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 (> 50000)	Who ?	When ?
7751	V(340138)	67336	Serge Batalov	03/2015
7752	43125^14528-106	67334	Enzo Doria	07/2012
7753	15275^16086-16086^15275	67304	Norbert Schneider	09/2018
7754	8*10^67302-51	67303	Robert Price	10/2017
7755	17458^7153+7153^17458	67292	Hans Havermann	08/2016
7756	16366^12925+12925^16366	67288	Hans Havermann	08/2016
7757	37^42906-2	67286	Lelio R Paula	08/2013
7758	18^53592-13	67273	Lelio R Paula	08/2013
7759	V(396221)	67256	Serge Batalov	03/2015
7760	(34*10^67245-7)/9/3^4/193/1381537	67236	Makoto Morimoto	04/2016
7761	(14*10^67235-101)/3	67236	Robert Price	04/2017
7762	53^38993-52^38993	67235	Robert Price	01/2013
7763	(2^223349-7)/6485	67231	Lelio R Paula	04/2012
7764	2^223333+315	67230	Lelio R Paula	04/2012
7765	2^223278-111041	67214	Enzo Doria	05/2014
7766	(23472^223281+1)/(351971213*1783)	67208	Jens K. Andersen	09/2007
7767	2^223256-45	67207	Lelio R Paula	02/2012
7768	2^223253-112111	67206	Enzo Doria	06/2014
7769	18407^4474+4474^18407	67199	Hans Havermann	08/2016
7770	47^40182+40182^47	67189	Norbert Schneider	11/2014
7771	13^60309+94	67181	Lelio R Paula	07/2013
7772	11^64503-84	67173	Lelio R Paula	07/2013
7773	3^140781+236	67170	Lelio R Paula	06/2013
7774	2^223107-865057	67162	Paul Bourdelais	03/2013
7775	2^223100-59	67160	Lelio R Paula	02/2012
7776	2^223087+71963	67156	Enzo Doria	04/2016
7777	18^53481-3779	67134	Enzo Doria	03/2013
7778	(326^26713-1)/325	67134	Eric Chen	09/2017
7779	4^111473-62573	67114	Mike Oakes	02/2011
7780	2^222943+29	67113	Henri Lifchitz	08/2005
7781	(2^222939-9)/103	67110	Lelio R Paula	04/2012
7782	2^222862-459161	67089	Enzo Doria	05/2015
7783	2^222828+8193	67078	Lelio R Paula	04/2012
7784	3^140570+2660	67069	Lelio R Paula	06/2013
7785	20731^1716+1716^20731	67055	Hans Havermann	08/2019
7786	2^222744+855	67053	Lelio R Paula	04/2012
7787	13^60189+84	67048	Lelio R Paula	07/2013
7788	2*10^67043-51	67044	Robert Price	11/2017
7789	22588^929+929^22588	67042	Hans Havermann	08/2019
7790	2^222701+577294575	67040	Lelio R Paula	02/2016
7791	(13*10^67038-31)/9	67039	Serge Batalov	11/2008
7792	(151*10^67027-7)/9	67029	Robert Price	07/2017
7793	(58695*2^222620-1)/61	67019	Lelio R Paula	04/2015
7794	2^222614-111041	67014	Enzo Doria	05/2014
7795	16255^13242+13242^16255	67003	Hans Havermann	08/2019
7796	16477^11650+11650^16477	67001	Hans Havermann	08/2019
7797	118^32333-117	66991	Norbert Schneider	08/2018
7798	2^222520-1907	66986	Yves Minet	03/2013
7799	(4^111231+23)/3	66968	Robert Price	02/2017
7800	16206^13549+13549^16206	66962	Hans Havermann	08/2019
7801	2^222408-111275	66952	Enzo Doria	05/2014
7802	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
7803	2^222378-1005	66943	Lelio R Paula	04/2012
7804	(9*2^222366+1)/73	66938	Lelio R Paula	08/2012
7805	7^79202-6^(79202+1)	66934	Robert Price	06/2016
7806	2^222325-112255	66927	Enzo Doria	06/2014
7807	21789^1178+1178^21789	66918	Hans Havermann	08/2019
7808	20^51428+33	66910	Lelio R Paula	08/2013
7810	2^222224-18509	66897	Enzo Doria	05/2013
7809	(38*10^66896+187)/9	66897	Robert Price	11/2017
7811	2^222192-869688105	66887	Lelio R Paula	02/2016
7812	(19*10^66878-43)/3	66879	Robert Price	10/2017
7813	11^64219-64	66878	Lelio R Paula	07/2013
7814	2^222151-17295	66875	Lelio R Paula	04/2012
7815	gcd(V(799885),5F(159977)(F(159977)+1)+1)	66867	Serge Batalov	04/2015
7816	2^222085-111031	66855	Enzo Doria	05/2014
7817	8*10^66848-13	66849	Robert Price	05/2017
7818	(3^140087+4)/13	66838	Lelio R Paula	04/2012
7819	(3^140102+4)/8843609437	66836	Lelio R Paula	04/2012
7820	19^52265+52	66835	Lelio R Paula	08/2013
7821	2*10^66826-27	66827	Robert Price	02/2017
7822	4*6^85867+5	66819	Lelio R Paula	09/2014
7823	11955^16384+2	66807	Matt Stath	12/2018
7824	15^56800+8	66802	Lelio R Paula	08/2013
7825	(2^221891-2^110946+1)/5	66796		11/2006
7826	10^66793+69441	66794	Patrick De Geest	05/2013
7827	10^66793-63	66793	Robert Price	05/2011
7828	35^43256-1704	66791	Enzo Doria	03/2013
7829	3^139976+2^(139976-1)	66786	Robert Price	05/2016
7830	88769!6-48	66786	Robert Price	08/2018
7831	7^79023-54	66783	Lelio R Paula	06/2013
7832	104^33109-103	66782	Norbert Schneider	11/2016
7833	(34*10^66778-7)/9/37/358901	66772	Makoto Morimoto	04/2016
7834	(-lucasV(1,2,443622)+2)/(7281487)	66766	Mike Oakes	04/2017
7836	2^221768+183	66759	Lelio R Paula	02/2012
7835	gcd(V(1197915),5F(239583)(F(239583)+1)+1)	66759	Serge Batalov	04/2015
7837	(154*10^66755-1)/9	66757	Serge Batalov	12/2014
7838	11^64097+48	66751	Lelio R Paula	07/2013
7839	(lucasV(1,2,443547)-2)/(713791327221773)	66749	Mike Oakes	04/2017
7840	(19*10^66748+413)/9	66749	Robert Price	10/2017
7841	(3*2^221696-1)/13	66737	Lelio R Paula	01/2014
7842	8*6^85758-7	66734	Lelio R Paula	09/2014
7843	135^31325+2	66733	Lelio R Paula	05/2013
7844	(49*10^66729+41)/9	66730	Robert Price	07/2015
7845	(349*10^66720-7)/9	66722	Robert Price	03/2017
7846	(-lucasV(1,2,443285)+2)/(3^2*307)	66718	Mike Oakes	04/2017
7847	(25*10^66714+71)/3	66715	Robert Price	01/2017
7848	11^64061-780	66713	Enzo Doria	11/2012
7849	7^78929+4	66703	Lelio R Paula	06/2013
7850	11^64048-930	66700	Enzo Doria	11/2012
7851	120^32079-119	66699	Norbert Schneider	09/2018
7852	2*7^78921+5	66697	Lelio R Paula	09/2014
7853	(25*2^221526+1)/409	66685	Lelio R Paula	08/2012
7854	16330^12117+12117^16330	66682	Hans Havermann	08/2019
7855	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
7856	2^221479+72953	66672	Enzo Doria	04/2016
7857	10^66666+275403	66667	Patrick De Geest	03/2010
7858	16317^12182+12182^16317	66667	Hans Havermann	08/2019
7859	10^66666-115521	66666	Patrick De Geest	03/2010
7860	(18*10^66657-81)/99	66657	Ray Chandler	01/2011
7861	4*10^66653+21	66654	Robert Price	08/2016
7862	(10^66650+149)/3	66650	Serge Batalov	12/2014
7863	9^69842+38^69842-24^69842-3*2^69842	66647	Mike Oakes	12/2010
7864	2^221391-2145	66646	Lelio R Paula	04/2012
7865	22952^801+801^22952	66645	Hans Havermann	08/2019
7866	(5*10^66613-119)/3	66614	Robert Price	04/2016
7867	2^221273-113233	66610	Enzo Doria	07/2014
7868	3^139571-46	66593	Lelio R Paula	06/2013
7869	(410^(233295)-2*(10^33295)+1)/3	66591	Robert Price	04/2018
7870	2^221181-869688105	66583	Lelio R Paula	02/2016
7871	(61*10^66575-7)/9	66576	Ray Chandler	02/2012
7872	2^221126+133	66566	Lelio R Paula	02/2012
7873	12^61680+91	66564	Lelio R Paula	07/2013
7874	(lucasV(1,2,442258)+2)/103	66564	Mike Oakes	04/2017
7875	(13*10^66551-73)/3	66552	Robert Price	12/2016
7876	11^63901-1590	66547	Enzo Doria	12/2012
7877	11^63901-1500	66547	Enzo Doria	12/2012
7878	6^85517+23	66546	Lelio R Paula	07/2013
7879	17^54069-40	66530	Lelio R Paula	08/2013
7880	(2^110503+4725)^2+(2^110503+4725)+41	66530	Makoto Morimoto	05/2016
7881	(2^110503+8099)^2+(2^110503+8099)+41	66530	Makoto Morimoto	05/2016
7883	(2^221008-1017)/78533	66526	Lelio R Paula	04/2012
7882	3^139432+26	66526	Lelio R Paula	06/2013
7884	((2^110503+5139)^2+(2^110503+5139)+41)/20865797	66523	Makoto Morimoto	05/2016
7885	((2^110503+6647)^2+(2^110503+6647)+41)/197/17327	66523	Makoto Morimoto	05/2016
7886	6^85481+85481	66518	Henri Lifchitz	08/2014
7887	(9179*2^220913-1)/399	66503	Lelio R Paula	04/2015
7888	13^59687+66	66488	Lelio R Paula	07/2013
7889	(49*10^66485-31)/9	66486	Robert Price	07/2015
7890	(46*10^66469+17)/9	66470	Robert Price	06/2015
7891	2^220790+97	66465	Lelio R Paula	02/2012
7892	(23*2^220790+1)/807	66463	Lelio R Paula	06/2012
7893	40009^14441-102	66460	Enzo Doria	07/2012
7894	2^220736-143	66449	Lelio R Paula	02/2012
7895	(79*10^66447-97)/99	66447	Ray Chandler	01/2011
7896	21235^1344+1344^21235	66432	Hans Havermann	08/2019
7897	2^220675+69	66430	Lelio R Paula	02/2012
7898	19049^3070+3070^19049	66427	Hans Havermann	08/2019
7899	88323!6-16	66419	Robert Price	08/2018
7900	2^220633-111381	66418	Enzo Doria	05/2014
7901	(2^220625-509203)/4000321	66409	Lelio R Paula	05/2012
7902	2^220596-15813	66407	Enzo Doria	04/2013
7903	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
7904	2^220549-1859173	66392	Enzo Doria	04/2016
7905	2^220478-161	66371	Lelio R Paula	02/2012
7906	5^94938-14636	66359	Enzo Doria	02/2013
7907	(F(67)^4861-F(66)^4861)/F(65)	66353	Wayne Halsdorf	03/2012
7908	15444^15839-15839^15444	66346	Norbert Schneider	08/2018
7909	2^220253-114871	66303	Enzo Doria	05/2015
7910	12^61432+95	66297	Lelio R Paula	07/2013
7911	2^220192-111563	66285	Enzo Doria	05/2014
7912	2^220188-111449	66284	Enzo Doria	05/2014
7913	(4*10^66284+23)/9	66284	Robert Price	11/2014
7914	32501!2+2	66266	Robert Price	01/2015
7915	(8*10^66261-101)/3	66262	Robert Price	10/2017
7916	1530*10^66254+R(66254)	66258	Patrick De Geest	05/2016
7917	(47^39623-1)/46	66252	Robert Price	06/2014
7918	2^220044-97305	66240	Lelio R Paula	04/2012
7919	(77*10^66237-257)/9	66238	Robert Price	10/2017
7920	29^45285+2	66225	Ray Chandler	08/2011
7921	16711^9178+9178^16711	66222	Hans Havermann	08/2019
7922	15^56289+38	66202	Lelio R Paula	08/2013
7923	3^138749+98	66201	Lelio R Paula	06/2013
7924	(21*2^219912-1)/5	66201	Lelio R Paula	01/2014
7926	2^219904-16995	66198	Lelio R Paula	10/2011
7925	2^219903-4615	66198	Yves Minet	05/2019
7927	(3^138712-2)/5297	66179	Lelio R Paula	04/2012
7928	Phi(198552,10)	66177	Ray Chandler	07/2010
7929	4*6^85041+7	66176	Lelio R Paula	09/2014
7930	2^219812-3149	66171	Yves Minet	10/2009
7931	2^219795-611167	66165	Paul Bourdelais	03/2013
7932	32455!2+512	66162	Robert Price	02/2015
7933	(27*2^219760-1)/227	66154	Lelio R Paula	01/2014
7935	(11^63521-4^63521)/7	66150	Robert Price	03/2013
7934	5*7^78274-6	66150	Lelio R Paula	09/2014
7936	15853^14872+14872^15853	66145	Hans Havermann	08/2019
7937	(-lucasV(1,2,439441)-2)/(31192781359)	66134	Mike Oakes	04/2017
7938	2^219679-112015	66130	Enzo Doria	05/2014
7939	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
7940	15445^15782-15782^15445	66108	Norbert Schneider	08/2018
7941	2^219600+76561	66107	Enzo Doria	05/2016
7942	2^219594+255255	66105	Lelio R Paula	10/2011
7943	4*7^78210-3	66096	Lelio R Paula	09/2014
7944	(15185*2^219557-1)/63	66096	Lelio R Paula	04/2015
7945	(19*2^219499-1)/13	66076	Lelio R Paula	01/2014
7946	2^219496+66615	66075	Lelio R Paula	10/2011
7947	(F(79021)^5-F(79020)^5)/F(79019)	66057	Wayne Halsdorf	03/2012
7948	15871^14500+14500^15871	66046	Hans Havermann	08/2019
7949	(2^219414+7)/443657	66045	Lelio R Paula	04/2012
7950	(115*10^66043-1)/3	66045	Serge Batalov	12/2014
7951	10^66033+19	66034	Robert Price	01/2011
7952	10^66033-78309	66033	Patrick De Geest	05/2013
7953	(lucasV(1,2,438701)+2)/7599419	66025	Mike Oakes	04/2017
7954	2^219304+454245	66018	Henri Lifchitz	03/2007
7955	(27*2^219293+1)/9145	66012	Lelio R Paula	08/2012
7956	2^219273-112635	66008	Enzo Doria	06/2014
7957	17548^5771+5771^17548	66003	Hans Havermann	08/2019
7958	2^219250+25	66001	Lelio R Paula	08/2011
7959	132^31123+131	65999	Norbert Schneider	03/2015
7960	19327^2598+2598^19327	65995	Hans Havermann	08/2019
7961	18440^3789+3789^18440	65988	Hans Havermann	08/2019
7962	V(319871)	65987	Serge Batalov	03/2015
7963	2^219189-195	65983	Lelio R Paula	08/2011
7964	(7*2^219143-1)/55	65968	Lelio R Paula	01/2014
7965	(73^35401-1)/72	65962	Paul Bourdelais	08/2017
7966	2^219112-17009	65960	Enzo Doria	05/2013
7967	2^219093-111201	65954	Enzo Doria	05/2014
7968	2^219089-112099	65953	Enzo Doria	06/2014
7969	46714!3+81	65950	Robert Price	09/2014
7970	(11*10^65944-131)/3	65945	Robert Price	02/2017
7971	2^219021-3553	65932	Yves Minet	03/2017
7972	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
7973	2^218990+73519	65923	Enzo Doria	04/2016
7974	58^37378-57	65914	Norbert Schneider	09/2014
7976	(2^218945-7)/1675	65906	Lelio R Paula	04/2012
7975	5*10^65905+81	65906	Robert Price	08/2017
7977	3*10^65899-13	65900	Robert Price	11/2017
7978	(-lucasV(1,2,437845)-2)/1679917	65896	Mike Oakes	04/2017
7979	127^31322-2	65896	Lelio R Paula	10/2017
7980	2^218897-111889	65895	Enzo Doria	05/2014
7981	2^218896+1869451	65895	Enzo Doria	05/2016
7982	63^36616+2	65885	Lelio R Paula	05/2013
7983	(3*2^218822-1)/11	65872	Lelio R Paula	01/2014
7984	2^218796-113297	65865	Enzo Doria	07/2014
7985	2^218797+73727	65865	Enzo Doria	04/2016
7986	3^138040-110	65862	Lelio R Paula	06/2013
7987	11^63240-1950	65858	Enzo Doria	12/2012
7988	2^218764-111873	65855	Enzo Doria	05/2014
7989	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
7990	3^137988+26	65838	Lelio R Paula	06/2013
7991	2^218680-719	65830	Yves Minet	05/2012
7992	18^52424+17	65807	Lelio R Paula	08/2013
7993	19062^2827+2827^19062	65790	Hans Havermann	08/2019
7994	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
7995	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
7996	(5*10^65773+1)/3	65774	Erik Branger	12/2013
7997	160^29839-159	65769	Norbert Schneider	12/2018
7998	2^218457-17329	65763	Enzo Doria	05/2013
7999	151703#+223381	65759	Nicolas PALAU	10/2016
8000	2^218436+40755	65756	Lelio R Paula	10/2011

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Probable Primes Top 10000

(253466 PRPs in the top)