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 ?
9251	(2^198481-5)/28311	59745	Lelio R Paula	02/2012
9252	(5^85487-1)/(4*25133179)	59745	Gord Palameta	07/2019
9253	2^198400-189	59725	Lelio R Paula	04/2011
9254	2^198384-12837	59720	Enzo Doria	10/2012
9255	42694!3-729	59719	Robert Price	09/2014
9256	2^198320-18717	59701	Enzo Doria	05/2013
9257	20^45881-1183	59693	Enzo Doria	03/2013
9258	2^198224-6855	59672	Lelio R Paula	05/2011
9259	2^198181-19101	59659	Enzo Doria	05/2013
9260	5*10^59650+41	59651	Robert Price	08/2017
9261	2^198149-112213	59649	Enzo Doria	06/2014
9262	2^198138+73699	59646	Enzo Doria	04/2016
9263	2^198129-55	59643	Lelio R Paula	04/2011
9264	16029^5258+5258^16029	59642	Hans Havermann	05/2019
9265	5^85318-14636	59635	Enzo Doria	02/2013
9266	(2^198119+47)/1560935	59634	Lelio R Paula	02/2012
9267	2^198090-16097	59632	Enzo Doria	04/2013
9268	9*10^59617+89	59618	Robert Price	11/2016
9269	42625!3+81	59612	Robert Price	09/2014
9270	5^85277-84	59607	Lelio R Paula	10/2012
9271	(871*10^59599-7)/9	59601	Robert Price	11/2017
9272	2^197984-18245	59600	Enzo Doria	05/2013
9273	12202^14583-14583^12202	59593	Norbert Schneider	01/2019
9275	2^197951-2137	59590	Yves Minet	06/2013
9274	(38*10^59589+187)/9	59590	Robert Price	11/2017
9276	66^32749-65^32749	59589	Robert Price	09/2013
9277	5*10^59586-3	59587	Dmitry Domanov	11/2010
9278	(35*10^59584-197)/9	59585	Robert Kinser	10/2017
9279	2^197932-3959	59584	Yves Minet	04/2017
9280	2^197909-18961	59577	Enzo Doria	05/2013
9281	(3^124871+2)/45031	59574	Lelio R Paula	04/2012
9282	2^197872+81	59566	Henri Lifchitz	10/2005
9283	2^197873-18469	59566	Enzo Doria	05/2013
9284	(22*10^59558-31)/9	59559	Robert Price	04/2015
9285	12003^14600-14600^12003	59558	Norbert Schneider	02/2019
9287	2^197840-465	59556	Lelio R Paula	05/2011
9286	(31*2^197856-1)/3889605	59556	Lelio R Paula	01/2014
9288	2^197808-17805	59547	Enzo Doria	05/2013
9289	2^197781-17905	59539	Enzo Doria	05/2013
9290	2^197777-17473	59537	Enzo Doria	05/2013
9291	6^76507-149	59535	Lelio R Paula	10/2012
9293	Phi(61456,109)	59526	Enzo Doria	05/2012
9292	18^47420+23	59526	Lelio R Paula	03/2013
9294	(59^33613+1)/60	59522	Paul Bourdelais	08/2017
9295	3^124747+94	59520	Lelio R Paula	10/2012
9296	17^48370+18	59517	Lelio R Paula	03/2013
9297	20^45740-1523	59510	Enzo Doria	03/2013
9298	(47*10^59509+493)/9	59510	Robert Price	11/2017
9299	(7*2^197642-1)/3051	59494	Lelio R Paula	01/2014
9300	18^47390-1853	59488	Enzo Doria	03/2013
9302	(2^197581-7)/1915	59475	Lelio R Paula	02/2012
9301	10621^14772-14772^10621	59475	Norbert Schneider	05/2019
9303	(24737*2^197559+1)/77	59474	Lelio R Paula	06/2014
9304	2^197540-2459	59466	Yves Minet	07/2014
9305	(44*10^59454+1)/9	59455	Serge Batalov	11/2010
9306	2^197494-17805	59452	Enzo Doria	05/2013
9307	2^197482-16821	59449	Enzo Doria	05/2013
9308	2^197485+75767	59449	Enzo Doria	04/2016
9309	(3*2^197483+1)/25	59448	Lelio R Paula	07/2012
9310	2^197466-1868351	59444	Enzo Doria	04/2016
9311	2^197411-17781	59427	Enzo Doria	05/2013
9313	(F(142164)^3-F(142163)^3)/F(142162)	59421	Wayne Halsdorf	03/2012
9312	2^197392-114629	59421	Enzo Doria	05/2015
9314	15441^7046+7046^15441	59417	Hans Havermann	05/2019
9315	2^197355-157	59410	Lelio R Paula	04/2011
9317	5^84992-84	59407	Lelio R Paula	10/2012
9316	9899^14868-14868^9899	59407	Norbert Schneider	07/2019
9318	2*3^124504-5	59404	Lelio R Paula	04/2014
9319	2^197307-19165	59396	Enzo Doria	05/2013
9320	2^197303+32769	59395	Lelio R Paula	05/2011
9321	2*10^59394-69	59395	Robert Price	07/2017
9322	(53*10^59389+1)/9	59390	Serge Batalov	11/2010
9323	6^76316-35	59386	Lelio R Paula	10/2012
9324	2^197259-2929	59381	Yves Minet	09/2014
9325	15036^8893+8893^15036	59378	Hans Havermann	05/2019
9326	lucasU(46,1,35715)-lucasU(46,1,35714)	59377	Mike Oakes	04/2009
9328	17^48253-6	59373	Lelio R Paula	03/2013
9327	14678^11091+11091^14678	59373	Hans Havermann	05/2019
9329	2^197156-15837	59350	Enzo Doria	04/2013
9330	2^197152-4295	59349	Yves Minet	08/2018
9331	2^197149-18481	59348	Enzo Doria	05/2013
9332	2^197142-17157	59346	Enzo Doria	05/2013
9334	(F(6)^65707-F(5)^65707)/F(4)	59339	Wayne Halsdorf	04/2010
9333	(8^65707-5^65707)/3	59339	Robert Price	12/2012
9335	(2*14283^14283+1)/7925497975	59334	David Broadhurst	09/2010
9336	15267^7682+7682^15267	59320	Hans Havermann	05/2019
9337	2^197012-111719	59307	Enzo Doria	05/2014
9338	2^196975+513	59296	Lelio R Paula	05/2011
9339	(61*10^59294+119)/9	59295	Robert Price	09/2017
9340	4*10^59292+39	59293	Robert Price	11/2017
9341	2^196960+97	59291	Lelio R Paula	04/2011
9342	9^62116+8^(62116-1)	59274	Robert Price	03/2016
9343	2^196900-97305	59273	Lelio R Paula	09/2011
9344	13706^14327-14327^13706	59270	Norbert Schneider	05/2019
9345	5*6^76155+7	59261	Lelio R Paula	09/2014
9346	15^50385-14	59258	Wojciech Florek	06/2006
9347	(136777#-1)/8823581477	59254	Donovan Johnson	05/2006
9348	(2^196744-3)*6-7	59227	Gilbert Mozzo	05/2016
9349	14694^10717+10717^14694	59218	Hans Havermann	05/2019
9350	(67607*2^196696+1)/3	59216	Lelio R Paula	05/2014
9351	2^196696-112967	59212	Enzo Doria	06/2014
9352	20^45508-4223	59208	Enzo Doria	03/2013
9353	gcd(Phi(325820,10),(10^16291+1)^3(10^16291+1-10^8146)+(10^32582+10^16291)(10^8146+1)+10^48873)	59201	Serge Batalov	04/2015
9354	14^51651-81	59199	Lelio R Paula	03/2013
9355	2^196650-1451	59198	Yves Minet	08/2012
9356	2^196636-2797799	59194	Enzo Doria	04/2016
9357	1111*2^196610-555	59189	Henri Lifchitz	04/2005
9358	3^124041+658	59183	Lelio R Paula	10/2012
9359	2^196590-111797	59180	Enzo Doria	05/2014
9360	(10^59174-13)/3	59174	Robert Price	02/2017
9361	(2*10^59174-113)/3	59174	Robert Price	09/2017
9362	(9179*2^196533-1)/783	59164	Lelio R Paula	04/2015
9363	11267^14600-14600^11267	59157	Norbert Schneider	02/2019
9364	379*10^59152+9	59155	Arkadiusz Wesolowski	10/2011
9365	13161^14360-14360^13161	59153	Norbert Schneider	06/2019
9366	(404*10^59149-53)/9	59151	Robert Price	11/2017
9367	13^53095+40	59145	Lelio R Paula	03/2013
9368	2*F(282999)-1	59144	Henri Lifchitz	12/2009
9369	4*7^69984+3	59144	Lelio R Paula	09/2014
9370	(5*10^59142+1)/3	59143	Erik Branger	12/2013
9371	2^196463+5711	59142	Lelio R Paula	10/2011
9372	2^196453-97305	59139	Lelio R Paula	09/2011
9373	(28*10^59135+53)/9	59136	Serge Batalov	11/2008
9374	(28*10^59133+113)/3	59134	Robert Price	03/2016
9375	2^196434+7	59133	Lelio R Paula	04/2011
9376	(8*10^59127-29)/3	59128	Robert Price	05/2016
9377	2^196414+255	59127	Lelio R Paula	05/2011
9378	5^84586-92	59124	Lelio R Paula	10/2012
9379	2^196388-17177	59119	Enzo Doria	05/2013
9380	79427!6-6	59119	Robert Price	08/2018
9381	3^123890+20	59111	Lelio R Paula	10/2012
9382	2^196355-1021777	59109	Paul Bourdelais	11/2012
9383	11^56754-1410	59104	Enzo Doria	11/2012
9384	10902^14635-14635^10902	59089	Norbert Schneider	02/2019
9385	(7*2^196297-1)/1200407	59087	Lelio R Paula	01/2014
9386	(16*10^59062-19)/3	59063	Robert Price	03/2016
9387	35^38249-1228	59060	Enzo Doria	03/2013
9388	5^84475-18	59046	Lelio R Paula	10/2012
9389	2^196123-17701	59039	Enzo Doria	05/2013
9390	12^54702-31	59034	Lelio R Paula	03/2013
9391	2^196101-175	59033	Lelio R Paula	04/2011
9392	2^196085+5775	59028	Lelio R Paula	05/2011
9393	2^196034+11715	59013	Lelio R Paula	05/2011
9394	2^196018-18485	59008	Enzo Doria	05/2013
9395	2^195984-2163	58998	Yves Minet	08/2013
9396	3^123645-16	58994	Lelio R Paula	10/2012
9397	39^37078-38	58994	Norbert Schneider	05/2014
9399	2^195958-16853	58990	Enzo Doria	05/2013
9398	12480^14401-14401^12480	58990	Norbert Schneider	07/2019
9400	2^195930-3071	58981	Yves Minet	10/2014
9401	2^195924+513	58980	Lelio R Paula	05/2011
9402	2^195863+155	58961	Lelio R Paula	04/2011
9403	(28*10^58956+113)/3	58957	Robert Price	03/2016
9404	11^56612-9300	58956	Enzo Doria	02/2013
9405	2^195833-17173	58952	Enzo Doria	05/2013
9406	(27*2^195833-1)/53	58952	Lelio R Paula	01/2014
9407	(13*2^195821-1)/122425	58945	Lelio R Paula	01/2014
9408	139^27504-138	58942	Norbert Schneider	10/2015
9409	a(222666)	58929	Robert Price	05/2019
9410	(418*10^58923+23)/9	58925	Robert Price	08/2017
9411	3^123495+44	58923	Lelio R Paula	10/2012
9412	2^195737-18565	58923	Enzo Doria	05/2013
9413	79185!6-16	58921	Robert Price	08/2018
9414	14^51407+47	58920	Lelio R Paula	03/2013
9415	2^195691-99	58909	Lelio R Paula	04/2011
9416	2^195667-1859827	58902	Enzo Doria	04/2016
9418	2^195642+75499	58895	Enzo Doria	04/2016
9417	(299*10^58893+1)/3	58895	Robert Price	11/2017
9421	8*6^75678+5	58890	Lelio R Paula	09/2014
9419	14222^13827+13827^14222	58890	Hans Havermann	05/2019
9420	9137^14868-14868^9137	58890	Norbert Schneider	07/2019
9422	2^195618+73189	58887	Enzo Doria	04/2016
9423	(3928^20480+1)/(3928^4096+1)	58887	Serge Batalov	01/2017
9424	t(197953)	58881	Robert Price	12/2014
9425	2^195581-16105	58876	Enzo Doria	04/2013
9426	(8*10^58872+67)/3	58873	Robert Price	01/2017
9427	7*2^195542-5	58865	Lelio R Paula	03/2014
9428	2*10^58861+9^58861	58862	Mike Oakes	04/2011
9429	11^56513-1620	58853	Enzo Doria	11/2012
9430	2^195496+165	58851	Lelio R Paula	04/2011
9431	5^84187+66	58845	Lelio R Paula	10/2012
9432	2^195478-4991	58845	Yves Minet	05/2019
9433	(28*10^58843-43)/3	58844	Robert Price	04/2016
9434	2^195462-17565	58840	Enzo Doria	05/2013
9435	2^195449-4171	58837	Yves Minet	02/2018
9436	2^195435+59273	58832	Yves Minet	01/2011
9437	2^195424-18605	58829	Enzo Doria	05/2013
9438	10295^14658-14658^10295	58818	Norbert Schneider	03/2019
9439	2^195385-111	58817	Lelio R Paula	04/2011
9440	7*10^58815-83	58816	Robert Price	09/2017
9441	10130^14683-14683^10130	58815	Norbert Schneider	03/2019
9442	2^195357-4303	58809	Yves Minet	08/2018
9443	14218^13631+13631^14218	58785	Hans Havermann	05/2019
9444	(47*2^195254+1)/268821	58774	Lelio R Paula	03/2015
9445	9039^14854-14854^9039	58765	Norbert Schneider	07/2019
9446	2^195207-18109	58764	Enzo Doria	05/2013
9447	2^195199-1567	58761	Yves Minet	08/2012
9448	2^195190+73759	58759	Enzo Doria	04/2016
9449	9*7^69525-4	58757	Lelio R Paula	09/2014
9450	2^195170-18045	58753	Enzo Doria	05/2013
9451	2^195166-165	58751	Lelio R Paula	04/2011
9452	(754*10^58748-7)/9	58750	Robert Price	11/2017
9453	(22699*2^195140+1)/175	58746	Lelio R Paula	05/2014
9454	7*3^123109-2	58739	Lelio R Paula	04/2014
9455	(8*10^58738-611)/9	58738	Robert Price	11/2017
9456	18^46790+77	58735	Lelio R Paula	03/2013
9458	2^195095-337297	58730	Gary Barnes	09/2009
9457	(14*10^58729+31)/9	58730	Robert Price	02/2015
9459	99^29424+98	58720	Norbert Schneider	07/2013
9460	(15185*2^195039-1)/219	58715	Lelio R Paula	04/2015
9461	2^195001-69	58702	Lelio R Paula	04/2011
9462	2^194978-487811	58695	Gary Barnes	09/2009
9463	163^26530+26530^163	58690	Serge Batalov	05/2014
9464	2^194940-194940+1	58683	Robert Price	10/2014
9465	(76*10^58669+41)/9	58670	Robert Price	10/2015
9466	14^51186+87	58666	Lelio R Paula	03/2013
9467	2^194878-97305	58665	Lelio R Paula	09/2011
9468	5^83927-18136	58663	Enzo Doria	05/2014
9469	(24737*2^194865+1)/1085	58662	Lelio R Paula	06/2014
9470	7^69411+40	58660	Lelio R Paula	10/2012
9471	6^75382-79	58659	Lelio R Paula	10/2012
9472	2^194854+27	58657	Lelio R Paula	04/2011
9473	2^194801+29835	58641	Lelio R Paula	10/2012
9474	2^194752+195	58627	Lelio R Paula	04/2011
9475	7^69371-6^69371	58626	Predrag Minovic	08/2004
9476	2^194747-112519	58625	Enzo Doria	06/2014
9477	(15*2^194737+1)/59	58622	Lelio R Paula	07/2012
9478	(23*2^194700+1)/3	58612	Lelio R Paula	02/2012
9479	10^58608+55273	58609	Patrick De Geest	07/2017
9480	10^58608-800001	58608	Robert Price	06/2017
9481	10^58608-60119	58608	Patrick De Geest	07/2017
9482	5^83836+76	58599	Lelio R Paula	10/2012
9483	18^46664+31	58577	Lelio R Paula	03/2013
9484	(34*10^58577-7)/9/19/463	58574	Makoto Morimoto	04/2016
9485	2^194574+165	58573	Lelio R Paula	04/2011
9488	2^194569-12211	58572	Enzo Doria	06/2014
9486	10^58571+5^58571+2^58571	58572	Robert Price	12/2016
9487	10^58571+202837	58572	Patrick De Geest	02/2017
9489	(10^58571+41)/3	58571	Robert Price	01/2017
9490	10^58571-343629	58571	Patrick De Geest	02/2017
9491	(43*10^58563-403)/9	58564	Robert Price	04/2017
9492	11^56235-7950	58563	Enzo Doria	02/2013
9493	145^27095-144	58563	Norbert Schneider	11/2018
9494	2^194505-4615	58552	Yves Minet	05/2019
9495	(14*10^58550+211)/9	58551	Robert Price	11/2017
9496	2^194479-113239	58545	Enzo Doria	07/2014
9497	2^194455-112249	58537	Enzo Doria	06/2014
9498	2^194405-111919	58522	Enzo Doria	05/2014
9499	(4*10^58521-19)/3	58522	Robert Price	06/2017
9500	5*7^69246+8	58521	Lelio R Paula	09/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(253476 PRPs in the top)