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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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 ?
6251	2^312404-869688105	94043	Lelio R Paula	09/2016
6252	2^312387+2793533	94038	Enzo Doria	03/2016
6254	10^94016+91	94017	Robert Price	04/2011
6253	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
6255	10^94016-188963	94016	Patrick De Geest	08/2013
6256	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
6257	23866^8691+8691^23866	94010	Hans Havermann	08/2020
6258	6^120802+7661	94003	Mike Oakes	04/2011
6259	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
6260	(2^312245+702)/2	93995	Stefano Morozzi	09/2020
6261	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
6262	2^312201+51	93982	Lelio R Paula	11/2012
6263	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
6264	3^196892+58	93942	Lelio R Paula	05/2016
6265	2^312060+18915	93940	Lelio R Paula	03/2016
6266	42^57867-41	93933	Norbert Schneider	08/2018
6267	2^311992-16209	93919	Enzo Doria	04/2013
6268	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
6269	2^311965-39	93911	Lelio R Paula	11/2012
6270	2^311920-111689	93898	Enzo Doria	05/2014
6272	130^44414+129	93889	Norbert Schneider	01/2019
6271	(2^311892+2730)/2	93889	Stefano Morozzi	09/2020
6273	7*10^93887-47	93888	Robert Price	02/2017
6274	(2^311778+1530)/2	93855	Stefano Morozzi	09/2020
6275	12^86965-13	93851	Lelio R Paula	06/2016
6276	24862^5953+5953^24862	93848	Hans Havermann	09/2020
6277	22299^16148+16148^22299	93837	Hans Havermann	08/2020
6278	2^311705+16095	93833	Lelio R Paula	03/2016
6279	(2^311701+3002)/2	93832	Stefano Morozzi	09/2020
6281	2^311665-81	93821	Lelio R Paula	11/2012
6280	(2^311665+2654)/2	93821	Stefano Morozzi	09/2020
6282	(2^311648+3058)/2	93816	Stefano Morozzi	09/2020
6283	(2^311639+2738)/2	93813	Stefano Morozzi	01/2021
6284	730^32761+32761^730	93806	Norbert Schneider	09/2017
6285	11^90073+92	93802	Lelio R Paula	05/2016
6286	6*10^93792+41	93793	Robert Price	01/2017
6287	10^93790+64611	93791	Patrick De Geest	04/2020
6290	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
6288	10^93790-123456789	93790	Robert Price	02/2020
6289	10^93790-157517	93790	Patrick De Geest	04/2020
6291	(49*10^93782+293)/9	93783	Robert Price	03/2021
6292	12^86900-77	93781	Lelio R Paula	06/2016
6293	2^311508-109769	93774	Enzo Doria	04/2014
6294	2^311486-1859621	93767	Enzo Doria	03/2016
6295	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
6296	(10^93811-1)/(996812952121099970133280113810431639637782545831)	93765	Gord Palameta	10/2018
6297	2^311471+311469	93763	Renaud Lifchitz	01/2003
6298	(88*10^93760-1)/3	93762	Robert Price	10/2017
6299	2^311426+79459	93749	Enzo Doria	06/2016
6300	21537^21634+21634^21537	93745	Norbert Schneider	04/2020
6301	(2^311360+3078)/2	93729	Stefano Morozzi	09/2020
6302	(2^311341+2186)/2	93723	Stefano Morozzi	09/2020
6303	(2^311313+774)/2	93715	Stefano Morozzi	09/2020
6305	2^311294+5775	93709	Lelio R Paula	03/2016
6304	25155^5312+5312^25155	93709	Hans Havermann	09/2020
6306	2^311252-1017	93697	Lelio R Paula	03/2016
6307	2^311247-112041	93695	Enzo Doria	06/2014
6308	7*10^93692-83	93693	Robert Price	09/2017
6309	2^311205-109645	93683	Enzo Doria	04/2014
6310	5^134027-84	93681	Lelio R Paula	04/2016
6311	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
6312	(2^311027-2^155514+1)/5	93628		11/2006
6313	26748^3161+3161^26748	93614	Hans Havermann	08/2020
6314	3^196192-28	93608	Robert Price	12/2013
6315	216091#+261433	93606	Makoto Morimoto	12/2015
6316	5^133917+68	93604	Lelio R Paula	04/2016
6317	2^310924-1709	93598	Yves Minet	03/2013
6318	24555^6476+6476^24555	93587	Hans Havermann	08/2020
6319	(2^310867+734)/2	93580	Stefano Morozzi	09/2020
6320	(266*10^93577-11)/3	93579	Robert Price	09/2016
6321	(16*10^93577+161)/3	93578	Robert Price	05/2016
6322	3^196113-56	93570	Lelio R Paula	04/2016
6323	2^310806-110345	93562	Enzo Doria	05/2014
6324	3^196093+86	93561	Lelio R Paula	04/2016
6325	2^310780-2327	93555	Yves Minet	10/2013
6326	30^63332+41	93550	Lelio R Paula	08/2012
6327	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
6328	8*5^133807+7	93528	Lelio R Paula	10/2014
6329	2^310686+8193	93526	Lelio R Paula	03/2016
6330	22681^13282+13282^22681	93520	Hans Havermann	09/2020
6331	2^310646+63	93514	Lelio R Paula	11/2012
6332	(77*10^93508+31)/9	93509	Robert Price	10/2015
6333	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
6334	(2*10^93497+7)/9	93497	Erik Branger	03/2011
6335	3^195958-112852	93496	Enzo Doria	07/2014
6336	2^310583+16385	93495	Lelio R Paula	03/2016
6337	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
6338	9*7^110614+2	93481	Lelio R Paula	11/2014
6339	(19*10^93467+83)/3	93468	Robert Price	08/2020
6340	2^310469-8295	93461	Lelio R Paula	03/2016
6341	2^310459-1159	93458	Yves Minet	11/2012
6342	6^120075-95	93437	Lelio R Paula	05/2016
6343	(2^310362+1758)/2	93428	Stefano Morozzi	09/2020
6344	148^43041-147	93411	Norbert Schneider	05/2019
6345	2^310289+98327	93407	Yves Minet	11/2010
6346	21769^19510+19510^21769	93395	Hans Havermann	08/2020
6347	2^310217-113143	93385	Enzo Doria	07/2014
6348	7^110494-68	93379	Lelio R Paula	04/2016
6349	2^310184-113093	93375	Enzo Doria	07/2014
6350	2^310180-110417	93374	Enzo Doria	05/2014
6351	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
6352	(2^310173+3150)/2	93372	Stefano Morozzi	09/2020
6353	3^195669+68	93358	Lelio R Paula	04/2016
6354	10^93356+91	93357	Robert Price	04/2011
6355	10^93356-28313	93356	Patrick De Geest	08/2013
6356	(85*10^93346+23)/9	93347	Robert Price	11/2015
6357	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
6358	3^195556+8680	93304	Lelio R Paula	04/2016
6359	2^309942-109991	93302	Enzo Doria	04/2014
6360	2^309926-1867301	93298	Enzo Doria	03/2016
6361	2^309924+85951	93297	Yves Minet	03/2011
6362	2^309896-4229	93288	Yves Minet	08/2018
6363	(86*10^93263-77)/9	93264	Robert Price	05/2016
6364	6^119836-125	93251	Lelio R Paula	05/2016
6365	(77*10^93249-257)/9	93250	Robert Price	10/2017
6366	21822^18749+18749^21822	93245	Hans Havermann	09/2020
6367	3^195430-2	93244	Theodore Burton	02/2007
6368	(13*10^93236+47)/3	93237	Robert Price	01/2017
6369	(67*10^93226-7)/3	93228	Robert Price	10/2017
6370	(86*10^93217-221)/9	93218	Robert Price	06/2017
6371	2^309637-16329	93211	Enzo Doria	04/2013
6372	(41*10^93207+49)/9	93208	Robert Price	04/2016
6373	14^81312-57	93194	Lelio R Paula	06/2016
6374	41^57783-40	93192	Theodore Burton	02/2007
6375	3*10^93179-97	93180	Robert Price	08/2017
6376	5*7^110252-4	93175	Lelio R Paula	11/2014
6377	22022^16959+16959^22022	93140	Hans Havermann	08/2020
6378	83061!4-512	93137	Robert Price	11/2019
6379	25169^5016+5016^25169	93135	Hans Havermann	08/2020
6380	(483641^16384+1)/2	93135	Richard Fischer	02/2021
6381	2^309380-27	93133	Lelio R Paula	11/2012
6382	25653^4268+4268^25653	93127	Hans Havermann	08/2020
6383	(2^309355+1826)/2	93125	Stefano Morozzi	02/2021
6384	(2^309334+2710)/2	93119	Stefano Morozzi	09/2020
6385	23*10^93116-7	93118	Robert Price	03/2016
6386	(2^309270+3214)/2	93100	Stefano Morozzi	09/2020
6387	(29*10^93082+1)/3	93083	Robert Price	11/2015
6388	(2^309198+3738)/2	93078	Stefano Morozzi	09/2020
6389	(58*10^93062-13)/9	93063	Robert Price	09/2015
6390	(2^309138+1794)/2	93060	Stefano Morozzi	01/2021
6391	2^309131+1869383	93058	Enzo Doria	05/2016
6392	(2^309114+3610)/2	93053	Stefano Morozzi	09/2020
6393	2^309066-93	93039	Lelio R Paula	11/2012
6394	2^309063-113269	93038	Enzo Doria	07/2014
6395	3^194965+16	93022	Robert Price	10/2013
6396	2^308979+1869143	93012	Enzo Doria	05/2016
6397	5^133064+54	93008	Lelio R Paula	04/2016
6398	(2^308947+2750)/2	93003	Stefano Morozzi	01/2021
6399	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
6400	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
6401	(2*10^92976-17)/3	92976	Robert Price	08/2014
6402	24783^5642+5642^24783	92972	Hans Havermann	08/2020
6403	(472489^16384+1)/2	92969	Richard Fischer	01/2021
6404	2^308809+37967	92961	Phil Moore	03/2008
6405	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
6406	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
6407	2^308650+513	92913	Lelio R Paula	02/2016
6408	5*7^109936+6	92908	Lelio R Paula	10/2014
6409	2*10^92897+89	92898	Robert Price	07/2016
6410	(2^308585+3182)/2	92894	Stefano Morozzi	09/2020
6411	(467307^16384+1)/2	92891	Richard Fischer	01/2021
6412	12^86073-29	92889	Lelio R Paula	06/2016
6413	2^308566-117	92888	Lelio R Paula	11/2012
6414	(17*10^92869-11)/3	92870	Robert Price	07/2015
6415	2^308459+75431	92856	Enzo Doria	04/2016
6416	2^308426-1866377	92846	Enzo Doria	03/2016
6417	24810^5521+5521^24810	92840	Hans Havermann	09/2020
6418	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
6419	2^308349-112111	92823	Enzo Doria	06/2014
6420	9*10^92821+19	92822	Robert Price	05/2016
6421	2^308337-75	92819	Lelio R Paula	11/2012
6422	4*3^194508+7	92805	Lelio R Paula	08/2014
6423	22*25^66379-113	92796	Curtis Bright	05/2015
6424	24538^6047+6047^24538	92792	Hans Havermann	09/2020
6425	11^89101-1080	92790	Enzo Doria	12/2012
6426	2^308236-1867859	92789	Enzo Doria	04/2016
6427	12^85963+25	92770	Lelio R Paula	06/2016
6428	23692^8221+8221^23692	92753	Hans Havermann	08/2020
6429	7^109750-66	92750	Lelio R Paula	04/2016
6430	9*10^92742+11	92743	Robert Kinser	01/2017
6431	(2^308054+778)/2	92734	Stefano Morozzi	09/2020
6432	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
6433	2^307997-110655	92717	Enzo Doria	05/2014
6434	L(443609)	92709	Renaud Lifchitz	11/2003
6435	10^92691+9	92692	Robert Price	03/2011
6436	10^92691-252291	92691	Patrick De Geest	08/2013
6437	(2^307883+3506)/2	92682	Stefano Morozzi	09/2020
6438	2^307879-2521	92681	Yves Minet	07/2014
6439	21269^21412+21412^21269	92666	Norbert Schneider	04/2020
6440	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
6441	14^80831+47	92643	Lelio R Paula	06/2016
6442	15^78744+92	92611	Lelio R Paula	07/2016
6443	65^51083-64	92610	Norbert Schneider	11/2014
6444	(2^307639+506)/2	92609	Stefano Morozzi	09/2020
6445	131^43737-130	92604	Norbert Schneider	02/2019
6446	6^118996-16943	92597	Enzo Doria	02/2013
6447	(16*10^92591+41)/3	92592	Robert Price	10/2017
6448	(2^307566+3094)/2	92587	Stefano Morozzi	09/2020
6449	(2^307528+1578)/2	92575	Stefano Morozzi	09/2020
6450	9*10^92573+83	92574	Robert Price	11/2020
6451	(3^194014-7)/2	92568	Lelio R Paula	04/2013
6452	(2^307498+570)/2	92566	Stefano Morozzi	09/2020
6453	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
6454	(26*10^92546-77)/3	92547	Robert Price	02/2017
6455	3^193954+340	92540	Lelio R Paula	04/2016
6456	2^307407-307407^2	92539	Henri Lifchitz	05/2005
6457	24299^6430+6430^24299	92536	Hans Havermann	08/2020
6458	(17*10^92513-11)/3	92514	Robert Price	07/2015
6459	2^307318-4211	92512	Yves Minet	06/2011
6460	2^307280+193	92501	Lelio R Paula	11/2012
6461	20^71075-33	92471	Lelio R Paula	05/2016
6462	2^307126-78795	92455	Lelio R Paula	02/2016
6463	2^307125-49789	92454	Henri Lifchitz	08/2005
6464	2^307099+23	92447	Lelio R Paula	11/2012
6465	129^43798+128	92440	Norbert Schneider	01/2019
6466	21826^17181+17181^21826	92435	Hans Havermann	09/2020
6467	Phi(277314,10)/3327769	92430	Makoto Kamada	05/2019
6468	(2^307022+1038)/2	92423	Stefano Morozzi	09/2020
6469	7*10^92414-69	92415	Robert Price	01/2017
6470	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
6471	22280^14037+14037^22280	92402	Hans Havermann	09/2020
6472	2^306915+1873373	92391	Enzo Doria	06/2016
6473	2^306908+12915	92389	Lelio R Paula	02/2016
6474	21620^18759+18759^21620	92387	Hans Havermann	09/2020
6475	(2^306897+1142)/2	92385	Stefano Morozzi	09/2020
6476	19^72244-80	92383	Lelio R Paula	06/2016
6478	2^306849+75	92371	Lelio R Paula	11/2012
6477	(397*10^92369+53)/9	92371	Robert Price	11/2017
6479	2^306813-869688105	92360	Lelio R Paula	08/2016
6480	(2^306797+2694)/2	92355	Stefano Morozzi	09/2020
6481	21713^17914+17914^21713	92350	Hans Havermann	09/2020
6482	2^306672-109059	92318	Enzo Doria	04/2014
6483	(430463^16384+1)/2	92307	Richard Fischer	09/2020
6484	6^118604-17063	92292	Enzo Doria	02/2013
6485	21969^15878+15878^21969	92288	Hans Havermann	08/2020
6486	21690^17959+17959^21690	92276	Hans Havermann	08/2020
6487	(7613^23773-1)/7612	92273	Serge Batalov	08/2020
6488	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
6489	2^306467-1835611	92256	Enzo Doria	04/2015
6490	2^306433+76427	92246	Enzo Doria	05/2016
6492	2^306430-113313	92245	Enzo Doria	07/2014
6491	(23*10^92244-59)/9	92245	Robert Price	03/2017
6493	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
6494	21436^20043+20043^21436	92217	Hans Havermann	09/2020
6495	(25*10^92186+59)/3	92187	Robert Price	05/2016
6496	2^306213-286183	92180	Enzo Doria	06/2015
6497	10^92178+61	92179	Robert Price	04/2011
6498	10^92178-175509	92178	Patrick De Geest	07/2013
6499	2^306200+1185	92176	Lelio R Paula	02/2016
6500	(2^306171+1514)/2	92167	Stefano Morozzi	09/2020

Find by discoverer :

PRP Records

Probable Primes Top 10000

(280932 PRPs in the top)