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 ?
3251	2^323720-6555	97450	Lelio R Paula	07/2016
3252	2^323694-1860401	97442	Enzo Doria	03/2016
3253	20^74886+3	97429	Lelio R Paula	06/2016
3255	3*10^97399+73	97400	Robert Price	04/2016
3254	7^115252-50	97400	Lelio R Paula	07/2016
3256	224737#+393581	97389	Nicolas PALAU	12/2016
3257	(26*10^97353+31)/3	97354	Robert Price	07/2016
3258	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
3259	6^125021-85	97286	Lelio R Paula	08/2016
3260	2^323164-47355	97283	Lelio R Paula	07/2016
3261	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
3262	2^323054-6555	97249	Lelio R Paula	07/2016
3263	9*10^97247-29	97248	Robert Price	05/2017
3264	(31*10^97242+41)/9	97243	Robert Price	04/2015
3265	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
3266	12^90098-41	97233	Lelio R Paula	07/2016
3267	2^322928-216929	97212	Enzo Doria	05/2014
3268	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
3269	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
3270	2^322725+75761	97150	Enzo Doria	04/2016
3271	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
3272	(41*10^97085+373)/9	97086	Robert Price	04/2017
3273	2^322413+77	97056	Lelio R Paula	12/2012
3274	2^322406+177	97054	Lelio R Paula	12/2012
3275	(14*10^97044+31)/9	97045	Robert Price	02/2015
3276	2^322302+255255	97023	Lelio R Paula	07/2016
3277	2^322196-113093	96991	Enzo Doria	07/2014
3278	2^322000-1861469	96932	Enzo Doria	03/2016
3279	2^321971-112747	96923	Enzo Doria	06/2014
3280	11^93062-92	96915	Lelio R Paula	06/2016
3281	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
3282	3^203051+34	96880	Lelio R Paula	05/2016
3283	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
3284	2^321716-2786939	96847	Enzo Doria	03/2016
3285	2^321701-113053	96842	Enzo Doria	07/2014
3286	2^321700-28635	96842	Lelio R Paula	06/2016
3287	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
3288	6^124433-124433	96828	Robert Price	01/2014
3289	2^321631+69	96821	Lelio R Paula	12/2012
3290	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
3291	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
3292	(59*10^96798+31)/9	96799	Robert Price	09/2015
3293	223319#+231223	96790	Makoto Morimoto	02/2016
3294	2^321519-28635	96787	Lelio R Paula	06/2016
3295	2^321487-1867237	96778	Enzo Doria	03/2016
3296	2^321461-63	96770	Lelio R Paula	12/2012
3297	2^321439+123	96763	Lelio R Paula	12/2012
3298	2^321434+709	96762	Lelio R Paula	02/2013
3299	14^84413+89	96749	Lelio R Paula	07/2016
3300	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
3301	13^86847+96	96743	Lelio R Paula	06/2016
3302	9*2^321336-7	96733	Lelio R Paula	08/2014
3303	(209*10^96722-17)/3	96724	Robert Price	05/2017
3304	2^321187-1159	96687	Yves Minet	11/2012
3305	2^321182-1850081	96686	Enzo Doria	08/2015
3306	2^321116-112829	96666	Enzo Doria	06/2014
3307	2^321108-109499	96664	Enzo Doria	04/2014
3308	2^321098+2793859	96661	Enzo Doria	03/2016
3309	2^321057+4097	96648	Lelio R Paula	06/2016
3310	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
3311	p(19849)#/2-64	96581	Robert Price	04/2017
3312	2^320817+189	96576	Lelio R Paula	12/2012
3313	2^320788-110327	96567	Enzo Doria	05/2014
3314	2^320764+793	96560	Lelio R Paula	02/2013
3315	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
3316	2^320616-78795	96516	Lelio R Paula	03/2016
3317	2^320612-461939	96514	Enzo Doria	07/2015
3318	5*2^320431+7	96461	Lelio R Paula	08/2014
3319	19^75431-90	96458	Lelio R Paula	06/2016
3320	(2^320370+3)/67	96440	Lelio R Paula	10/2013
3321	2^320309+1871477	96423	Enzo Doria	05/2016
3322	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
3323	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
3324	2^320232-173	96400	Lelio R Paula	12/2012
3325	10^96377+199911	96378	Patrick De Geest	12/2016
3326	10^96377-20001	96377	Robert Price	11/2016
3327	2^320124-2790449	96367	Enzo Doria	03/2016
3328	2^320043-108775	96343	Enzo Doria	04/2014
3329	10^96338+424939	96339	Patrick De Geest	03/2016
3330	10^96338-9281	96338	Robert Price	09/2015
3331	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
3332	2^319838+4257	96281	Lelio R Paula	03/2016
3333	2^319830-16995	96279	Lelio R Paula	03/2016
3334	6^123713+143	96268	Lelio R Paula	05/2016
3335	(28*10^96265-97)/3	96266	Robert Price	07/2016
3336	103^47825-102	96264	Norbert Schneider	10/2016
3337	2^319713-81	96244	Lelio R Paula	11/2012
3338	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
3339	12^89153-43	96213	Lelio R Paula	06/2016
3340	(2*10^96195-59)/3	96195	Robert Price	05/2017
3341	2^319545+147	96193	Lelio R Paula	11/2012
3342	(50^56597+1)/51	96155	Robert Price	03/2014
3343	2^319353-110343	96135	Enzo Doria	05/2014
3344	11^92309-42	96130	Lelio R Paula	05/2016
3345	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
3346	(7*10^96112+143)/3	96113	Robert Price	04/2016
3347	2^319237+65835	96100	Lelio R Paula	03/2016
3348	2^319194-1841	96087	Yves Minet	03/2013
3349	20^73847-31	96078	Lelio R Paula	05/2016
3350	2^319107-109555	96061	Enzo Doria	04/2014
3351	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
3352	2^319098-112157	96059	Enzo Doria	06/2014
3353	15^81673+94	96055	Lelio R Paula	07/2016
3354	2^319074+1871749	96051	Enzo Doria	05/2016
3355	2^319007-112111	96031	Enzo Doria	06/2014
3356	2^318946-1421	96013	Yves Minet	01/2013
3357	2^318834-110411	95979	Enzo Doria	05/2014
3358	2^318831-1965	95978	Lelio R Paula	03/2016
3359	(5*10^95976+7)/3	95977	Erik Branger	03/2014
3360	5*3^201089-8	95945	Lelio R Paula	08/2014
3361	2^318711-139	95942	Lelio R Paula	11/2012
3362	2^318635-1167	95919	Lelio R Paula	03/2016
3363	15^81555+16	95917	Lelio R Paula	07/2016
3364	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
3365	2^318496-97305	95877	Lelio R Paula	03/2016
3366	2^318466+15015	95868	Lelio R Paula	03/2016
3367	6^123187-173129	95859	Mike Oakes	04/2011
3368	2^318423-487	95855	Yves Minet	03/2012
3369	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
3370	45369!2+1024	95787	Robert Price	02/2015
3371	3^200758-86	95786	Lelio R Paula	05/2016
3372	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
3373	(11*10^95641-113)/3	95642	Robert Price	01/2017
3374	(13*10^95588+11)/3	95589	Robert Price	05/2015
3375	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
3376	3^200325+70	95580	Lelio R Paula	05/2016
3377	(25*10^95574-7)/9	95575	Robert Price	12/2014
3378	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
3379	2^317464+31	95567	Lelio R Paula	11/2012
3380	7^113073+82	95558	Lelio R Paula	04/2016
3381	2^317251+465	95503	Lelio R Paula	03/2016
3382	19^74684+58	95503	Lelio R Paula	06/2016
3383	(2^317250-7)/339	95500	Lelio R Paula	07/2013
3384	6^122718-79	95494	Lelio R Paula	05/2016
3385	2^317141-110491	95469	Enzo Doria	05/2014
3386	2^317094+76309	95455	Enzo Doria	05/2016
3387	2^317085+95	95453	Lelio R Paula	11/2012
3388	2^317057-109551	95444	Enzo Doria	04/2014
3389	3^200026+28	95437	Lelio R Paula	05/2016
3390	2^317024+93	95434	Donovan Johnson	06/2008
3391	2^316999+1605	95427	Lelio R Paula	03/2016
3392	2^316995-110427	95426	Enzo Doria	05/2014
3393	2^316937+177	95408	Lelio R Paula	11/2012
3394	2^316908+1915	95399	Lelio R Paula	03/2016
3395	2^316894+99	95395	Lelio R Paula	11/2012
3396	6^122547+11	95361	Lelio R Paula	05/2016
3397	2^316771+82875	95358	Lelio R Paula	03/2016
3399	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
3398	1*10^95326+57	95327	Robert Price	03/2011
3400	10^95326-393687	95326	Patrick De Geest	09/2013
3401	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
3402	2^316654-109481	95323	Enzo Doria	04/2014
3403	8*10^95316+51	95317	Robert Price	05/2017
3404	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
3405	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
3406	19^74503-56	95271	Lelio R Paula	06/2016
3407	11^91475-4380	95262	Enzo Doria	01/2013
3408	(62*10^95251-611)/9	95252	Robert Price	05/2017
3409	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
3410	(79*10^95214-43)/9	95215	Erik Branger	11/2013
3411	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
3412	5*2^316213+9	95191	Lelio R Paula	08/2014
3413	2^316205-1848163	95188	Enzo Doria	07/2015
3414	2^316185-2787913	95182	Enzo Doria	04/2016
3415	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
3416	2^316140-5	95168	Henri Lifchitz	02/2006
3417	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
3418	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
3419	2^316069+76817	95147	Enzo Doria	05/2016
3420	(199*10^95134-7)/3	95136	Robert Price	02/2017
3421	2^316027-97305	95134	Lelio R Paula	03/2016
3422	2^316006-2798051	95128	Enzo Doria	04/2016
3423	2^315921-2797603	95102	Enzo Doria	04/2016
3424	2^315857+1299	95083	Lelio R Paula	03/2016
3425	14^82955-43	95078	Lelio R Paula	06/2016
3426	(2*10^95072-17)/3	95072	Robert Price	08/2014
3427	2^315727+65	95044	Lelio R Paula	11/2012
3428	2^315725+1885757	95043	Enzo Doria	03/2017
3429	1*10^94983+21	94984	Robert Price	03/2011
3430	10^94983-717	94983	Patrick De Geest	08/2013
3431	17^77187-82	94975	Lelio R Paula	07/2016
3432	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
3433	2^315423-110329	94952	Enzo Doria	05/2014
3434	11^91169-7230	94943	Enzo Doria	02/2013
3435	7*10^94938+61	94939	Robert Price	02/2017
3436	2^315351+1025	94931	Lelio R Paula	03/2016
3437	2^315350-112253	94930	Enzo Doria	06/2014
3440	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
3439	2^315268+7	94906	Lelio R Paula	10/2012
3438	11^91133+62	94906	Lelio R Paula	05/2016
3441	30^64244+41	94897	Lelio R Paula	08/2012
3442	(151*10^94885-7)/9	94887	Robert Price	07/2017
3443	4^157583+22147	94875	Mike Oakes	01/2011
3444	2^315098+123	94854	Lelio R Paula	11/2012
3445	3^198791-34	94848	Robert Price	11/2013
3446	3*2^315067+7	94846	Lelio R Paula	08/2014
3447	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
3448	(16*10^94822+53)/3	94823	Robert Price	12/2016
3449	8*6^121849-7	94818	Lelio R Paula	10/2014
3450	(85*10^94802+473)/9	94803	Robert Price	03/2017
3451	2^314870-108761	94786	Enzo Doria	03/2014
3452	5*2^314841-3	94778	Lelio R Paula	08/2014
3453	6^121772+113	94758	Lelio R Paula	05/2016
3454	6^121756-16253	94745	Enzo Doria	02/2013
3455	2^314718-112793	94740	Enzo Doria	06/2014
3456	2^314697-1847293	94734	Enzo Doria	07/2015
3458	2^314548-249	94689	Yves Minet	02/2012
3457	5^135469+42	94689	Lelio R Paula	04/2016
3459	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
3460	3*2^314152+5	94570	Lelio R Paula	08/2014
3461	2*6^121530-5	94570	Lelio R Paula	10/2014
3462	7*10^94563+87	94564	Robert Price	11/2016
3463	2^314114-109677	94558	Enzo Doria	04/2014
3464	2^314059+76583	94542	Enzo Doria	05/2016
3465	2^314041-4035	94536	Lelio R Paula	03/2016
3466	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
3467	11^90760-4710	94517	Enzo Doria	01/2013
3468	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
3469	94*10^94493-3	94495	Robert Price	11/2016
3470	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
3471	7^111792-32	94476	Lelio R Paula	04/2016
3472	11^90680-5850	94434	Enzo Doria	01/2013
3473	2^313675-110125	94426	Enzo Doria	04/2014
3474	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
3475	2^313609-112225	94406	Enzo Doria	06/2014
3476	2^313584+72901	94399	Enzo Doria	04/2016
3477	2^313510-112865	94376	Enzo Doria	06/2014
3478	7*10^94373+87	94374	Robert Price	11/2016
3479	(9^98897+8^98897)/17	94371	Robert Price	12/2012
3480	2^313453-114703	94359	Enzo Doria	04/2015
3481	(379*10^94337-1)/9	94339	Robert Price	08/2017
3482	2^313344-313344+1	94326	Robert Price	10/2014
3483	20^72481-49	94300	Lelio R Paula	05/2016
3484	44725!2+128	94289	Robert Price	03/2015
3485	4*10^94286+9	94287	Robert Price	05/2015
3486	17^76621+24	94279	Lelio R Paula	07/2016
3487	2^313156-112859	94270	Enzo Doria	06/2014
3488	6^121130-59	94258	Lelio R Paula	05/2016
3489	3^197542+28	94252	Robert Price	11/2013
3490	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
3491	2^313045-5955	94236	Lelio R Paula	03/2016
3492	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
3493	2^312909-1865203	94195	Enzo Doria	03/2016
3494	2^312848-149	94177	Lelio R Paula	11/2012
3495	4^156403-77597	94164	Mike Oakes	04/2011
3496	18^75004-85	94151	Lelio R Paula	06/2016
3497	19^73622-48	94145	Lelio R Paula	06/2016
3498	(11^90397-3^90397)/8	94138	Robert Price	04/2011
3499	(3^197287+5)/16	94129	Lelio R Paula	04/2013
3500	12^87212-37	94118	Lelio R Paula	06/2016

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PRP Records

Probable Primes Top 10000

(180278 PRPs in the top)