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 (> 30000)	Who ?	When ?
9501	14147^5892+5892^14147	53338	Hans Havermann	07/2016
9502	7^63109+46	53334	Lelio R Paula	10/2012
9503	20^40986-1343	53325	Enzo Doria	03/2013
9504	4*10^53324-89	53325	Robert Price	08/2017
9505	20^40977-8883	53313	Enzo Doria	03/2013
9506	3^111711+2660	53300	Lelio R Paula	10/2012
9507	2^177040-11865	53295	Enzo Doria	10/2012
9508	(7*10^53287+17)/3	53288	Erik Branger	03/2014
9509	35^34506-10758	53280	Enzo Doria	03/2013
9510	(11*10^53274-17)/3	53275	Erik Branger	03/2014
9511	(1017*2^176971-1)/335	53275	Lelio R Paula	03/2015
9512	2^176961-2833	53271	Yves Minet	09/2014
9513	3^111642+110	53267	Lelio R Paula	10/2012
9514	17^43290-98	53267	Lelio R Paula	01/2013
9515	7^63028+36	53265	Lelio R Paula	10/2012
9516	(22*10^53264+71)/3	53265	Robert Price	05/2017
9517	7^63023-36	53261	Lelio R Paula	10/2012
9518	19783^492+492^19783	53256	Anatoly F. Selevich	02/2007
9519	13350^9739+9739^13350	53247	Hans Havermann	10/2015
9520	14394^4993+4993^14394	53235	Hans Havermann	10/2015
9521	2^176823-112807	53230	Enzo Doria	06/2014
9522	1684^16495+16495^1684	53219	Serge Batalov	05/2014
9523	15277^3042+3042^15277	53213	Hans Havermann	06/2016
9524	(50322^11317-1)/50321	53206	Serge Batalov	04/2015
9525	2^176742-1595	53205	Lelio R Paula	10/2009
9526	(27*2^176767-1)/20455056355	53204	Lelio R Paula	01/2014
9527	72149!6-12	53200	Robert Price	08/2018
9528	(-lucasV(1,2,353460)-2)/(3^2*5^2)	53199	Mike Oakes	03/2017
9529	(3*2^176696-1)/299	53189	Lelio R Paula	01/2014
9530	(7*10^53185-1)/3	53186	Erik Branger	03/2014
9531	2^176629+465	53171	Lelio R Paula	07/2012
9532	(3*2^176604-1)/359	53162	Lelio R Paula	01/2014
9533	10955^13158-13158^10955	53154	Norbert Schneider	11/2017
9534	5^76038-14366	53149	Enzo Doria	02/2013
9535	15156^3209+3209^15156	53143	Hans Havermann	06/2016
9536	2^176532-2837	53142	Yves Minet	09/2014
9537	52^30967-51	53140	Norbert Schneider	08/2014
9538	9*5^76023-2	53139	Lelio R Paula	09/2014
9539	(14283!+1)/464216177	53135	Michael Porter	03/2016
9540	2^176461-165	53121	Lelio R Paula	02/2011
9541	(62*10^53111+1)/9	53112	Serge Batalov	05/2010
9542	2^176403-139	53103	Lelio R Paula	02/2011
9543	55^30508-2	53095	Lelio R Paula	08/2013
9544	(48591^11329-1)/48590	53090	Serge Batalov	04/2015
9545	3^111254-88	53082	Lelio R Paula	10/2012
9546	15^45129-56	53076	Lelio R Paula	01/2013
9547	(640^18913-1)/639	53071	Eric Chen	09/2018
9548	2^176293-73	53070	Lelio R Paula	01/2011
9549	(67*10^53068+41)/9	53069	Robert Price	09/2015
9550	15271^2986+2986^15271	53069	Hans Havermann	06/2016
9551	2^176255-667	53059	Yves Minet	01/2012
9552	36471*2^176221+8647	53053	Paul Vanderveen	04/2016
9553	(19*10^53049-1)/9	53050	Serge Batalov	03/2009
9554	9*2^176203-5	53044	Lelio R Paula	03/2014
9555	2^176205-94395	53043	Lelio R Paula	08/2011
9556	(19*2^176224-1)/217916913	53042	Lelio R Paula	01/2014
9557	8600^13481-13481^8600	53041	Norbert Schneider	05/2018
9558	17^43103+14	53037	Lelio R Paula	01/2013
9559	(31*2^176188-1)/3555	53036	Lelio R Paula	01/2014
9560	2^176177+60947	53035	David Broadhurst	05/2002
9561	(22*10^53033-7)/3	53034	Erik Branger	09/2014
9562	13810^6909+6909^13810	53023	Hans Havermann	06/2016
9563	2^176108+16095	53014	Lelio R Paula	10/2009
9564	2^176107+18915	53014	Lelio R Paula	07/2012
9565	3^111080-9628	52999	Enzo Doria	02/2013
9566	2^176047-1551	52996	Yves Minet	08/2012
9567	2^176042+73519	52994	Enzo Doria	04/2016
9568	lucasV(1715,1,2^14)/65537	52986	Mike Oakes	04/2009
9569	2^175984-112259	52977	Enzo Doria	06/2014
9570	11^50870+10	52976	Lelio R Paula	01/2013
9571	(11*10^52956+19)/3	52957	Robert Price	03/2016
9572	gcd(V(949965),5F(189993)(F(189993)+1)+1)	52941	Serge Batalov	04/2015
9573	(-lucasV(1,2,351735)+2)/(37263)	52938	Mike Oakes	03/2017
9575	(98*10^52931-89)/99	52931	Ray Chandler	11/2010
9574	13774^6963+6963^13774	52931	Hans Havermann	06/2016
9576	2^175812-1367	52925	Yves Minet	05/2013
9577	2^175801+1155*175801	52922	Henri Lifchitz	01/2005
9578	11^50801-9090	52904	Enzo Doria	02/2013
9579	7803^13592-13592^7803	52904	Norbert Schneider	07/2018
9580	43^32374+12	52882	Robert Price	11/2013
9581	2^175628+13	52870	Lelio R Paula	01/2011
9582	2^175615-1747	52866	Yves Minet	09/2012
9583	(13*10^52861+107)/3	52862	Robert Price	11/2017
9584	9*2^175586-7	52858	Lelio R Paula	03/2014
9585	12174^12937+12937^12174	52854	Norbert Schneider	04/2016
9586	(15*2^175565+1)/8359	52848	Lelio R Paula	07/2012
9587	(2^175631-1)/330463093135534238072561/92733169	52839	Robert Kinser	03/2017
9588	14256^5077+5077^14256	52828	Hans Havermann	06/2016
9589	2^175467+82875	52821	Lelio R Paula	07/2012
9590	(7*10^52819+167)/3	52820	Robert Kinser	10/2017
9592	(67607*2^175426+1)/3	52813	Lelio R Paula	05/2014
9591	71671!6-32	52813	Robert Price	08/2018
9593	13^47400-60	52801	Lelio R Paula	01/2013
9594	4*10^52792+63	52793	Robert Price	06/2016
9596	(78557*2^175360+1)/3087	52791	Lelio R Paula	06/2014
9595	18^42055-2929	52791	Enzo Doria	03/2013
9597	9*5^75521+2	52788	Lelio R Paula	09/2014
9598	6^67814+31	52770	Lelio R Paula	10/2012
9599	70^28600+69	52770	Norbert Schneider	10/2012
9600	14^46038+97	52766	Lelio R Paula	01/2013
9601	(61*10^52763-7)/9	52764	Serge Batalov	02/2009
9602	2*5^75474+9	52755	Lelio R Paula	09/2014
9603	10^52753+2826430609	52754	Robert Price	05/2015
9604	10^52753+183997	52754	Patrick De Geest	01/2016
9605	10^52753-50153	52753	Patrick De Geest	03/2016
9606	19846^455+455^19846	52751	Anatoly F. Selevich	02/2007
9607	2^175217+72977	52746	Enzo Doria	04/2016
9608	p(11466)#/2-256	52746	Robert Price	05/2017
9609	(4*10^52740+41)/9	52740	Robert Price	11/2014
9610	2^175189+5385	52738	Lelio R Paula	08/2009
9611	2^175160+9385	52729	Lelio R Paula	07/2008
9612	12356^12885+12885^12356	52724	Norbert Schneider	03/2016
9613	2^175137+11	52722	Lelio R Paula	01/2011
9614	65^29077-64^29077	52715	Robert Price	08/2013
9615	2*10^52713-87	52714	Robert Price	06/2016
9616	2^175106-465	52713	Lelio R Paula	08/2009
9617	2^175089-58695	52708	Lelio R Paula	08/2009
9619	2^175045+195	52694	Lelio R Paula	02/2011
9618	195^23010-2	52694	Lelio R Paula	10/2017
9620	2^175025+149	52688	Lelio R Paula	02/2011
9621	(19^41201+1)/20	52685	Paul Bourdelais	03/2010
9622	(436*10^52683-13)/9	52685	Robert Price	10/2017
9623	2*12^48815-5^48815	52681	Mike Oakes	10/2010
9624	335^20862-20862^335	52678	Norbert Schneider	09/2015
9625	2^174983-7605	52676	Lelio R Paula	07/2009
9626	4*10^52667+19	52668	Robert Price	04/2016
9627	(10^52667+77)/3	52667	Robert Price	01/2017
9628	11434^12977+12977^11434	52664	Norbert Schneider	04/2016
9629	2^174941-1203	52663	Lelio R Paula	07/2009
9630	8501^13400-13400^8501	52655	Norbert Schneider	03/2018
9631	2^174910+12705	52654	Lelio R Paula	07/2012
9632	3^110338+74	52645	Lelio R Paula	10/2012
9633	5^75303+12	52635	Lelio R Paula	10/2012
9634	2^174836+255255	52631	Lelio R Paula	07/2009
9635	(66^28921+1)/67	52622	Paul Bourdelais	08/2017
9636	20^40443+9	52618	Lelio R Paula	01/2013
9637	(11*2^174788+1)/9	52617	Lelio R Paula	01/2012
9638	(11*2^174786-1)/703	52615	Lelio R Paula	01/2014
9639	11^50520-1290	52612	Enzo Doria	11/2012
9640	(670^18617-1)/669	52611	Eric Chen	09/2018
9641	(10^52608-19)/9	52608	Robert Price	10/2017
9642	(9913*2^174736-1)/333	52603	Lelio R Paula	03/2015
9643	13145^10024+10024^13145	52594	Hans Havermann	05/2016
9644	5003^14217-150	52592	Enzo Doria	07/2012
9645	2^174698-4055	52590	Yves Minet	02/2018
9646	19^41123+10	52587	Lelio R Paula	01/2013
9647	2^174683+12909	52585	Lelio R Paula	01/2011
9648	2^174643+59	52573	Lelio R Paula	01/2011
9649	(1017*2^174640-1)/773	52572	Lelio R Paula	03/2015
9650	13529^7662+7662^13529	52552	Hans Havermann	06/2016
9651	121421#+188767	52548	Makoto Morimoto	02/2016
9652	20^40375-5923	52530	Enzo Doria	03/2013
9653	(67607*2^174503+1)/90948079	52528	Lelio R Paula	05/2014
9654	(-lucasV(1,2,349014)+2)/(7508731047043)	52521	Mike Oakes	03/2017
9655	2^174462+345	52519	Lelio R Paula	07/2009
9656	t(178863)	52509	Robert Price	10/2014
9657	2^174416+855	52505	Lelio R Paula	07/2009
9658	6^67467-103	52500	Lelio R Paula	10/2012
9659	(2^174533-1)/(193594572654550537*91917886778031629891960890057)	52494	Dario Alpern	06/2017
9660	7888^13467-13467^7888	52481	Norbert Schneider	05/2018
9661	2^174329-11265	52479	Enzo Doria	06/2014
9662	2^174314-1241	52474	Yves Minet	05/2009
9663	52^30577-51	52471	Norbert Schneider	08/2014
9664	9403^13206-13206^9403	52471	Norbert Schneider	12/2017
9665	15692^2205+2205^15692	52465	Hans Havermann	06/2016
9666	(2^174281-7)/628817029615	52453	Lelio R Paula	02/2012
9667	(2^174240+5)/3	52451	Lelio R Paula	02/2012
9668	(86*10^52450-221)/9	52451	Robert Price	06/2017
9669	(62*10^52448-197)/9	52449	Robert Price	10/2017
9670	(15*2^174221+1)/403	52445	Lelio R Paula	07/2012
9671	26313!2-32	52443	Robert Price	10/2015
9672	(3*2^174214-1)/3748729	52438	Lelio R Paula	01/2014
9673	2*3^109900-5	52436	Lelio R Paula	03/2014
9675	4159^14488-150	52432	Enzo Doria	07/2012
9674	(89*10^52431-71)/9	52432	Robert Price	11/2015
9676	2^174170-3941	52431	Yves Minet	04/2017
9677	(7*2^174171-1)/685	52429	Lelio R Paula	01/2014
9678	(260137^9679+1)/260138	52409	Faysal YAtim	03/2008
9679	2^174098+79	52409	Lelio R Paula	01/2011
9680	35^33940-2214	52406	Enzo Doria	03/2013
9681	15^44557+2	52404	Ray Chandler	07/2011
9682	2^174049-439	52394	Yves Minet	01/2012
9683	6^67329+115	52393	Lelio R Paula	10/2012
9685	2^174041+262145	52392	Lelio R Paula	07/2009
9684	141^24377+2	52392	Lelio R Paula	05/2013
9686	lucasU(285,1,21339)-lucasU(285,1,21338)	52382	Mike Oakes	05/2009
9687	2^174001-5955	52380	Lelio R Paula	07/2009
9688	lucasV(-1,2,347969)	52375	Mike Oakes	02/2017
9689	3^109764-140	52371	Lelio R Paula	10/2012
9690	2*3^109761+7	52370	Lelio R Paula	03/2014
9691	9863^13112-13112^9863	52370	Norbert Schneider	10/2017
9692	(145^24229+1)/146	52366	Richard Fischer	02/2018
9693	8094^13399-13399^8094	52366	Norbert Schneider	03/2018
9694	2^173944-112253	52363	Enzo Doria	06/2014
9696	2^173940+1111	52362	Lelio R Paula	01/2011
9695	(3126^14983-1)/3125	52362	Richard Fischer	03/2015
9697	15214^2763+2763^15214	52358	Hans Havermann	05/2016
9698	13200^9247+9247^13200	52352	Hans Havermann	05/2016
9699	(1017*2^173867-1)/7175	52339	Lelio R Paula	03/2015
9700	13732^6465+6465^13732	52327	Hans Havermann	05/2016
9701	(2^173867-1)/52536637502689	52326	Donovan Johnson	06/2005
9702	2^173811-684877	52323	Paul Bourdelais	11/2012
9703	2^173807-5955	52322	Lelio R Paula	06/2009
9704	2^173796-1044689	52318	Paul Bourdelais	11/2012
9705	10^52317+64497	52318	Patrick De Geest	12/2012
9706	10^52317+64743	52318	Patrick De Geest	12/2012
9708	10^52317-71	52317	Robert Price	05/2011
9707	10821^12968+12968^10821	52317	Norbert Schneider	04/2016
9709	(298*10^52308-7)/3	52310	Robert Price	06/2017
9710	(2^173778-3)/57959	52308	Lelio R Paula	02/2012
9711	10232^13043-13043^10232	52302	Norbert Schneider	08/2017
9712	2^173727+9	52298	Lelio R Paula	01/2011
9713	(14^45631+13^45631)/27	52298	Robert Price	04/2013
9714	37856!3+6561	52293	Robert Price	11/2015
9715	4*3^109596+5	52292	Lelio R Paula	03/2014
9716	15436^2441+2441^15436	52291	Hans Havermann	05/2016
9717	43^32005+24	52280	Robert Price	11/2013
9718	2^173650-165	52274	Lelio R Paula	02/2011
9719	4*10^52272+93	52273	Robert Price	01/2017
9720	19^40873+84	52267	Lelio R Paula	01/2013
9721	2^173621+4242429	52266	Jason Earls	09/2008
9722	9999^13064-13064^9999	52256	Norbert Schneider	09/2017
9723	numbpart(46909^2-1)	52247	Serge Batalov	04/2017
9724	14^45579-31	52240	Lelio R Paula	01/2013
9725	7395^13502-13502^7395	52239	Norbert Schneider	05/2018
9726	(10223*2^173518+1)/903	52236	Lelio R Paula	05/2014
9727	20^40147-6123	52233	Enzo Doria	03/2013
9728	4^86754-3^(86754+1)	52232	Robert Price	04/2016
9729	7452^13487-13487^7452	52226	Norbert Schneider	05/2018
9730	2^173477-3433	52222	Yves Minet	04/2009
9731	(22*10^52217-73)/3	52218	Robert Price	09/2017
9732	(25*2^173446+1)/61	52213	Lelio R Paula	07/2012
9733	3^109431-38	52212	Lelio R Paula	10/2012
9734	2^173424-3959	52206	Yves Minet	04/2017
9735	13^46861-72	52201	Lelio R Paula	01/2013
9736	2^173373-1363	52191	Yves Minet	03/2009
9737	11^50114-1740	52189	Enzo Doria	11/2012
9738	13735^6304+6304^13735	52188	Hans Havermann	05/2016
9739	11^50111-1110	52186	Enzo Doria	11/2012
9740	lucasU(46,1,31387)+lucasU(46,1,31386)	52181	Mike Oakes	04/2009
9741	20^40105-8583	52178	Enzo Doria	03/2013
9742	(10322^13001+2679^13001)/13001^2	52175	Lelio R Paula	08/2008
9743	2^173314-3941	52173	Yves Minet	04/2017
9744	2^173294+1155	52167	Lelio R Paula	07/2012
9746	(19*2^173301-1)/23489	52166	Lelio R Paula	01/2014
9745	15146^2781+2781^15146	52166	Hans Havermann	06/2016
9747	11^50088-32	52162	Lelio R Paula	01/2013
9748	3^109320+236	52159	Lelio R Paula	10/2012
9749	2^173246-28635	52153	Lelio R Paula	06/2009
9750	2*10^52147+11	52148	Robert Price	01/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(225451 PRPs in the top)