)/2	92587	Stefano Morozzi	09/2020
8468	(2^307528+1578)/2	92575	Stefano Morozzi	09/2020
8469	9*10^92573+83	92574	Robert Price	11/2020
8470	(3^194014-7)/2	92568	Lelio R Paula	04/2013
8471	(2^307498+570)/2	92566	Stefano Morozzi	09/2020
8472	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
8473	(26*10^92546-77)/3	92547	Robert Price	02/2017
8474	3^193954+340	92540	Lelio R Paula	04/2016
8475	2^307407-307407^2	92539	Henri Lifchitz	05/2005
8476	24299^6430+6430^24299	92536	Hans Havermann	08/2020
8478	(17*10^92513-11)/3	92514	Robert Price	07/2015
8477	2^307322-399071	92514	Harrison Mesh	06/2022
8479	2^307318-4211	92512	Yves Minet	06/2011
8480	2^307280+193	92501	Lelio R Paula	11/2012
8481	20^71075-33	92471	Lelio R Paula	05/2016
8482	2^307126-78795	92455	Lelio R Paula	02/2016
8483	2^307125-49789	92454	Henri Lifchitz	08/2005
8484	2^307099+23	92447	Lelio R Paula	11/2012
8485	129^43798+128	92440	Norbert Schneider	01/2019
8486	21826^17181+17181^21826	92435	Hans Havermann	09/2020
8487	Phi(277314,10)/3327769	92430	Makoto Kamada	05/2019
8488	(2^307022+1038)/2	92423	Stefano Morozzi	09/2020
8489	7*10^92414-69	92415	Robert Price	01/2017
8490	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
8491	22280^14037+14037^22280	92402	Hans Havermann	09/2020
8492	2^306915+1873373	92391	Enzo Doria	06/2016
8493	2^306908+12915	92389	Lelio R Paula	02/2016
8494	21620^18759+18759^21620	92387	Hans Havermann	09/2020
8495	(2^306897+1142)/2	92385	Stefano Morozzi	09/2020
8496	19^72244-80	92383	Lelio R Paula	06/2016
8498	2^306849+75	92371	Lelio R Paula	11/2012
8497	(397*10^92369+53)/9	92371	Robert Price	11/2017
8499	2^306813-869688105	92360	Lelio R Paula	08/2016
8500	(2^306797+2694)/2	92355	Stefano Morozzi	09/2020

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