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	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
3252	3^203051+34	96880	Lelio R Paula	05/2016
3253	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
3254	2^321716-2786939	96847	Enzo Doria	03/2016
3255	2^321701-113053	96842	Enzo Doria	07/2014
3256	2^321700-28635	96842	Lelio R Paula	06/2016
3257	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
3258	6^124433-124433	96828	Robert Price	01/2014
3259	2^321631+69	96821	Lelio R Paula	12/2012
3260	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
3261	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
3262	(59*10^96798+31)/9	96799	Robert Price	09/2015
3263	223319#+231223	96790	Makoto Morimoto	02/2016
3264	2^321519-28635	96787	Lelio R Paula	06/2016
3265	2^321487-1867237	96778	Enzo Doria	03/2016
3266	2^321461-63	96770	Lelio R Paula	12/2012
3267	2^321439+123	96763	Lelio R Paula	12/2012
3268	2^321434+709	96762	Lelio R Paula	02/2013
3269	14^84413+89	96749	Lelio R Paula	07/2016
3270	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
3271	13^86847+96	96743	Lelio R Paula	06/2016
3272	9*2^321336-7	96733	Lelio R Paula	08/2014
3273	(209*10^96722-17)/3	96724	Robert Price	05/2017
3274	2^321187-1159	96687	Yves Minet	11/2012
3275	2^321182-1850081	96686	Enzo Doria	08/2015
3276	2^321116-112829	96666	Enzo Doria	06/2014
3277	2^321108-109499	96664	Enzo Doria	04/2014
3278	2^321098+2793859	96661	Enzo Doria	03/2016
3279	2^321057+4097	96648	Lelio R Paula	06/2016
3280	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
3281	p(19849)#/2-64	96581	Robert Price	04/2017
3282	2^320817+189	96576	Lelio R Paula	12/2012
3283	2^320788-110327	96567	Enzo Doria	05/2014
3284	2^320764+793	96560	Lelio R Paula	02/2013
3285	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
3286	2^320616-78795	96516	Lelio R Paula	03/2016
3287	2^320612-461939	96514	Enzo Doria	07/2015
3288	5*2^320431+7	96461	Lelio R Paula	08/2014
3289	19^75431-90	96458	Lelio R Paula	06/2016
3290	(2^320370+3)/67	96440	Lelio R Paula	10/2013
3291	2^320309+1871477	96423	Enzo Doria	05/2016
3292	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
3293	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
3294	2^320232-173	96400	Lelio R Paula	12/2012
3295	10^96377+199911	96378	Patrick De Geest	12/2016
3296	10^96377-20001	96377	Robert Price	11/2016
3297	2^320124-2790449	96367	Enzo Doria	03/2016
3298	2^320043-108775	96343	Enzo Doria	04/2014
3299	10^96338+424939	96339	Patrick De Geest	03/2016
3300	10^96338-9281	96338	Robert Price	09/2015
3301	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
3302	2^319838+4257	96281	Lelio R Paula	03/2016
3303	2^319830-16995	96279	Lelio R Paula	03/2016
3304	6^123713+143	96268	Lelio R Paula	05/2016
3305	(28*10^96265-97)/3	96266	Robert Price	07/2016
3306	103^47825-102	96264	Norbert Schneider	10/2016
3307	2^319713-81	96244	Lelio R Paula	11/2012
3308	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
3309	12^89153-43	96213	Lelio R Paula	06/2016
3310	(2*10^96195-59)/3	96195	Robert Price	05/2017
3311	2^319545+147	96193	Lelio R Paula	11/2012
3312	(50^56597+1)/51	96155	Robert Price	03/2014
3313	2^319353-110343	96135	Enzo Doria	05/2014
3314	11^92309-42	96130	Lelio R Paula	05/2016
3315	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
3316	(7*10^96112+143)/3	96113	Robert Price	04/2016
3317	2^319237+65835	96100	Lelio R Paula	03/2016
3318	2^319194-1841	96087	Yves Minet	03/2013
3319	20^73847-31	96078	Lelio R Paula	05/2016
3320	2^319107-109555	96061	Enzo Doria	04/2014
3321	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
3322	2^319098-112157	96059	Enzo Doria	06/2014
3323	15^81673+94	96055	Lelio R Paula	07/2016
3324	2^319074+1871749	96051	Enzo Doria	05/2016
3325	2^319007-112111	96031	Enzo Doria	06/2014
3326	2^318946-1421	96013	Yves Minet	01/2013
3327	2^318834-110411	95979	Enzo Doria	05/2014
3328	2^318831-1965	95978	Lelio R Paula	03/2016
3329	(5*10^95976+7)/3	95977	Erik Branger	03/2014
3330	5*3^201089-8	95945	Lelio R Paula	08/2014
3331	2^318711-139	95942	Lelio R Paula	11/2012
3332	2^318635-1167	95919	Lelio R Paula	03/2016
3333	15^81555+16	95917	Lelio R Paula	07/2016
3334	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
3335	2^318496-97305	95877	Lelio R Paula	03/2016
3336	2^318466+15015	95868	Lelio R Paula	03/2016
3337	6^123187-173129	95859	Mike Oakes	04/2011
3338	2^318423-487	95855	Yves Minet	03/2012
3339	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
3340	45369!2+1024	95787	Robert Price	02/2015
3341	3^200758-86	95786	Lelio R Paula	05/2016
3342	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
3343	(11*10^95641-113)/3	95642	Robert Price	01/2017
3344	(13*10^95588+11)/3	95589	Robert Price	05/2015
3345	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
3346	3^200325+70	95580	Lelio R Paula	05/2016
3347	(25*10^95574-7)/9	95575	Robert Price	12/2014
3348	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
3349	2^317464+31	95567	Lelio R Paula	11/2012
3350	7^113073+82	95558	Lelio R Paula	04/2016
3351	2^317251+465	95503	Lelio R Paula	03/2016
3352	19^74684+58	95503	Lelio R Paula	06/2016
3353	(2^317250-7)/339	95500	Lelio R Paula	07/2013
3354	6^122718-79	95494	Lelio R Paula	05/2016
3355	2^317141-110491	95469	Enzo Doria	05/2014
3356	2^317094+76309	95455	Enzo Doria	05/2016
3357	2^317085+95	95453	Lelio R Paula	11/2012
3358	2^317057-109551	95444	Enzo Doria	04/2014
3359	3^200026+28	95437	Lelio R Paula	05/2016
3360	2^317024+93	95434	Donovan Johnson	06/2008
3361	2^316999+1605	95427	Lelio R Paula	03/2016
3362	2^316995-110427	95426	Enzo Doria	05/2014
3363	2^316937+177	95408	Lelio R Paula	11/2012
3364	2^316908+1915	95399	Lelio R Paula	03/2016
3365	2^316894+99	95395	Lelio R Paula	11/2012
3366	6^122547+11	95361	Lelio R Paula	05/2016
3367	2^316771+82875	95358	Lelio R Paula	03/2016
3369	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
3368	1*10^95326+57	95327	Robert Price	03/2011
3370	10^95326-393687	95326	Patrick De Geest	09/2013
3371	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
3372	2^316654-109481	95323	Enzo Doria	04/2014
3373	8*10^95316+51	95317	Robert Price	05/2017
3374	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
3375	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
3376	19^74503-56	95271	Lelio R Paula	06/2016
3377	11^91475-4380	95262	Enzo Doria	01/2013
3378	(62*10^95251-611)/9	95252	Robert Price	05/2017
3379	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
3380	(79*10^95214-43)/9	95215	Erik Branger	11/2013
3381	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
3382	5*2^316213+9	95191	Lelio R Paula	08/2014
3383	2^316205-1848163	95188	Enzo Doria	07/2015
3384	2^316185-2787913	95182	Enzo Doria	04/2016
3385	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
3386	2^316140-5	95168	Henri Lifchitz	02/2006
3387	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
3388	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
3389	2^316069+76817	95147	Enzo Doria	05/2016
3390	(199*10^95134-7)/3	95136	Robert Price	02/2017
3391	2^316027-97305	95134	Lelio R Paula	03/2016
3392	2^316006-2798051	95128	Enzo Doria	04/2016
3393	2^315921-2797603	95102	Enzo Doria	04/2016
3394	2^315857+1299	95083	Lelio R Paula	03/2016
3395	14^82955-43	95078	Lelio R Paula	06/2016
3396	(2*10^95072-17)/3	95072	Robert Price	08/2014
3397	2^315727+65	95044	Lelio R Paula	11/2012
3398	2^315725+1885757	95043	Enzo Doria	03/2017
3399	1*10^94983+21	94984	Robert Price	03/2011
3400	10^94983-717	94983	Patrick De Geest	08/2013
3401	17^77187-82	94975	Lelio R Paula	07/2016
3402	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
3403	2^315423-110329	94952	Enzo Doria	05/2014
3404	11^91169-7230	94943	Enzo Doria	02/2013
3405	7*10^94938+61	94939	Robert Price	02/2017
3406	2^315351+1025	94931	Lelio R Paula	03/2016
3407	2^315350-112253	94930	Enzo Doria	06/2014
3408	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
3410	2^315268+7	94906	Lelio R Paula	10/2012
3409	11^91133+62	94906	Lelio R Paula	05/2016
3411	30^64244+41	94897	Lelio R Paula	08/2012
3412	4^157583+22147	94875	Mike Oakes	01/2011
3413	2^315098+123	94854	Lelio R Paula	11/2012
3414	3^198791-34	94848	Robert Price	11/2013
3415	3*2^315067+7	94846	Lelio R Paula	08/2014
3416	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
3417	(16*10^94822+53)/3	94823	Robert Price	12/2016
3418	8*6^121849-7	94818	Lelio R Paula	10/2014
3419	(85*10^94802+473)/9	94803	Robert Price	03/2017
3420	2^314870-108761	94786	Enzo Doria	03/2014
3421	5*2^314841-3	94778	Lelio R Paula	08/2014
3422	6^121772+113	94758	Lelio R Paula	05/2016
3423	6^121756-16253	94745	Enzo Doria	02/2013
3424	2^314718-112793	94740	Enzo Doria	06/2014
3425	2^314697-1847293	94734	Enzo Doria	07/2015
3427	2^314548-249	94689	Yves Minet	02/2012
3426	5^135469+42	94689	Lelio R Paula	04/2016
3428	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
3429	3*2^314152+5	94570	Lelio R Paula	08/2014
3430	2*6^121530-5	94570	Lelio R Paula	10/2014
3431	7*10^94563+87	94564	Robert Price	11/2016
3432	2^314114-109677	94558	Enzo Doria	04/2014
3433	2^314059+76583	94542	Enzo Doria	05/2016
3434	2^314041-4035	94536	Lelio R Paula	03/2016
3435	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
3436	11^90760-4710	94517	Enzo Doria	01/2013
3437	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
3438	94*10^94493-3	94495	Robert Price	11/2016
3439	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
3440	7^111792-32	94476	Lelio R Paula	04/2016
3441	11^90680-5850	94434	Enzo Doria	01/2013
3442	2^313675-110125	94426	Enzo Doria	04/2014
3443	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
3444	2^313609-112225	94406	Enzo Doria	06/2014
3445	2^313584+72901	94399	Enzo Doria	04/2016
3446	2^313510-112865	94376	Enzo Doria	06/2014
3447	7*10^94373+87	94374	Robert Price	11/2016
3448	(9^98897+8^98897)/17	94371	Robert Price	12/2012
3449	2^313453-114703	94359	Enzo Doria	04/2015
3450	2^313344-313344+1	94326	Robert Price	10/2014
3451	20^72481-49	94300	Lelio R Paula	05/2016
3452	44725!2+128	94289	Robert Price	03/2015
3453	4*10^94286+9	94287	Robert Price	05/2015
3454	17^76621+24	94279	Lelio R Paula	07/2016
3455	2^313156-112859	94270	Enzo Doria	06/2014
3456	6^121130-59	94258	Lelio R Paula	05/2016
3457	3^197542+28	94252	Robert Price	11/2013
3458	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
3459	2^313045-5955	94236	Lelio R Paula	03/2016
3460	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
3461	2^312909-1865203	94195	Enzo Doria	03/2016
3462	2^312848-149	94177	Lelio R Paula	11/2012
3463	4^156403-77597	94164	Mike Oakes	04/2011
3464	18^75004-85	94151	Lelio R Paula	06/2016
3465	19^73622-48	94145	Lelio R Paula	06/2016
3466	(11^90397-3^90397)/8	94138	Robert Price	04/2011
3467	(3^197287+5)/16	94129	Lelio R Paula	04/2013
3468	12^87212-37	94118	Lelio R Paula	06/2016
3469	11^90376+76	94117	Lelio R Paula	05/2016
3470	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
3471	2^312562-112685	94091	Enzo Doria	06/2014
3472	2^312404-869688105	94043	Lelio R Paula	09/2016
3473	2^312387+2793533	94038	Enzo Doria	03/2016
3475	10^94016+91	94017	Robert Price	04/2011
3474	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
3477	10^94016-188963	94016	Patrick De Geest	08/2013
3476	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
3478	6^120802+7661	94003	Mike Oakes	04/2011
3479	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
3480	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
3481	2^312201+51	93982	Lelio R Paula	11/2012
3482	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
3483	3^196892+58	93942	Lelio R Paula	05/2016
3484	2^312060+18915	93940	Lelio R Paula	03/2016
3485	2^311992-16209	93919	Enzo Doria	04/2013
3486	2^311965-39	93911	Lelio R Paula	11/2012
3487	2^311920-111689	93898	Enzo Doria	05/2014
3488	7*10^93887-47	93888	Robert Price	02/2017
3489	12^86965-13	93851	Lelio R Paula	06/2016
3490	2^311705+16095	93833	Lelio R Paula	03/2016
3491	2^311665-81	93821	Lelio R Paula	11/2012
3492	11^90073+92	93802	Lelio R Paula	05/2016
3493	6*10^93792+41	93793	Robert Price	01/2017
3494	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
3495	12^86900-77	93781	Lelio R Paula	06/2016
3496	2^311508-109769	93774	Enzo Doria	04/2014
3497	2^311486-1859621	93767	Enzo Doria	03/2016
3498	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
3499	2^311471+311469	93763	Renaud Lifchitz	01/2003
3500	2^311426+79459	93749	Enzo Doria	06/2016

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PRP Records

Probable Primes Top 10000

(174961 PRPs in the top)