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	10^102244+122961	102245	Patrick De Geest	12/2016
3252	10^102244-27	102244	Lelio R Paula	09/2016
3253	7^120982-62	102242	Lelio R Paula	10/2016
3254	4*6^131382-5	102236	Lelio R Paula	11/2014
3255	2^339586-1091	102226	Yves Minet	11/2012
3256	11^98161-3072000	102225	Enzo Doria	12/2012
3257	9*7^120961-4	102225	Lelio R Paula	11/2014
3258	5*3^214250+2	102224	Serge Batalov	10/2010
3259	12^94713-59	102213	Lelio R Paula	10/2016
3260	12^94705+89	102204	Lelio R Paula	10/2016
3261	2^339407-177	102172	Lelio R Paula	08/2011
3262	4*10^102163-57	102164	Robert Price	10/2018
3263	2^339355+65	102157	Lelio R Paula	07/2011
3264	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
3265	2^339168+21	102100	Lelio R Paula	07/2011
3266	2^339167-108807	102100	Enzo Doria	03/2014
3267	2^339156+163	102097	Lelio R Paula	08/2011
3268	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
3269	2^338891-18885	102017	Enzo Doria	05/2013
3270	2^338829-113239	101998	Enzo Doria	07/2014
3271	2^338828-113297	101998	Enzo Doria	07/2014
3272	2^338796+93	101988	Donovan Johnson	06/2008
3273	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
3274	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
3275	2^338682-19865	101954	Enzo Doria	06/2013
3276	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
3277	2^338568+37	101920	Lelio R Paula	07/2011
3278	2^338559-1858777	101917	Enzo Doria	04/2016
3279	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
3280	2^338497-17041	101898	Enzo Doria	05/2013
3281	2^338475+54615	101892	Lelio R Paula	10/2016
3282	2^338426-19797	101877	Enzo Doria	06/2013
3283	2^338368-20369	101859	Enzo Doria	06/2013
3284	2^338366+74179	101859	Enzo Doria	04/2016
3285	2^338280-19745	101833	Enzo Doria	06/2013
3286	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
3287	6^130841+103	101815	Lelio R Paula	10/2016
3288	2^338122-20117	101785	Enzo Doria	06/2013
3289	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
3290	35^65917-7092	101781	Enzo Doria	03/2013
3291	2^338010-19833	101752	Enzo Doria	06/2013
3292	3^213215-76	101730	Lelio R Paula	09/2016
3293	2^337930+63	101728	Lelio R Paula	07/2011
3294	2^337920+1869661	101725	Enzo Doria	05/2016
3295	2^337859-19645	101706	Enzo Doria	05/2013
3296	2^337754+1869169	101675	Enzo Doria	05/2016
3297	3*10^101657-37	101658	Robert Price	07/2018
3298	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
3299	11^97605-24	101646	Lelio R Paula	10/2016
3300	8^112539-112539	101633	Robert Price	01/2014
3301	25694^9003+9003^25694	101605	Hans Havermann	12/2018
3302	2^337515-19869	101603	Enzo Doria	06/2013
3303	2^337473+719	101590	Lelio R Paula	08/2011
3304	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
3306	2^337452-108815	101584	Enzo Doria	03/2014
3305	2^337453+1185	101584	Lelio R Paula	09/2016
3307	2^337410-113561	101571	Enzo Doria	08/2014
3308	2^337387+855	101564	Lelio R Paula	09/2016
3309	2^337367-17295	101558	Lelio R Paula	09/2016
3310	2^337342-109035	101551	Enzo Doria	04/2014
3311	23703^19238+19238^23703	101548	Hans Havermann	12/2018
3312	2^337267-19	101528	Lelio R Paula	07/2011
3313	2^337183-19989	101503	Enzo Doria	06/2013
3314	2^337149+72425	101492	Enzo Doria	04/2016
3315	2^337101-20241	101478	Enzo Doria	06/2013
3316	2^337035-20001	101458	Enzo Doria	06/2013
3317	2^337017-16995	101453	Lelio R Paula	09/2016
3318	2^336979-115315	101441	Enzo Doria	06/2015
3319	2^336970-20885	101439	Enzo Doria	06/2013
3320	2^336958+79	101435	Lelio R Paula	10/2009
3321	2^336942+169	101430	Lelio R Paula	10/2009
3322	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
3323	4*10^101415-89	101416	Robert Price	11/2018
3324	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
3325	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
3326	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
3327	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
3328	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
3329	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
3330	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
3331	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
3332	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
3333	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
3334	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
3335	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
3336	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
3337	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
3338	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
3339	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
3340	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
3341	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
3342	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3343	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
3344	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3345	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
3346	24097^16150+16150^24097	101405	Hans Havermann	12/2018
3347	2^336842+94065	101400	Lelio R Paula	09/2016
3348	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
3349	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
3350	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
3351	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
3352	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
3353	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
3354	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
3355	10^101369+203811	101370	Patrick De Geest	11/2016
3356	10^101369-99	101369	Lelio R Paula	09/2016
3357	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
3358	2^336701-113563	101358	Enzo Doria	08/2014
3359	2^336644-109023	101340	Enzo Doria	04/2014
3360	2^336601-21081	101327	Enzo Doria	06/2013
3361	20^77869+63	101310	Lelio R Paula	09/2016
3362	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
3363	6^130179-137	101299	Lelio R Paula	10/2016
3364	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
3365	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
3366	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
3367	2^336369-19753	101258	Enzo Doria	05/2013
3368	23842^17653+17653^23842	101253	Hans Havermann	11/2018
3369	2^336350-344291	101252	Enzo Doria	07/2015
3370	2^336243-108777	101220	Enzo Doria	03/2014
3371	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
3372	23535^19954+19954^23535	101202	Hans Havermann	11/2018
3373	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
3374	2^336150-20393	101192	Enzo Doria	06/2013
3375	23996^16473+16473^23996	101186	Hans Havermann	11/2018
3376	2^336112-1865249	101180	Enzo Doria	03/2016
3377	2^336103-109015	101178	Enzo Doria	04/2014
3378	13^90809-96	101157	Lelio R Paula	10/2016
3379	26199^7258+7258^26199	101150	Hans Havermann	11/2018
3380	19^79098-30	101147	Lelio R Paula	10/2016
3381	19^79095+88	101144	Lelio R Paula	10/2016
3382	15^85976+32	101116	Lelio R Paula	10/2016
3383	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
3384	(4^167933+17)/3	101106	Robert Price	02/2017
3385	2^335858+153	101104	Lelio R Paula	10/2009
3386	6^129918-35	101096	Lelio R Paula	10/2016
3387	3^211885-70	101095	Lelio R Paula	09/2016
3388	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
3389	2^335818-20033	101092	Enzo Doria	06/2013
3390	2^335813-110083	101090	Enzo Doria	04/2014
3391	2^335804+2155	101088	Lelio R Paula	09/2016
3392	2^335784-16145	101082	Enzo Doria	04/2013
3393	11^97051+62	101069	Lelio R Paula	10/2016
3394	3*10^101065+11	101066	Robert Price	07/2018
3395	27820^4293+4293^27820	101064	Hans Havermann	10/2018
3396	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
3397	2^335658-94395	101044	Lelio R Paula	09/2016
3398	24514^13215+13215^24514	101024	Hans Havermann	11/2018
3399	2^335586+169	101022	Lelio R Paula	10/2009
3400	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
3401	(19*10^100997+737)/9	100998	Robert Price	07/2018
3402	47599!2+1024	100991	Robert Price	02/2015
3403	2^335468-18629	100986	Enzo Doria	05/2013
3404	2^335454-20961	100982	Enzo Doria	06/2013
3405	10^100978+61	100979	Lelio R Paula	09/2016
3406	10^100978-156437	100978	Patrick De Geest	11/2016
3407	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
3408	2^335403-1859167	100967	Enzo Doria	03/2016
3409	23599^18976+18976^23599	100962	Hans Havermann	10/2018
3410	9*2^335364-5	100956	Lelio R Paula	08/2014
3411	2^335349+72287	100951	Enzo Doria	04/2016
3412	2^335329+16095	100945	Lelio R Paula	09/2016
3413	232823#+233663	100937	Makoto Morimoto	10/2017
3414	2^335237-20893	100917	Enzo Doria	06/2013
3415	2^335222-19337	100912	Enzo Doria	05/2013
3416	2^335222-109985	100912	Enzo Doria	04/2014
3417	2^335182-17237	100900	Enzo Doria	05/2013
3418	2^335043-16737	100858	Enzo Doria	05/2013
3419	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
3420	2^335038-20633	100857	Enzo Doria	06/2013
3421	2^335031+1873373	100855	Enzo Doria	06/2016
3422	23489^19650+19650^23489	100847	Hans Havermann	10/2018
3423	3^211354-8816	100842	Enzo Doria	05/2014
3424	2^334984-112757	100841	Enzo Doria	06/2014
3425	29451^2648+2648^29451	100809	Hans Havermann	09/2018
3426	25583^8716+8716^25583	100806	Hans Havermann	08/2018
3428	2^334857+48527	100803	Lelio R Paula	08/2011
3427	12^93406+29	100803	Lelio R Paula	10/2016
3429	28780^3179+3179^28780	100796	Hans Havermann	09/2018
3430	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
3431	2^334809-13	100788	Lelio R Paula	04/2011
3432	(82*10^100780-1)/9	100781	Robert Price	12/2014
3433	31395^1622+1622^31395	100780	Hans Havermann	09/2018
3434	(2^334779+47)/5	100778	Lelio R Paula	12/2013
3435	2^334751+2049	100771	Lelio R Paula	09/2016
3436	13^90443-98	100749	Lelio R Paula	10/2016
3437	(7*10^100737+71)/3	100738	Robert Price	05/2018
3438	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
3439	15^85639-28	100720	Lelio R Paula	10/2016
3440	27068^5259+5259^27068	100718	Hans Havermann	08/2018
3441	2^334562+577294575	100711	Lelio R Paula	09/2016
3442	4*3^211077-5	100710	Lelio R Paula	08/2014
3443	2^334524+145	100702	Lelio R Paula	07/2009
3444	27648^4375+4375^27648	100666	Hans Havermann	09/2018
3445	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
3446	2^334294-113111	100633	Enzo Doria	07/2014
3447	25581^8582+8582^25581	100626	Hans Havermann	08/2018
3448	6^129308-17723	100622	Enzo Doria	03/2013
3449	6^129305+95	100619	Lelio R Paula	10/2016
3450	2^334244-1167	100618	Lelio R Paula	09/2016
3451	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
3452	24885^10984+10984^24885	100555	Hans Havermann	07/2018
3453	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
3454	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
3455	23578^18367+18367^23578	100538	Hans Havermann	07/2018
3456	13^90251+24	100535	Lelio R Paula	10/2016
3457	2^333963+789	100533	Lelio R Paula	08/2011
3458	2^333919-1840087	100520	Enzo Doria	06/2015
3459	2^333911+72623	100518	Enzo Doria	04/2016
3460	24605^12168+12168^24605	100517	Hans Havermann	08/2018
3461	18^80064-67	100503	Lelio R Paula	10/2016
3462	5^143742-48	100472	Lelio R Paula	10/2016
3463	24095^14784+14784^24095	100472	Hans Havermann	08/2018
3464	2^333757-112123	100471	Enzo Doria	06/2014
3465	27358^4693+4693^27358	100444	Hans Havermann	07/2018
3466	2^333603-108861	100425	Enzo Doria	03/2014
3467	9*7^118818-2	100414	Lelio R Paula	11/2014
3468	2^333546-17097	100408	Enzo Doria	05/2013
3469	17^81597+72	100401	Lelio R Paula	10/2016
3470	p(20559)#/2+8	100384	Robert Price	01/2017
3471	11^96390-24	100380	Lelio R Paula	10/2016
3473	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
3472	23565^18136+18136^23565	100353	Hans Havermann	07/2018
3474	2^333354+763	100350	Lelio R Paula	08/2011
3475	2^333289-109483	100330	Enzo Doria	04/2014
3476	2^333240-2790209	100316	Enzo Doria	03/2016
3477	23601^17798+17798^23601	100314	Hans Havermann	05/2018
3479	(2^333227-2^166614+1)/5	100311		11/2006
3478	2^333225+719	100311	Lelio R Paula	08/2011
3480	2^333221-2785333	100310	Enzo Doria	10/2015
3481	76^53332-75	100308	Norbert Schneider	02/2015
3482	6^128892-17573	100298	Enzo Doria	03/2013
3483	2^333105-113215	100275	Enzo Doria	07/2014
3484	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
3485	4*10^100257-83	100258	Robert Price	10/2018
3486	17^81476-74	100253	Lelio R Paula	10/2016
3487	23392^19207+19207^23392	100199	Hans Havermann	06/2018
3488	17^81417-16	100180	Theodore Burton	11/2005
3489	2^332739-113215	100165	Enzo Doria	07/2014
3490	2^332730-1865621	100162	Enzo Doria	03/2016
3491	91^51127-2	100160	Lelio R Paula	09/2013
3492	15^85159-32	100155	Lelio R Paula	10/2016
3493	6^128661+97	100118	Lelio R Paula	10/2016
3494	19^78285+40	100108	Lelio R Paula	07/2016
3495	6^128640+5	100102	Lelio R Paula	11/2014
3496	(14*10^100075+61)/3	100076	Robert Price	12/2018
3497	28562^3189+3189^28562	100072	Hans Havermann	05/2018
3498	6^128565-127	100044	Lelio R Paula	08/2016
3499	2^332309-133	100035	Lelio R Paula	02/2011
3500	2^332307+731	100035	Lelio R Paula	07/2011

Find by discoverer :

PRP Records

Probable Primes Top 10000

(252402 PRPs in the top)