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	2^624008+1874941	187846	Enzo Doria	06/2016
3252	2^623870+78679	187804	Enzo Doria	05/2016
3253	2^623714-114035	187757	Enzo Doria	11/2014
3254	2^623651-1834251	187738	Enzo Doria	07/2015
3255	(7*10^187645+53)/3	187646	Robert Price	05/2018
3256	21650^43269+43269^21650	187591	Norbert Schneider	02/2023
3257	2^623146+1879609	187586	Enzo Doria	09/2016
3258	(401*10^187512+13)/9	187514	Robert Price	09/2021
3259	(5*10^187471+91)/3	187472	Robert Price	04/2018
3260	2^622500+81931	187392	Enzo Doria	08/2016
3261	(13*10^187382-157)/9	187383	Robert Price	05/2021
3262	2^622300-1861739	187331	Enzo Doria	12/2015
3263	(22*10^187317-91)/3	187318	Robert Price	02/2022
3264	(38*10^187281+349)/9	187282	Robert Price	10/2018
3265	2^622052+76771	187257	Enzo Doria	05/2016
3266	2^622005-24091	187243	Enzo Doria	08/2013
3267	7*10^187205-57	187206	Robert Price	06/2020
3268	2^621879-351787	187205	Enzo Doria	07/2015
3269	(5*10^187168-53)/3	187169	Robert Price	09/2020
3270	(23*10^187164-143)/3	187165	Robert Price	12/2019
3271	2^621700+79411	187151	Enzo Doria	06/2016
3272	2^621597+39	187120	Jon Grantham	08/2023
3273	Phi(271207,-5)	187112	Henri Lifchitz	12/2025
3274	(7*10^187101+131)/3	187102	Robert Price	06/2020
3275	(2*10^187062-71)/3	187062	Robert Price	12/2017
3276	V(1118570)	187013	Serge Batalov	07/2024
3277	2^620929-113203	186919	Enzo Doria	07/2014
3278	10^186842+168223	186843	Patrick De Geest	07/2018
3279	10^186842-8001	186842	Robert Price	03/2018
3280	V(1117640)/13411681/26823361/575709775681/989889277441	186814	Serge Batalov	07/2024
3281	2^620347-1777	186744	Lelio R Paula	07/2013
3282	(11*10^186659+133)/9	186660	Robert Price	04/2022
3283	11^179143-4170	186559	Enzo Doria	12/2012
3284	(13^186535)%(10^186535)	186535	Henri Lifchitz	05/2025
3286	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
3285	Phi(266863,-5)	186529	Henri Lifchitz	12/2025
3287	2*10^186517+33	186518	Robert Price	11/2021
3288	2^619297-2792353	186427	Enzo Doria	02/2016
3289	(49*10^186409+383)/9	186410	Robert Price	04/2019
3290	2^618940-460139	186320	Enzo Doria	06/2015
3291	Phi(343570,2^5)	186109	Henri Lifchitz	12/2025
3292	2^618046+74179	186051	Enzo Doria	04/2016
3293	3*10^186019+11	186020	Robert Price	07/2018
3294	(16*10^185978-19)/3	185979	Robert Price	02/2019
3295	(22*10^185950-7)/3	185951	Robert Price	12/2022
3296	2*10^185930-3	185931	Robert Price	07/2015
3297	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
3298	4*10^185905+91	185906	Robert Price	08/2018
3299	(34*10^185902-601)/9	185903	Robert Price	07/2022
3300	(19*10^185873+131)/3	185874	Robert Price	06/2020
3301	(37*10^185811+377)/9	185812	Robert Price	11/2018
3302	2^617250+9385	185811	Lelio R Paula	07/2013
3303	2^617130+9	185775	Stefano Morozzi	05/2021
3304	39^116749+2	185756	Robert Price	04/2015
3305	2^616924-39719	185713	Enzo Doria	09/2015
3306	2^616712+1867621	185649	Enzo Doria	04/2016
3307	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
3308	8*10^185529-67	185530	Robert Price	08/2019
3309	(5*10^185520-11)/3	185521	Tyler Busby	02/2023
3310	5*2^616124+3	185473	Jon Grantham	07/2023
3311	2^615916+26791	185410	Enzo Doria	12/2023
3312	4*10^185355+9	185356	Robert Price	05/2015
3313	(16*10^185347+89)/3	185348	Robert Price	03/2021
3314	40247^40247-56^56	185327	Henri Lifchitz	08/2024
3315	2^615622+76639	185321	Enzo Doria	05/2016
3316	2^615591+1879223	185312	Enzo Doria	08/2016
3317	2^615587+217013	185311	Enzo Doria	12/2023
3318	2^615503+1876643	185285	Enzo Doria	07/2016
3319	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
3321	(4*10^185221-91)/3	185222	Robert Price	03/2018
3320	(7*10^185221+131)/3	185222	Robert Price	06/2020
3322	(62*10^185216-413)/9	185217	Robert Price	09/2021
3323	(232*10^185180+17)/3	185182	Robert Price	04/2021
3324	56*10^185139-3	185141	Robert Price	03/2020
3325	(28*10^185105+47)/3	185106	Robert Price	02/2021
3326	2^614783-2790097	185069	Enzo Doria	12/2015
3327	2^614745-29323	185057	Enzo Doria	07/2015
3328	(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840	185052	Serge Batalov	07/2013
3329	(49*10^184993-67)/9	184994	Robert Price	03/2019
3330	(5*10^184954-191)/3	184955	Robert Price	05/2021
3331	(14*10^184950+211)/9	184951	Robert Price	04/2018
3332	2^614360+215221	184941	Enzo Doria	11/2023
3333	2^614315+81353	184928	Enzo Doria	08/2016
3334	2^614294-1849961	184921	Enzo Doria	08/2015
3335	2^614266+1877809	184913	Enzo Doria	08/2016
3336	(185*10^184878-11)/3	184880	Robert Price	10/2020
3337	91*10^184867-9	184869	Robert Price	06/2021
3338	(37^117841-1)/581320056003516	184784	Paul Vanderveen	06/2025
3339	39803^40170-40170^39803	184779	Norbert Schneider	05/2024
3340	(14789^44521-1)/(14789^211-1)	184770	Ryan Propper	11/2023
3341	(85*10^184768+77)/9	184769	Robert Price	07/2022
3342	2^613715-1860727	184747	Enzo Doria	11/2015
3343	(4*10^184730+89)/3	184731	Robert Price	08/2021
3344	2*10^184723+41	184724	Robert Price	05/2018
3345	(49*10^184703+293)/9	184704	Robert Price	03/2021
3346	2^613487-349987	184678	Enzo Doria	07/2015
3347	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
3348	14^161089-161089^14	184629	Serge Batalov	05/2016
3349	40008^40109-40109^40008	184588	Norbert Schneider	05/2024
3350	2^613033-114621	184542	Enzo Doria	05/2015
3351	3*2^612759+5	184460	Jon Grantham	07/2023
3352	2^612587+213413	184408	Enzo Doria	09/2023
3354	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
3353	Phi(193247,-9)	184404	Henri Lifchitz	12/2025
3355	2^612424+212341	184358	Enzo Doria	08/2023
3356	2^612341-1604809	184334	Enzo Doria	05/2015
3357	(11*10^184308-161)/3	184309	Robert Price	11/2021
3358	625^65919+624	184302	Alfred Reich	04/2026
3359	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
3360	(14*10^184150+37)/3	184151	Robert Price	12/2018
3361	2^611731-4837	184150	Yves Minet	08/2018
3362	3*10^184124-7	184125	Robert Price	08/2015
3363	2^611644+29371	184124	Enzo Doria	02/2024
3364	9*10^184122-11	184123	Mischa Rodermond	04/2023
3365	2^611628-24537	184119	Enzo Doria	08/2013
3366	3*10^184110+13	184111	Robert Price	07/2018
3367	(14280^44521-1)/(14280^211-1)	184097	Ryan Propper	11/2023
3368	(194*10^184093+1)/3	184095	Robert Price	01/2022
3369	2^611460+71881	184068	Enzo Doria	04/2016
3370	4*10^184004-63	184005	Robert Price	10/2018
3371	2^611111+84083	183963	Boyan Hu	05/2024
3372	2^610982-1867301	183924	Enzo Doria	03/2016
3373	(10^183917+1)/11/9952852373	183906	Alfred Reich	02/2024
3374	3*10^183872-49	183873	Robert Price	07/2018
3375	2^610597+1178897	183809	Enzo Doria	05/2016
3376	(8*10^183773-269)/9	183773	Robert Price	09/2021
3377	(65*10^183768-29)/9	183769	Robert Price	01/2021
3378	(17*10^183764+31)/3	183765	Robert Price	01/2019
3379	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
3380	2^610401+1277	183750	Lelio R Paula	07/2013
3381	2^610356-1849019	183736	Enzo Doria	08/2015
3382	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
3383	23*10^183710-7	183712	Robert Price	02/2020
3384	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
3385	(4*10^183659+149)/9	183659	Robert Price	04/2018
3386	(4*10^183657+41)/9	183657	Serge Batalov	11/2022
3387	(11^176327-1)/31738870	183619	Paul Vanderveen	05/2025
3388	7*10^183596+39	183597	Robert Price	01/2023
3389	2^609846-1834251	183582	Enzo Doria	07/2015
3390	10^183546+1547323	183547	Patrick De Geest	02/2021
3392	10^183546-800000001	183546	Robert Price	09/2020
3391	10^183546-584297	183546	Patrick De Geest	02/2021
3393	7*10^183511+39	183512	Robert Price	01/2023
3394	(23*10^183477-71)/3	183478	Robert Price	07/2020
3395	11^176176-240	183469	Enzo Doria	11/2012
3396	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
3397	6*10^183429+53	183430	Robert Price	05/2020
3398	(28*10^183403+191)/3	183404	Robert Price	02/2020
3399	U(1096855)	183383	Serge Batalov	07/2024
3400	(5^262337-1)/363486427756606700767551233751524443601036	183325	Paul Vanderveen	05/2025
3401	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
3402	2^608965-113989	183317	Enzo Doria	10/2014
3403	A005165(43592)	183312	Serge Batalov	07/2017
3404	(61*10^183294+119)/9	183295	Robert Price	05/2019
3405	2^608814-461261	183272	Enzo Doria	06/2015
3406	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
3407	2^608541-608541^2	183190	Henri Lifchitz	02/2018
3408	2^608293+143807	183115	Enzo Doria	10/2016
3409	Phi(612539,-2)	183111	Henri Lifchitz	02/2026
3410	2^608164-462419	183076	Enzo Doria	08/2015
3411	2^607950-1862303	183012	Enzo Doria	12/2015
3412	5*3^383376+2^383376	182918	Jon Grantham	08/2023
3413	(46*10^182896+683)/9	182897	Robert Price	03/2019
3414	(2*10^182787+73)/3	182787	Robert Price	09/2020
3415	2^607101+1871987	182756	Enzo Doria	05/2016
3416	2^606869-69175	182686	Enzo Doria	11/2015
3417	8*10^182671+71	182672	Robert Price	05/2022
3418	(23*10^182666-71)/3	182667	Robert Price	07/2020
3419	3*10^182614-11	182615	Robert Price	07/2018
3420	2^606560-357	182593	Enzo Doria	05/2014
3421	66*10^182420+7	182422	Robert Price	07/2020
3422	2^605687+1866983	182330	Enzo Doria	03/2016
3423	2^605655-114445	182321	Enzo Doria	02/2015
3424	94*10^182291-3	182293	Robert Price	05/2020
3425	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
3426	(14*10^182177-221)/9	182178	Robert Price	04/2018
3427	2^605174-112751	182176	Enzo Doria	06/2014
3428	(905^61609-1)/904	182154	Anonymous	05/2024
3429	2^604761+1874507	182052	Enzo Doria	06/2016
3430	2^604705+1871957	182035	Enzo Doria	05/2016
3431	(14*10^182000+229)/9	182001	Robert Price	03/2018
3432	(10^181996+41)/3	181996	Robert Price	12/2017
3433	(17*10^181979+91)/9	181980	Robert Price	02/2022
3434	(10^181960+3)/7	181960	Jinyuan Wang	11/2024
3435	(5*10^181950-101)/3	181951	Robert Price	04/2018
3436	2^603915+75233	181797	Enzo Doria	04/2016
3437	39470^39537+39537^39470	181723	Norbert Schneider	12/2022
3438	(10^181710+7)/563747/2019847	181698	Alfred Reich	08/2021
3439	7*10^181594-57	181595	Robert Price	06/2020
3440	8*10^181580+29	181581	Robert Price	11/2021
3441	(83*10^181544+61)/9	181545	Serge Batalov	01/2023
3442	(2*10^181457+7)/9	181457	Rytis Slatkevicius	01/2023
3443	3*10^181445+23	181446	Robert Price	03/2022
3444	Phi(306341,-5)	181375	Henri Lifchitz	02/2026
3445	(194*10^181369-11)/3	181371	Robert Price	09/2020
3446	11^174145-360	181354	Enzo Doria	10/2012
3447	2^602351-396765	181326	Enzo Doria	08/2013
3448	6*10^181306+17	181307	Robert Price	04/2019
3449	(353^71143-1)/352	181254	Anonymous	04/2024
3450	(286*10^181220-1)/3	181222	Robert Price	11/2020
3451	2^601957-113833	181208	Enzo Doria	09/2014
3452	66^99581-65^99581	181193	Robert Price	09/2013
3453	10^181182+383973	181183	Patrick De Geest	04/2016
3454	10^181182-21	181182	Serge Batalov	12/2014
3455	(797*10^181171-41)/9	181173	Robert Price	04/2022
3456	33385^40046-40046^33385	181151	Norbert Schneider	02/2026
3457	2^601722+74209	181137	Enzo Doria	08/2023
3458	(5*10^181127-29)/3	181128	Robert Price	03/2018
3459	2^601521-29143	181076	Enzo Doria	07/2015
3460	2^601442-2797811	181053	Enzo Doria	04/2016
3461	44*10^181029+3	181031	Robert Price	04/2020
3462	5*10^180992-9	180993	Robert Price	05/2015
3463	10^180979+79477	180980	Patrick De Geest	04/2016
3464	10^180979+107739	180980	Patrick De Geest	04/2016
3465	10^180979-11	180979	Serge Batalov	12/2014
3466	2^601023-113851	180926	Enzo Doria	10/2014
3467	(23*10^180862-143)/3	180863	Robert Price	12/2019
3468	3*10^180852+29	180853	Robert Price	05/2018
3469	(277*10^180782-7)/9	180784	Robert Price	02/2022
3470	2^600412+29851	180743	Enzo Doria	03/2024
3471	(8*10^180725-629)/9	180725	Robert Price	01/2022
3472	(79*10^180710-1)/3	180712	Robert Price	02/2020
3473	2^600300-1852559	180709	Enzo Doria	08/2015
3474	(2*10^180706-77)/3	180706	Robert Price	02/2021
3475	(156^82393-1)/155	180696	Anonymous	06/2024
3476	(10^180689+71)/9	180689	Serge Batalov	07/2015
3477	2^600209+76487	180681	Enzo Doria	05/2016
3478	2^599999+378461	180618	Norman Luhn	09/2023
3479	(8*10^180536-269)/9	180536	Robert Price	09/2021
3480	2^599702-369885	180529	Enzo Doria	11/2013
3481	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
3482	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
3483	(29*10^180432-17)/3	180433	Robert Price	09/2019
3484	4*10^180360+93	180361	Robert Price	08/2018
3485	2^599035+219323	180328	Enzo Doria	03/2024
3486	2^598942+80779	180300	Enzo Doria	07/2016
3487	(38*10^180296+403)/9	180297	Robert Price	10/2018
3488	(85*10^180241+77)/9	180242	Robert Price	07/2022
3489	2^598591-1844797	180194	Enzo Doria	06/2015
3490	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
3491	Phi(90089,-100)	180176	Henri Lifchitz	12/2025
3492	2^598301+28517	180107	Enzo Doria	01/2024
3493	(29*10^180072+691)/9	180073	Robert Price	08/2021
3494	(59*10^180038+157)/9	180039	Robert Price	12/2021
3495	95*10^180019-9	180021	Robert Price	01/2022
3496	6*10^179970+91	179971	Robert Price	05/2019
3497	(4*10^179963-79)/3	179964	Robert Price	02/2018
3498	(403*10^179944-43)/9	179946	Robert Price	06/2021
3499	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
3500	2^597424-1859729	179843	Enzo Doria	11/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(303264 PRPs in the top)