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 (> 30000)	Who ?	When ?
9251	2^179120+2533	53921	Henri Lifchitz	09/2004
9252	(2^179126+78557)/4649321187	53913	Lelio R Paula	05/2012
9253	74^28842+73	53913	Norbert Schneider	11/2012
9254	1271^17368+17368^1271	53913	Serge Batalov	05/2014
9255	2^179079+53	53909	Lelio R Paula	02/2011
9256	17^43807+54	53903	Lelio R Paula	01/2013
9257	17^43807+30	53903	Lelio R Paula	01/2013
9258	3^112951-310	53892	Lelio R Paula	10/2012
9259	Phi(7,2957!)	53888	Robert Price	05/2015
9260	(10223*2^178975+1)/33985	53877	Lelio R Paula	05/2014
9261	2^178944-219209	53868	Enzo Doria	11/2012
9262	(10^53859+149)/3	53859	Serge Batalov	12/2014
9263	2^178910-191	53858	Lelio R Paula	02/2011
9264	16170^2141+2141^16170	53857	Hans Havermann	07/2016
9265	(5*10^53855-107)/3	53856	Robert Price	01/2017
9266	(72*10^53847-27)/99	53847	Patrick De Geest	08/2004
9267	2^178841-869688105	53837	Lelio R Paula	06/2012
9268	2*10^53834-27	53835	Robert Price	02/2017
9270	2^178821-1011523	53831	Paul Bourdelais	11/2012
9269	12601^13128-13128^12601	53831	Norbert Schneider	10/2017
9271	2^178819-15	53830	Lelio R Paula	02/2011
9272	(14450!-1)/225296581	53829	Donovan Johnson	04/2006
9273	(124351#+125386)/(2^57188344891039820259)	53826	Makoto Morimoto	10/2017
9274	10530^13381-13381^10530	53825	Norbert Schneider	03/2018
9275	2^178761-465	53813	Lelio R Paula	10/2009
9276	18900^703+703^18900	53808	Anatoly F. Selevich	02/2007
9277	13918^7343+7343^13918	53806	Hans Havermann	08/2016
9278	10^53804+31749	53805	Patrick De Geest	12/2012
9279	10^53804-71	53804	Robert Price	05/2011
9280	t(178994)	53804	Robert Price	03/2015
9281	(2^178693-lucasV(1,2,178693)+1)/2	53792	Mike Oakes	11/2016
9282	2^178671-113215	53786	Enzo Doria	07/2014
9283	15110^3621+3621^15110	53774	Hans Havermann	07/2016
9284	2^178611+95	53768	Lelio R Paula	02/2011
9285	2^178597+5711	53764	Lelio R Paula	10/2011
9286	2^178598+12915	53764	Lelio R Paula	07/2012
9287	(9179*2^178579-1)/303	53760	Lelio R Paula	03/2015
9288	10671^13342-13342^10671	53745	Norbert Schneider	02/2018
9289	5*7^63589+2	53740	Lelio R Paula	09/2014
9290	2^178516-112515	53739	Enzo Doria	06/2014
9291	20^41302-27	53736	Lelio R Paula	01/2013
9292	6^69054-39209	53735	Mike Oakes	12/2010
9293	13086^12769+12769^13086	53734	Hans Havermann	07/2016
9294	2^178455+76043	53721	Enzo Doria	04/2016
9295	(10^53718-7)/3	53718	Makoto Kamada	10/2004
9296	(67607*2^178426+1)/3	53716	Lelio R Paula	05/2014
9297	9*10^53707+11	53708	Robert Kinser	01/2017
9298	94601!8-2	53708	Robert Price	04/2017
9299	13214^11595+11595^13214	53706	Hans Havermann	07/2016
9300	Phi(134350,10)/537401/8011962251	53705	Maksym Voznyy	10/2011
9301	2^178367-379	53694	Yves Minet	03/2013
9302	(2^178364-5)/11	53692	Lelio R Paula	02/2012
9303	4339^14760-168	53688	Enzo Doria	06/2012
9304	12^49746-11	53685	Lelio R Paula	01/2013
9305	12950^13051-13051^12950	53670	Norbert Schneider	08/2017
9306	(9913*2^178266-1)/2247	53665	Lelio R Paula	03/2015
9307	13725^8128+8128^13725	53665	Hans Havermann	07/2016
9308	2^178250-113261	53659	Enzo Doria	07/2014
9309	2^178226+11715	53652	Lelio R Paula	10/2009
9310	35^34742-1976	53645	Enzo Doria	03/2013
9311	20^41228-563	53639	Enzo Doria	03/2013
9312	359^20992+20992^359	53637	Norbert Schneider	08/2014
9313	(27*2^178183-1)/29065	53636	Lelio R Paula	01/2014
9314	(3^112414+7)/37381696	53628	Lelio R Paula	03/2012
9315	17994^955+955^17994	53623	Anatoly F. Selevich	10/2006
9316	2^178117-1551	53619	Yves Minet	08/2012
9317	2^178099-11287	53614	Enzo Doria	06/2014
9318	10751^13298-13298^10751	53611	Norbert Schneider	01/2018
9319	(15*2^178080-1)/309071	53604	Lelio R Paula	01/2014
9320	5^76672-13766	53592	Enzo Doria	02/2013
9321	6^68868-137	53590	Lelio R Paula	10/2012
9322	(5*2^178021+1)/8173	53587	Lelio R Paula	07/2012
9323	5^76654-26	53579	Lelio R Paula	10/2012
9324	(3^112297-2)/7627	53576	Lelio R Paula	03/2012
9325	3*2^177948-7	53569	Lelio R Paula	03/2014
9326	10^53558+18543	53559	Patrick De Geest	12/2012
9327	10^53558-21	53558	Robert Price	03/2011
9328	2^177792-95	53521	Lelio R Paula	02/2011
9329	13392^9919+9919^13392	53521	Hans Havermann	07/2016
9330	13105^12132+12132^13105	53520	Hans Havermann	07/2016
9331	13^48042+82	53517	Lelio R Paula	01/2013
9332	2^177768+39121	53514	Yves Minet	10/2010
9333	13835^7366+7366^13835	53504	Hans Havermann	07/2016
9334	17^43477+84	53497	Lelio R Paula	01/2013
9335	5*10^53492+9	53493	Dmitry Domanov	11/2010
9336	2^177683+95	53488	Lelio R Paula	01/2011
9337	11057^13226-13226^11057	53482	Norbert Schneider	12/2017
9338	(2^177678+3)/514627	53481	Lelio R Paula	02/2012
9339	2^177641-255463	53476	Gary Barnes	08/2009
9340	p(11608)#/2+16	53469	Robert Price	12/2016
9341	(14*10^53465+211)/9	53466	Robert Price	11/2017
9342	37302#*10^(37302+52)+p(37302+1)	53457	Jason Earls	08/2008
9343	12001^13104-13104^12001	53455	Norbert Schneider	10/2017
9344	1829^16384+1828^16384	53449	Henri Lifchitz	01/2007
9345	10^53442+12621	53443	Patrick De Geest	06/2018
9346	10^53442-2007	53442	Patrick De Geest	06/2018
9347	35^34608-9602	53438	Enzo Doria	03/2013
9348	(3^111992+8)/14867	53430	Lelio R Paula	03/2012
9350	2^177480+1869661	53427	Enzo Doria	05/2016
9349	11791^13122-13122^11791	53427	Norbert Schneider	10/2017
9351	(8*10^53411+1)/9	53411	Serge Batalov	12/2008
9352	4*5^76410-3	53409	Lelio R Paula	09/2014
9353	2^177380-113045	53397	Enzo Doria	07/2014
9355	5^76362-2*3^76362	53375	Mike Oakes	11/2009
9354	72365!6-24	53375	Robert Price	08/2018
9356	4159^14747-140	53370	Enzo Doria	07/2012
9357	(lucasV(1,2,354503)-2)/3	53358	Mike Oakes	03/2017
9358	p(11586)#/2+32	53357	Robert Price	12/2016
9359	15^45362-46	53350	Lelio R Paula	01/2013
9360	14147^5892+5892^14147	53338	Hans Havermann	07/2016
9361	7^63109+46	53334	Lelio R Paula	10/2012
9362	20^40986-1343	53325	Enzo Doria	03/2013
9363	4*10^53324-89	53325	Robert Price	08/2017
9364	20^40977-8883	53313	Enzo Doria	03/2013
9365	3^111711+2660	53300	Lelio R Paula	10/2012
9366	2^177040-11865	53295	Enzo Doria	10/2012
9367	(7*10^53287+17)/3	53288	Erik Branger	03/2014
9368	35^34506-10758	53280	Enzo Doria	03/2013
9369	(11*10^53274-17)/3	53275	Erik Branger	03/2014
9370	(1017*2^176971-1)/335	53275	Lelio R Paula	03/2015
9371	2^176961-2833	53271	Yves Minet	09/2014
9372	3^111642+110	53267	Lelio R Paula	10/2012
9373	17^43290-98	53267	Lelio R Paula	01/2013
9374	7^63028+36	53265	Lelio R Paula	10/2012
9375	(22*10^53264+71)/3	53265	Robert Price	05/2017
9376	7^63023-36	53261	Lelio R Paula	10/2012
9377	19783^492+492^19783	53256	Anatoly F. Selevich	02/2007
9378	13350^9739+9739^13350	53247	Hans Havermann	10/2015
9379	14394^4993+4993^14394	53235	Hans Havermann	10/2015
9380	2^176823-112807	53230	Enzo Doria	06/2014
9381	1684^16495+16495^1684	53219	Serge Batalov	05/2014
9382	15277^3042+3042^15277	53213	Hans Havermann	06/2016
9383	(50322^11317-1)/50321	53206	Serge Batalov	04/2015
9384	2^176742-1595	53205	Lelio R Paula	10/2009
9385	(27*2^176767-1)/20455056355	53204	Lelio R Paula	01/2014
9386	72149!6-12	53200	Robert Price	08/2018
9387	(-lucasV(1,2,353460)-2)/(3^2*5^2)	53199	Mike Oakes	03/2017
9388	(3*2^176696-1)/299	53189	Lelio R Paula	01/2014
9389	(7*10^53185-1)/3	53186	Erik Branger	03/2014
9390	2^176629+465	53171	Lelio R Paula	07/2012
9391	(3*2^176604-1)/359	53162	Lelio R Paula	01/2014
9392	10955^13158-13158^10955	53154	Norbert Schneider	11/2017
9393	5^76038-14366	53149	Enzo Doria	02/2013
9394	15156^3209+3209^15156	53143	Hans Havermann	06/2016
9395	2^176532-2837	53142	Yves Minet	09/2014
9396	52^30967-51	53140	Norbert Schneider	08/2014
9397	9*5^76023-2	53139	Lelio R Paula	09/2014
9398	(14283!+1)/464216177	53135	Michael Porter	03/2016
9399	2^176461-165	53121	Lelio R Paula	02/2011
9400	(62*10^53111+1)/9	53112	Serge Batalov	05/2010
9401	2^176403-139	53103	Lelio R Paula	02/2011
9402	55^30508-2	53095	Lelio R Paula	08/2013
9403	(48591^11329-1)/48590	53090	Serge Batalov	04/2015
9404	3^111254-88	53082	Lelio R Paula	10/2012
9405	15^45129-56	53076	Lelio R Paula	01/2013
9406	2^176293-73	53070	Lelio R Paula	01/2011
9407	(67*10^53068+41)/9	53069	Robert Price	09/2015
9408	15271^2986+2986^15271	53069	Hans Havermann	06/2016
9409	2^176255-667	53059	Yves Minet	01/2012
9410	36471*2^176221+8647	53053	Paul Vanderveen	04/2016
9411	(19*10^53049-1)/9	53050	Serge Batalov	03/2009
9412	9*2^176203-5	53044	Lelio R Paula	03/2014
9413	2^176205-94395	53043	Lelio R Paula	08/2011
9414	(19*2^176224-1)/217916913	53042	Lelio R Paula	01/2014
9415	8600^13481-13481^8600	53041	Norbert Schneider	05/2018
9416	17^43103+14	53037	Lelio R Paula	01/2013
9417	(31*2^176188-1)/3555	53036	Lelio R Paula	01/2014
9418	2^176177+60947	53035	David Broadhurst	05/2002
9419	(22*10^53033-7)/3	53034	Erik Branger	09/2014
9420	13810^6909+6909^13810	53023	Hans Havermann	06/2016
9421	2^176108+16095	53014	Lelio R Paula	10/2009
9422	2^176107+18915	53014	Lelio R Paula	07/2012
9423	3^111080-9628	52999	Enzo Doria	02/2013
9424	2^176047-1551	52996	Yves Minet	08/2012
9425	2^176042+73519	52994	Enzo Doria	04/2016
9426	lucasV(1715,1,2^14)/65537	52986	Mike Oakes	04/2009
9427	2^175984-112259	52977	Enzo Doria	06/2014
9428	11^50870+10	52976	Lelio R Paula	01/2013
9429	(11*10^52956+19)/3	52957	Robert Price	03/2016
9430	gcd(V(949965),5F(189993)(F(189993)+1)+1)	52941	Serge Batalov	04/2015
9431	(-lucasV(1,2,351735)+2)/(37263)	52938	Mike Oakes	03/2017
9433	(98*10^52931-89)/99	52931	Ray Chandler	11/2010
9432	13774^6963+6963^13774	52931	Hans Havermann	06/2016
9434	2^175812-1367	52925	Yves Minet	05/2013
9435	2^175801+1155*175801	52922	Henri Lifchitz	01/2005
9436	11^50801-9090	52904	Enzo Doria	02/2013
9437	7803^13592-13592^7803	52904	Norbert Schneider	07/2018
9438	43^32374+12	52882	Robert Price	11/2013
9439	2^175628+13	52870	Lelio R Paula	01/2011
9440	2^175615-1747	52866	Yves Minet	09/2012
9441	(13*10^52861+107)/3	52862	Robert Price	11/2017
9442	9*2^175586-7	52858	Lelio R Paula	03/2014
9443	12174^12937+12937^12174	52854	Norbert Schneider	04/2016
9444	(15*2^175565+1)/8359	52848	Lelio R Paula	07/2012
9445	(2^175631-1)/330463093135534238072561/92733169	52839	Robert Kinser	03/2017
9446	14256^5077+5077^14256	52828	Hans Havermann	06/2016
9447	2^175467+82875	52821	Lelio R Paula	07/2012
9448	(7*10^52819+167)/3	52820	Robert Kinser	10/2017
9449	(67607*2^175426+1)/3	52813	Lelio R Paula	05/2014
9450	71671!6-32	52813	Robert Price	08/2018
9451	13^47400-60	52801	Lelio R Paula	01/2013
9452	4*10^52792+63	52793	Robert Price	06/2016
9454	(78557*2^175360+1)/3087	52791	Lelio R Paula	06/2014
9453	18^42055-2929	52791	Enzo Doria	03/2013
9455	9*5^75521+2	52788	Lelio R Paula	09/2014
9456	6^67814+31	52770	Lelio R Paula	10/2012
9457	70^28600+69	52770	Norbert Schneider	10/2012
9458	14^46038+97	52766	Lelio R Paula	01/2013
9459	(61*10^52763-7)/9	52764	Serge Batalov	02/2009
9460	2*5^75474+9	52755	Lelio R Paula	09/2014
9461	10^52753+2826430609	52754	Robert Price	05/2015
9462	10^52753+183997	52754	Patrick De Geest	01/2016
9463	10^52753-50153	52753	Patrick De Geest	03/2016
9464	19846^455+455^19846	52751	Anatoly F. Selevich	02/2007
9465	2^175217+72977	52746	Enzo Doria	04/2016
9466	p(11466)#/2-256	52746	Robert Price	05/2017
9467	(4*10^52740+41)/9	52740	Robert Price	11/2014
9468	2^175189+5385	52738	Lelio R Paula	08/2009
9469	2^175160+9385	52729	Lelio R Paula	07/2008
9470	12356^12885+12885^12356	52724	Norbert Schneider	03/2016
9471	2^175137+11	52722	Lelio R Paula	01/2011
9472	65^29077-64^29077	52715	Robert Price	08/2013
9473	2*10^52713-87	52714	Robert Price	06/2016
9474	2^175106-465	52713	Lelio R Paula	08/2009
9475	2^175089-58695	52708	Lelio R Paula	08/2009
9477	2^175045+195	52694	Lelio R Paula	02/2011
9476	195^23010-2	52694	Lelio R Paula	10/2017
9478	2^175025+149	52688	Lelio R Paula	02/2011
9479	(19^41201+1)/20	52685	Paul Bourdelais	03/2010
9480	(436*10^52683-13)/9	52685	Robert Price	10/2017
9481	2*12^48815-5^48815	52681	Mike Oakes	10/2010
9482	335^20862-20862^335	52678	Norbert Schneider	09/2015
9483	2^174983-7605	52676	Lelio R Paula	07/2009
9484	4*10^52667+19	52668	Robert Price	04/2016
9485	(10^52667+77)/3	52667	Robert Price	01/2017
9486	11434^12977+12977^11434	52664	Norbert Schneider	04/2016
9487	2^174941-1203	52663	Lelio R Paula	07/2009
9488	8501^13400-13400^8501	52655	Norbert Schneider	03/2018
9489	2^174910+12705	52654	Lelio R Paula	07/2012
9490	3^110338+74	52645	Lelio R Paula	10/2012
9491	5^75303+12	52635	Lelio R Paula	10/2012
9492	2^174836+255255	52631	Lelio R Paula	07/2009
9493	(66^28921+1)/67	52622	Paul Bourdelais	08/2017
9494	20^40443+9	52618	Lelio R Paula	01/2013
9495	(11*2^174788+1)/9	52617	Lelio R Paula	01/2012
9496	(11*2^174786-1)/703	52615	Lelio R Paula	01/2014
9497	11^50520-1290	52612	Enzo Doria	11/2012
9498	(10^52608-19)/9	52608	Robert Price	10/2017
9499	(9913*2^174736-1)/333	52603	Lelio R Paula	03/2015
9500	13145^10024+10024^13145	52594	Hans Havermann	05/2016

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Probable Primes Top 10000

(218736 PRPs in the top)