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 ?
5251	(2^335562+1258)/2	101014	Stefano Morozzi	09/2020
5252	(19*10^100997+737)/9	100998	Robert Price	07/2018
5253	47599!2+1024	100991	Robert Price	02/2015
5254	2^335468-18629	100986	Enzo Doria	05/2013
5255	2^335454-20961	100982	Enzo Doria	06/2013
5256	(2^335454+3258)/2	100982	Stefano Morozzi	02/2021
5257	10^100978+61	100979	Lelio R Paula	09/2016
5258	10^100978-156437	100978	Patrick De Geest	11/2016
5259	(2^335422+3114)/2	100972	Stefano Morozzi	09/2020
5260	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
5261	2^335403-1859167	100967	Enzo Doria	03/2016
5262	23599^18976+18976^23599	100962	Hans Havermann	10/2018
5263	6*10^100958+43	100959	Robert Price	07/2020
5264	9*2^335364-5	100956	Lelio R Paula	08/2014
5265	2^335349+72287	100951	Enzo Doria	04/2016
5266	2^335329+16095	100945	Lelio R Paula	09/2016
5267	232823#+233663	100937	Makoto Morimoto	10/2017
5268	(232823#+10141)/(10141*1674461)	100927	Makoto Morimoto	06/2019
5269	2^335237-20893	100917	Enzo Doria	06/2013
5270	2^335222-19337	100912	Enzo Doria	05/2013
5271	2^335222-109985	100912	Enzo Doria	04/2014
5272	2^335182-17237	100900	Enzo Doria	05/2013
5273	(2^335107+1634)/2	100877	Stefano Morozzi	09/2020
5275	2^335043-16737	100858	Enzo Doria	05/2013
5274	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
5276	2^335038-20633	100857	Enzo Doria	06/2013
5277	2^335031+1873373	100855	Enzo Doria	06/2016
5278	23489^19650+19650^23489	100847	Hans Havermann	10/2018
5279	3^211354-8816	100842	Enzo Doria	05/2014
5280	2^334984-112757	100841	Enzo Doria	06/2014
5281	(746*10^100827+1)/9	100829	Robert Price	03/2020
5282	29451^2648+2648^29451	100809	Hans Havermann	09/2018
5283	25583^8716+8716^25583	100806	Hans Havermann	08/2018
5285	2^334857+48527	100803	Lelio R Paula	08/2011
5284	12^93406+29	100803	Lelio R Paula	10/2016
5286	28780^3179+3179^28780	100796	Hans Havermann	09/2018
5287	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
5288	2^334809-13	100788	Lelio R Paula	04/2011
5289	(82*10^100780-1)/9	100781	Robert Price	12/2014
5290	31395^1622+1622^31395	100780	Hans Havermann	09/2018
5291	(2^334779+47)/5	100778	Lelio R Paula	12/2013
5292	2^334751+2049	100771	Lelio R Paula	09/2016
5293	13^90443-98	100749	Lelio R Paula	10/2016
5294	(2^334674+3190)/2	100747	Stefano Morozzi	09/2020
5295	(2^334651+1050)/2	100740	Stefano Morozzi	09/2020
5296	(7*10^100737+71)/3	100738	Robert Price	05/2018
5297	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
5298	15^85639-28	100720	Lelio R Paula	10/2016
5299	27068^5259+5259^27068	100718	Hans Havermann	08/2018
5300	2^334562+577294575	100711	Lelio R Paula	09/2016
5301	4*3^211077-5	100710	Lelio R Paula	08/2014
5302	2^334524+145	100702	Lelio R Paula	07/2009
5303	(2^334451+714)/2	100680	Stefano Morozzi	09/2020
5304	27648^4375+4375^27648	100666	Hans Havermann	09/2018
5305	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
5306	(2^334309+3122)/2	100637	Stefano Morozzi	09/2020
5307	2^334294-113111	100633	Enzo Doria	07/2014
5308	25581^8582+8582^25581	100626	Hans Havermann	08/2018
5309	6^129308-17723	100622	Enzo Doria	03/2013
5310	6^129305+95	100619	Lelio R Paula	10/2016
5311	2^334244-1167	100618	Lelio R Paula	09/2016
5312	(2^334233+3066)/2	100614	Stefano Morozzi	09/2020
5313	(76*10^100611+77)/9	100612	Robert Price	10/2019
5314	7*10^100606-93	100607	Robert Price	08/2020
5315	(26*10^100566+49)/3	100567	Robert Price	08/2019
5316	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
5317	24885^10984+10984^24885	100555	Hans Havermann	07/2018
5318	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
5319	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
5320	23578^18367+18367^23578	100538	Hans Havermann	07/2018
5321	13^90251+24	100535	Lelio R Paula	10/2016
5322	2^333963+789	100533	Lelio R Paula	08/2011
5323	2^333919-1840087	100520	Enzo Doria	06/2015
5324	(2^333916+1698)/2	100519	Stefano Morozzi	09/2020
5325	2^333911+72623	100518	Enzo Doria	04/2016
5326	24605^12168+12168^24605	100517	Hans Havermann	08/2018
5327	66*10^100502+7	100504	Robert Price	07/2020
5328	18^80064-67	100503	Lelio R Paula	10/2016
5329	5^143742-48	100472	Lelio R Paula	10/2016
5330	24095^14784+14784^24095	100472	Hans Havermann	08/2018
5331	2^333757-112123	100471	Enzo Doria	06/2014
5332	7*10^100457-57	100458	Robert Price	06/2020
5333	27358^4693+4693^27358	100444	Hans Havermann	07/2018
5334	8*10^100439-51	100440	Robert Price	08/2019
5335	2^333603-108861	100425	Enzo Doria	03/2014
5336	9*7^118818-2	100414	Lelio R Paula	11/2014
5337	2^333546-17097	100408	Enzo Doria	05/2013
5338	17^81597+72	100401	Lelio R Paula	10/2016
5339	p(20559)#/2+8	100384	Robert Price	01/2017
5340	11^96390-24	100380	Lelio R Paula	10/2016
5341	(2^333385+2730)/2	100359	Stefano Morozzi	09/2020
5343	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
5342	23565^18136+18136^23565	100353	Hans Havermann	07/2018
5344	2^333354+763	100350	Lelio R Paula	08/2011
5345	(25*10^100343-67)/3	100344	Robert Price	06/2019
5346	2^333289-109483	100330	Enzo Doria	04/2014
5347	2^333240-2790209	100316	Enzo Doria	03/2016
5348	23601^17798+17798^23601	100314	Hans Havermann	05/2018
5350	(2^333227-2^166614+1)/5	100311		11/2006
5349	2^333225+719	100311	Lelio R Paula	08/2011
5351	2^333221-2785333	100310	Enzo Doria	10/2015
5352	76^53332-75	100308	Norbert Schneider	02/2015
5353	6^128892-17573	100298	Enzo Doria	03/2013
5354	(47*10^100283-119)/9	100284	Robert Price	05/2019
5355	2^333105-113215	100275	Enzo Doria	07/2014
5356	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
5357	4*10^100257-83	100258	Robert Price	10/2018
5358	17^81476-74	100253	Lelio R Paula	10/2016
5359	23392^19207+19207^23392	100199	Hans Havermann	06/2018
5360	(2^332830+750)/2	100192	Stefano Morozzi	09/2020
5361	(206*10^100189-17)/9	100191	Robert Price	01/2020
5362	17^81417-16	100180	Theodore Burton	11/2005
5363	(2^332773+590)/2	100175	Stefano Morozzi	09/2020
5364	2^332739-113215	100165	Enzo Doria	07/2014
5365	2^332730-1865621	100162	Enzo Doria	03/2016
5366	91^51127-2	100160	Lelio R Paula	09/2013
5367	15^85159-32	100155	Lelio R Paula	10/2016
5368	6^128661+97	100118	Lelio R Paula	10/2016
5369	19^78285+40	100108	Lelio R Paula	07/2016
5370	6^128640+5	100102	Lelio R Paula	11/2014
5371	22779^22970-22970^22779	100093	Norbert Schneider	08/2020
5372	(2^332468+3130)/2	100083	Stefano Morozzi	09/2020
5373	(14*10^100075+61)/3	100076	Robert Price	12/2018
5374	(2^332435+3098)/2	100073	Stefano Morozzi	09/2020
5375	28562^3189+3189^28562	100072	Hans Havermann	05/2018
5376	6^128565-127	100044	Lelio R Paula	08/2016
5377	(2^332317+2106)/2	100038	Stefano Morozzi	09/2020
5378	2^332309-133	100035	Lelio R Paula	02/2011
5379	2^332307+731	100035	Lelio R Paula	07/2011
5380	2^332301+12927	100033	Lelio R Paula	04/2013
5381	23406^18781+18781^23406	100031	Hans Havermann	04/2018
5382	2^332277-4573	100026	Yves Minet	03/2019
5383	12^92684-13	100023	Lelio R Paula	07/2016
5384	78557*2^332193+55669	100005	Jorge Menendez	04/2019
5385	78557*2^332192+72689	100005	Jorge Menendez	04/2019
5386	10^100003+45799	100004	Stefano Morozzi	04/2019
5387	10^100003+155461	100004	Stefano Morozzi	04/2019
5388	10^100003+211389	100004	Stefano Morozzi	04/2019
5389	10^100003+381027	100004	Stefano Morozzi	04/2019
5390	10^100003+540703	100004	Stefano Morozzi	04/2019
5391	10^100003+823977	100004	Stefano Morozzi	04/2019
5403	10^100002+236023	100003	Stefano Morozzi	05/2018
5404	10^100002+433741	100003	Stefano Morozzi	05/2018
5392	2^332202+104659	100003	Stefano Morozzi	04/2019
5393	2^332202+857539	100003	Stefano Morozzi	04/2019
5394	2^332202+181773	100003	Stefano Morozzi	04/2019
5395	2^332202+687543	100003	Stefano Morozzi	04/2019
5396	2^332202+941595	100003	Stefano Morozzi	04/2019
5397	2^332202+445813	100003	Stefano Morozzi	04/2019
5398	2^332202+1599727	100003	Stefano Morozzi	04/2019
5399	2^332202+1389567	100003	Stefano Morozzi	04/2019
5400	2^332202+1206315	100003	Stefano Morozzi	04/2019
5401	2^332202+1958647	100003	Stefano Morozzi	04/2019
5402	10^100003-562857	100003	Patrick De Geest	07/2019
5405	(10^100002-1)/9-10^33441	100002	Akihiko Yoshida	03/2018
5406	(10^100002-1)/9-10^44692	100002	Akihiko Yoshida	03/2018
5407	10^100002-249519	100002	Patrick De Geest	07/2018
5408	10^100001+314199	100002	Patrick De Geest	07/2018
5498	10^100000+1751769	100001	Robert Price	08/2012
5499	10^100000+2155489	100001	Robert Price	10/2012
5500	10^100000+2483527	100001	Robert Price	12/2012
5445	10^100000+3938473	100001	Robert Price	05/2015
5446	10^100000+3979761	100001	Robert Price	05/2015
5447	10^100000+4293973	100001	Robert Price	09/2015
5451	10^100000+4858267	100001	Robert Price	12/2015
5452	10^100000+5113299	100001	Robert Price	02/2016
5453	10^100000+5169411	100001	Robert Price	02/2016
5454	10^100000+5354043	100001	Robert Price	05/2016
5455	10^100000+5717979	100001	Robert Price	05/2016
5456	10^100000+6080631	100001	Robert Price	07/2016
5457	10^100000+6308469	100001	Robert Price	07/2016
5458	10^100000+6512023	100001	Robert Price	08/2016
5459	10^100000+6596557	100001	Robert Price	08/2016
5460	10^100000+7115409	100001	Robert Price	10/2016
5461	10^100000+7235803	100001	Robert Price	10/2016
5485	10^100000+7867333	100001	Robert Price	12/2016
5486	10^100000+8743093	100001	Robert Price	02/2017
5487	10^100000+8955391	100001	Robert Price	03/2017
5488	10^100000+9180019	100001	Robert Price	03/2017
5489	10^100000+9225987	100001	Robert Price	04/2017
5490	10^100000+9265587	100001	Robert Price	04/2017
5491	10^100000+9287049	100001	Robert Price	04/2017
5492	10^100000+9425053	100001	Robert Price	05/2017
5493	10^100000+9450769	100001	Robert Price	05/2017
5494	10^100000+9528747	100001	Robert Smith	05/2017
5495	10^100000+9548071	100001	Robert Price	06/2017
5496	10^100000+10064287	100001	Robert Price	08/2017
5497	10^100000+10229569	100001	Robert Price	10/2017
5409	10^100000+11187931	100001	Robert Price	03/2018
5410	10^100000+11264721	100001	Robert Price	04/2018
5411	10^100000+11477661	100001	Robert Price	05/2018
5412	10^100000+11644653	100001	Robert Price	07/2018
5413	10^100001-431439	100001	Patrick De Geest	07/2018
5414	10^100000+11769399	100001	Robert Price	08/2018
5415	10^100000+11848159	100001	Robert Price	08/2018
5416	10^100000+11863467	100001	Robert Price	08/2018
5448	10^100000+11992051	100001	Robert Price	09/2018
5449	2^332196-1-2*29696	100001	Matt Stath	11/2018
5450	10^100000+12363957	100001	Robert Price	11/2018
5417	2^332196+1+2*17152	100001	Matt Stath	12/2018
5418	10^100000+12778033	100001	Robert Price	02/2019
5419	10^100000+13581679	100001	Robert Price	05/2019
5420	10^100000+13613199	100001	Robert Price	05/2019
5421	10^100000+13752327	100001	Robert Price	05/2019
5422	10^100000+14139243	100001	Robert Price	06/2019
5423	10^100000+14151057	100001	Robert Price	06/2019
5424	10^100000+14218923	100001	Robert Price	06/2019
5425	10^100000+15136771	100001	Robert Price	09/2019
5426	10^100000+15219873	100001	Robert Price	10/2019
5427	10^100000+15274039	100001	Robert Price	10/2019
5428	10^100000+15394069	100001	Robert Price	10/2019
5429	10^100000+15547119	100001	Robert Price	10/2019
5430	10^100000+15932923	100001	Robert Price	11/2019
5431	10^100000+16345467	100001	Robert Price	12/2019
5432	10^100000+16672143	100001	Robert Price	01/2020
5433	10^100000+16731939	100001	Robert Price	02/2020
5434	10^100000+16907049	100001	Robert Price	03/2020
5435	10^100000+17652523	100001	Robert Price	05/2020
5436	10^100000+18047167	100001	Robert Price	05/2020
5437	10^100000+18471819	100001	Robert Price	06/2020
5438	10^100000+18494793	100001	Robert Price	07/2020
5439	10^100000+18762609	100001	Robert Price	07/2020
5440	10^100000+19204141	100001	Robert Price	08/2020
5441	10^100000+19349793	100001	Robert Price	08/2020
5442	10^100000+19495699	100001	Robert Price	09/2020
5443	10^100000+19668927	100001	Robert Price	09/2020
5444	10^100000+19704313	100001	Robert Price	09/2020
5462	10^100000+19956229	100001	Robert Price	09/2020
5463	10^100000+3(10^37093-1)/910^31454+1	100001	Makoto Morimoto	09/2020
5464	10^100000+4(10^36149-1)/910^31926+1	100001	Makoto Morimoto	09/2020
5465	10^100000+6(10^41029-1)/910^29486+1	100001	Makoto Morimoto	09/2020
5466	10^100000+7(10^55505-1)/910^22248+1	100001	Makoto Morimoto	09/2020
5467	10^100000+20234607	100001	Robert Price	10/2020
5468	10^100000+20752303	100001	Robert Price	11/2020
5469	10^100000+20774041	100001	Robert Price	11/2020
5470	10^100000+20854741	100001	Robert Price	11/2020
5471	10^100000+20908917	100001	Robert Price	11/2020
5472	10^100000+20994793	100001	Robert Price	11/2020
5473	10^100000+21354249	100001	Robert Price	12/2020
5474	10^100000+21455559	100001	Robert Price	12/2020
5475	10^100000+21538873	100001	Robert Price	12/2020
5476	10^100000+21830901	100001	Robert Price	01/2021
5477	10^100000+21842629	100001	Robert Price	01/2021
5478	10^100000+21930861	100001	Robert Price	01/2021
5479	10^100000+22092943	100001	Robert Price	03/2021
5480	10^100000+22278417	100001	Robert Price	03/2021
5481	10^100000+22388581	100001	Robert Price	03/2021
5482	10^100000+22390933	100001	Robert Price	03/2021
5483	10^100000+22436169	100001	Robert Price	03/2021
5484	10^100000+22714557	100001	Robert Price	04/2021

Find by discoverer :

PRP Records

Probable Primes Top 10000

(280932 PRPs in the top)