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 (> 50000)	Who ?	When ?
3251	3^216685-113056	103386	Enzo Doria	07/2014
3252	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
3253	11^99262-20	103371	Lelio R Paula	12/2016
3254	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
3256	2^343356-2791889	103361	Enzo Doria	03/2016
3255	(25*10^103360-241)/9	103361	Robert Price	05/2018
3257	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
3258	2^343182-171	103309	Lelio R Paula	08/2011
3259	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
3260	2^343079-1835611	103278	Enzo Doria	05/2015
3261	2^343063-1147	103273	Yves Minet	06/2013
3262	9*6^132689+7	103254	Lelio R Paula	11/2014
3263	2^342979-18085	103247	Enzo Doria	05/2013
3264	(16*10^103244-31)/3	103245	Robert Price	03/2019
3265	2^342966-16995	103244	Lelio R Paula	11/2016
3266	(16*10^103214-31)/3	103215	Robert Price	03/2019
3267	(37*10^103211+611)/9	103212	Robert Price	11/2018
3268	5^147650+16	103203	Lelio R Paula	11/2016
3269	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
3270	2^342817+2707067	103199	Enzo Doria	03/2016
3271	43^63177-42	103198	Theodore Burton	02/2007
3272	2^342805-21025	103195	Enzo Doria	06/2013
3273	2^342714+12285	103168	Lelio R Paula	11/2016
3274	18^82178-4481	103156	Enzo Doria	03/2013
3275	2^342665-17349	103153	Enzo Doria	05/2013
3276	2^342612+175	103137	Lelio R Paula	08/2011
3277	5*2^342585-3	103130	Lelio R Paula	09/2014
3278	(16*10^103127+77)/3	103128	Robert Price	03/2019
3279	2^342503-19209	103104	Enzo Doria	05/2013
3280	2^342476+51	103096	Lelio R Paula	08/2011
3281	2^342460-18885	103091	Enzo Doria	05/2013
3282	7^121968+82	103075	Lelio R Paula	10/2016
3283	2^342392-108863	103071	Enzo Doria	03/2014
3284	3^216014+28	103065	Lelio R Paula	11/2016
3285	2^342353-108879	103059	Enzo Doria	03/2014
3286	10^103055+276081	103056	Patrick De Geest	12/2016
3287	10^103055-53	103055	Lelio R Paula	11/2016
3288	7^121933+4	103046	Lelio R Paula	11/2014
3289	19^80560-68	103017	Lelio R Paula	10/2016
3290	2^342209+76607	103016	Enzo Doria	05/2016
3292	328^40945+40945^328	103013	Norbert Schneider	12/2014
3291	12^95454-91	103013	Lelio R Paula	10/2016
3293	25833^9716+9716^25833	103009	Hans Havermann	01/2019
3294	65^56809-64^56809	102990	Robert Price	08/2013
3295	5^147338-6	102985	Lelio R Paula	11/2014
3296	2^342084-112739	102978	Enzo Doria	06/2014
3297	9*6^132330+7	102974	Lelio R Paula	11/2014
3298	2^342034-16737	102963	Enzo Doria	05/2013
3299	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
3300	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
3301	2^341991-17421	102950	Enzo Doria	05/2013
3302	2^341969-112225	102943	Enzo Doria	06/2014
3303	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
3305	2^341859+1869413	102910	Enzo Doria	05/2016
3304	10^102909+61	102910	Lelio R Paula	11/2016
3306	10^102909-67049	102909	Patrick De Geest	12/2016
3307	23814^20935+20935^23814	102898	Hans Havermann	02/2019
3308	28345^4264+4264^28345	102888	Hans Havermann	02/2019
3309	25665^10204+10204^25665	102886	Hans Havermann	02/2019
3310	26288^8181+8181^26288	102860	Hans Havermann	02/2019
3311	2^341659+1836773	102850	Enzo Doria	03/2016
3312	2^341608-110639	102835	Enzo Doria	05/2014
3313	10^102824+49	102825	Lelio R Paula	11/2016
3314	10^102824-168011	102824	Patrick De Geest	12/2016
3315	11^98708-8	102794	Lelio R Paula	10/2016
3316	2^341466+4429	102792	Lelio R Paula	09/2011
3317	2^341460-107	102790	Lelio R Paula	08/2011
3318	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
3319	2^341355+21	102759	Lelio R Paula	08/2011
3320	2^341246+40755	102726	Lelio R Paula	11/2016
3321	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
3322	7^121547+78	102720	Lelio R Paula	10/2016
3323	2^341223-461197	102719	Enzo Doria	06/2015
3324	27838^4893+4893^27838	102711	Hans Havermann	03/2019
3326	2^341190-20577	102709	Enzo Doria	06/2013
3325	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
3327	6^131976-65	102698	Lelio R Paula	10/2016
3328	2^341134+2533	102692	Henri Lifchitz	09/2005
3329	13^92184-54	102688	Lelio R Paula	10/2016
3330	2^341116-20873	102687	Enzo Doria	06/2013
3331	2^341094-19953	102680	Enzo Doria	06/2013
3332	23761^20950+20950^23761	102676	Hans Havermann	03/2019
3333	2^341053+129	102668	Lelio R Paula	08/2011
3334	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
3335	7^121471+94	102655	Lelio R Paula	10/2016
3337	2^341004-173	102653	Lelio R Paula	08/2011
3336	20^78901+3	102653	Lelio R Paula	10/2016
3338	5^146853-52	102646	Lelio R Paula	10/2016
3339	2^340969-216931	102642	Enzo Doria	05/2014
3340	122^49196+121	102641	Norbert Schneider	10/2018
3341	2^340952+1870021	102637	Enzo Doria	05/2016
3342	5*2^340940-3	102634	Lelio R Paula	08/2014
3343	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
3344	25876^9239+9239^25876	102615	Hans Havermann	02/2019
3345	(4*10^102612+83)/3	102613	Robert Price	02/2018
3347	75^54717+74	102598	Norbert Schneider	01/2015
3346	(17*10^102597+13)/3	102598	Robert Price	01/2019
3348	2^340806-20393	102593	Enzo Doria	06/2013
3349	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
3350	6^131821+77	102577	Lelio R Paula	10/2016
3351	2^340688-29	102558	Henri Lifchitz	05/2005
3352	2^340685-109101	102557	Enzo Doria	04/2014
3353	65^56567-64	102552	Norbert Schneider	11/2014
3354	26230^8121+8121^26230	102550	Hans Havermann	03/2019
3355	2^340547-108897	102515	Enzo Doria	03/2014
3356	25592^10119+10119^25592	102500	Hans Havermann	02/2019
3357	7^121268+82	102484	Lelio R Paula	10/2016
3358	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
3359	2^340434-5955	102481	Lelio R Paula	11/2016
3360	(2^340381+47)/7	102465	Lelio R Paula	12/2013
3361	111^50095+110	102461	Norbert Schneider	04/2017
3362	2^340291-20301	102438	Enzo Doria	06/2013
3363	12^94915+89	102431	Lelio R Paula	10/2016
3364	24466^15349+15349^24466	102417	Hans Havermann	03/2019
3365	2^340208-20373	102413	Enzo Doria	06/2013
3366	6^131598-17273	102404	Enzo Doria	02/2013
3367	2^340115-21181	102385	Enzo Doria	06/2013
3368	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
3369	89^52511-88^52511	102365	Robert Price	06/2015
3370	3^214539-112756	102362	Enzo Doria	07/2014
3371	2^340000-19877	102351	Enzo Doria	06/2013
3372	2^339990-114845	102348	Enzo Doria	05/2015
3373	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
3374	20^78661-99	102341	Lelio R Paula	09/2016
3375	2^339951-19585	102336	Enzo Doria	05/2013
3376	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
3377	2^339889+29327	102317	Yves Minet	06/2010
3378	26348^7641+7641^26348	102314	Hans Havermann	03/2019
3379	2^339834-109493	102301	Enzo Doria	04/2014
3380	(16*10^102299-19)/3	102300	Robert Price	02/2019
3381	(11^98221-5^98221)/6	102286	Robert Price	01/2013
3382	3^214365+1820	102279	Lelio R Paula	10/2016
3383	31978^1579+1579^31978	102278	Hans Havermann	03/2019
3384	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
3385	2^339694-16995	102259	Lelio R Paula	09/2016
3386	122^49008+121	102249	Norbert Schneider	10/2018
3387	7^120985-38	102245	Lelio R Paula	10/2016
3388	10^102244+122961	102245	Patrick De Geest	12/2016
3389	10^102244-27	102244	Lelio R Paula	09/2016
3390	7^120982-62	102242	Lelio R Paula	10/2016
3391	4*6^131382-5	102236	Lelio R Paula	11/2014
3392	2^339586-1091	102226	Yves Minet	11/2012
3393	11^98161-3072000	102225	Enzo Doria	12/2012
3394	9*7^120961-4	102225	Lelio R Paula	11/2014
3395	5*3^214250+2	102224	Serge Batalov	10/2010
3396	12^94713-59	102213	Lelio R Paula	10/2016
3397	12^94705+89	102204	Lelio R Paula	10/2016
3398	2^339407-177	102172	Lelio R Paula	08/2011
3399	4*10^102163-57	102164	Robert Price	10/2018
3400	2^339355+65	102157	Lelio R Paula	07/2011
3401	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
3402	2^339168+21	102100	Lelio R Paula	07/2011
3403	2^339167-108807	102100	Enzo Doria	03/2014
3404	2^339156+163	102097	Lelio R Paula	08/2011
3405	2^339081-4543	102074	Yves Minet	03/2019
3406	24327^15668+15668^24327	102053	Hans Havermann	02/2019
3407	25080^11711+11711^25080	102041	Hans Havermann	02/2019
3408	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
3409	2^338891-18885	102017	Enzo Doria	05/2013
3410	2^338829-113239	101998	Enzo Doria	07/2014
3411	2^338828-113297	101998	Enzo Doria	07/2014
3412	2^338796+93	101988	Donovan Johnson	06/2008
3413	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
3414	25295^10744+10744^25295	101969	Hans Havermann	01/2019
3415	25712^9243+9243^25712	101969	Hans Havermann	01/2019
3416	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
3417	2^338682-19865	101954	Enzo Doria	06/2013
3418	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
3419	28594^3673+3673^28594	101939	Hans Havermann	02/2019
3420	2^338568+37	101920	Lelio R Paula	07/2011
3421	2^338559-1858777	101917	Enzo Doria	04/2016
3422	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
3423	24502^14419+14419^24502	101903	Hans Havermann	01/2019
3424	2^338497-17041	101898	Enzo Doria	05/2013
3425	2^338475+54615	101892	Lelio R Paula	10/2016
3426	2^338426-19797	101877	Enzo Doria	06/2013
3427	2^338368-20369	101859	Enzo Doria	06/2013
3428	2^338366+74179	101859	Enzo Doria	04/2016
3429	27088^5755+5755^27088	101853	Hans Havermann	01/2019
3430	2^338280-19745	101833	Enzo Doria	06/2013
3431	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
3432	6^130841+103	101815	Lelio R Paula	10/2016
3433	2^338122-20117	101785	Enzo Doria	06/2013
3434	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
3435	35^65917-7092	101781	Enzo Doria	03/2013
3436	2^338010-19833	101752	Enzo Doria	06/2013
3437	3^213215-76	101730	Lelio R Paula	09/2016
3438	23907^17998+17998^23907	101730	Hans Havermann	01/2019
3439	2^337930+63	101728	Lelio R Paula	07/2011
3440	2^337920+1869661	101725	Enzo Doria	05/2016
3441	24116^16509+16509^24116	101715	Hans Havermann	01/2019
3442	2^337859-19645	101706	Enzo Doria	05/2013
3443	2^337754+1869169	101675	Enzo Doria	05/2016
3444	3*10^101657-37	101658	Robert Price	07/2018
3445	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
3446	11^97605-24	101646	Lelio R Paula	10/2016
3447	8^112539-112539	101633	Robert Price	01/2014
3448	25694^9003+9003^25694	101605	Hans Havermann	12/2018
3449	2^337515-19869	101603	Enzo Doria	06/2013
3450	2^337473+719	101590	Lelio R Paula	08/2011
3451	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
3452	2^337452-108815	101584	Enzo Doria	03/2014
3453	2^337453+1185	101584	Lelio R Paula	09/2016
3454	2^337410-113561	101571	Enzo Doria	08/2014
3455	2^337387+855	101564	Lelio R Paula	09/2016
3456	2^337367-17295	101558	Lelio R Paula	09/2016
3457	2^337342-109035	101551	Enzo Doria	04/2014
3458	23703^19238+19238^23703	101548	Hans Havermann	12/2018
3459	2^337267-19	101528	Lelio R Paula	07/2011
3460	2^337183-19989	101503	Enzo Doria	06/2013
3461	2^337149+72425	101492	Enzo Doria	04/2016
3462	24041^16642+16642^24041	101483	Hans Havermann	12/2018
3463	33982^969+969^33982	101482	Hans Havermann	12/2018
3464	2^337101-20241	101478	Enzo Doria	06/2013
3465	2^337035-20001	101458	Enzo Doria	06/2013
3466	2^337017-16995	101453	Lelio R Paula	09/2016
3467	2^336979-115315	101441	Enzo Doria	06/2015
3468	2^336970-20885	101439	Enzo Doria	06/2013
3469	2^336958+79	101435	Lelio R Paula	10/2009
3470	2^336942+169	101430	Lelio R Paula	10/2009
3471	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
3472	4*10^101415-89	101416	Robert Price	11/2018
3473	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
3474	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
3475	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
3476	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
3477	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
3478	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
3479	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
3480	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
3481	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
3482	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
3483	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
3484	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
3485	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
3486	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
3487	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
3488	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
3489	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
3490	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
3491	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3492	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
3493	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3494	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
3495	24097^16150+16150^24097	101405	Hans Havermann	12/2018
3496	2^336842+94065	101400	Lelio R Paula	09/2016
3497	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
3498	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
3499	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
3500	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016

Find by discoverer :

PRP Records

Probable Primes Top 10000

(252675 PRPs in the top)