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	2^355494-19901	107015	Enzo Doria	06/2013
3252	2^355454-869688105	107003	Lelio R Paula	01/2017
3253	2^355366+54615	106976	Lelio R Paula	01/2017
3254	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
3255	2^355275-19861	106949	Enzo Doria	06/2013
3256	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
3257	4*10^106892-3	106893	Robert Price	10/2015
3258	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
3259	2^354946-3	106850	M. Frind & P. Underwood	08/2002
3260	2^354873-18693	106828	Enzo Doria	05/2013
3261	2^354828+4257	106814	Lelio R Paula	01/2017
3262	436^40459+40459^436	106791	Norbert Schneider	03/2019
3263	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
3264	(115*10^106772-7)/9	106774	Robert Price	02/2020
3265	2^354640-354640+1	106758	Robert Price	10/2014
3266	2^354585+95	106741	Lelio R Paula	10/2011
3267	2^354553+189	106732	Lelio R Paula	10/2011
3268	2^354514-109031	106720	Enzo Doria	04/2014
3269	2^354509-109465	106718	Enzo Doria	04/2014
3270	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
3271	Phi(217618,10)/899798636917	106693	Makoto Kamada	06/2019
3272	15^90710+28	106684	Lelio R Paula	04/2017
3273	7^126237+34	106683	Lelio R Paula	03/2017
3274	2^354385-115315	106681	Enzo Doria	06/2015
3275	2^354327-19305	106664	Enzo Doria	06/2013
3276	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
3277	10^106636+97	106637	Lelio R Paula	02/2017
3278	10^106636-22923	106636	Patrick De Geest	03/2017
3279	2^354220-57	106631	Lelio R Paula	10/2011
3280	(29*10^106620-77)/3	106621	Robert Price	02/2020
3281	(746*10^106618+1)/9	106620	Robert Price	03/2020
3282	2^354157-17041	106612	Enzo Doria	05/2013
3283	12^98778+73	106600	Lelio R Paula	02/2017
3284	2^354064+1870651	106584	Enzo Doria	05/2016
3285	2^353992-57	106563	Lelio R Paula	10/2011
3286	9*10^106559+59	106560	Robert Price	01/2020
3287	NSW(139160)	106535	Robert Price	12/2018
3288	(7*10^106516+113)/3	106517	Robert Price	02/2018
3289	2^353832-1853849	106515	Enzo Doria	09/2015
3290	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
3291	2^353794-18453	106503	Enzo Doria	05/2013
3292	2^353728+7695	106483	Lelio R Paula	01/2017
3293	2^353672-303	106466	Yves Minet	02/2012
3294	6^136811+101	106460	Lelio R Paula	02/2017
3295	2^353641+1871981	106457	Enzo Doria	05/2016
3296	(8*10^106454-29)/3	106455	Robert Price	07/2018
3297	2^353553+54615	106431	Lelio R Paula	01/2017
3298	2^353544-18897	106428	Enzo Doria	05/2013
3299	6^136729-133	106396	Lelio R Paula	02/2017
3300	2^353418+1605	106390	Lelio R Paula	01/2017
3301	2^353387+65	106381	Lelio R Paula	10/2011
3302	2^353372+74311	106376	Enzo Doria	04/2016
3303	2^353344-3693	106368	Yves Minet	03/2017
3305	2^353277-20089	106347	Enzo Doria	06/2013
3304	2^353275+72173	106347	Enzo Doria	04/2016
3306	2^353268-17705	106345	Enzo Doria	05/2013
3307	2^353267-19857	106344	Enzo Doria	06/2013
3308	(46*10^106343+143)/9	106344	Robert Price	01/2019
3309	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
3310	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
3311	2^353025+72257	106272	Enzo Doria	04/2016
3313	2^352932-20345	106244	Enzo Doria	06/2013
3312	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
3314	2^352883-187	106229	Lelio R Paula	10/2011
3315	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
3316	(55*10^106222+377)/9	106223	Robert Price	02/2019
3317	2^352814-131	106208	Lelio R Paula	10/2011
3318	2^352752+73951	106189	Enzo Doria	04/2016
3319	6^136434+5	106167	Lelio R Paula	11/2014
3320	8*10^106157-13	106158	Robert Price	08/2019
3321	7*5^151872-8	106155	Lelio R Paula	11/2014
3322	105^52520-2	106153	Lelio R Paula	10/2017
3323	2^352601-1604809	106144	Enzo Doria	05/2015
3324	12^98353-43	106141	Lelio R Paula	02/2017
3325	2^352585-18901	106139	Enzo Doria	05/2013
3326	(2^352554-3)/193	106128	Lelio R Paula	12/2013
3327	2^352540+15015	106126	Lelio R Paula	01/2017
3328	2^352524-3149	106121	Yves Minet	10/2014
3329	2^352486-1858781	106109	Enzo Doria	04/2016
3330	2^352444+12705	106097	Lelio R Paula	01/2017
3331	(182*10^106083+43)/9	106085	Robert Price	02/2020
3332	2^352228-18953	106032	Enzo Doria	05/2013
3333	2^352107+1872533	105995	Enzo Doria	05/2016
3334	2^352066-2591	105983	Yves Minet	07/2014
3335	2^352030+715	105972	Lelio R Paula	10/2011
3336	9*6^136176-5	105967	Lelio R Paula	11/2014
3337	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
3338	155^48377+2	105962	Lelio R Paula	08/2013
3339	2^351865+1869707	105922	Enzo Doria	05/2016
3340	2^351831+23	105912	Lelio R Paula	10/2011
3341	9*2^351784-5	105899	Lelio R Paula	09/2014
3342	2^351671-112387	105864	Enzo Doria	06/2014
3343	2^351669-109501	105863	Enzo Doria	04/2014
3344	2^351644+74731	105856	Enzo Doria	04/2016
3345	13^95025-42	105853	Lelio R Paula	12/2016
3346	2^351599+15015	105842	Lelio R Paula	01/2017
3347	19^82763+90	105834	Lelio R Paula	01/2017
3348	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
3349	20^81329-51	105812	Lelio R Paula	01/2017
3350	(5*10^105811+211)/9	105811	Robert Price	02/2018
3351	2^351483+28425	105807	Lelio R Paula	01/2017
3352	15^89960+86	105802	Lelio R Paula	02/2017
3353	2^351460-17289	105801	Enzo Doria	05/2013
3354	19^82735+22	105798	Lelio R Paula	01/2017
3355	2^351435-109077	105793	Enzo Doria	04/2014
3356	2^351393+1089	105780	Lelio R Paula	01/2017
3357	2^351364+72631	105772	Enzo Doria	04/2016
3358	2^351305+1872467	105754	Enzo Doria	05/2016
3359	3^221649+16	105754	Lelio R Paula	11/2016
3360	8*3^221637-5	105749	Lelio R Paula	09/2014
3361	2^351279-2780449	105746	Enzo Doria	03/2016
3362	15^89903-26	105735	Lelio R Paula	02/2017
3363	2^351213-73	105726	Lelio R Paula	10/2011
3364	2^351192-4589	105720	Yves Minet	07/2011
3365	20^81250-33	105709	Lelio R Paula	12/2016
3366	2^351076-113159	105685	Enzo Doria	07/2014
3367	93^53688-2	105684	Lelio R Paula	09/2013
3368	2^351060-4559	105680	Yves Minet	07/2011
3369	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
3370	11^101473-750	105674	Enzo Doria	11/2012
3371	3*5^151181-8	105672	Lelio R Paula	11/2014
3372	15^89831-34	105650	Lelio R Paula	02/2017
3374	11^101448-360	105648	Enzo Doria	08/2012
3373	3*7^125011+4	105648	Lelio R Paula	11/2014
3375	2^350943-113269	105645	Enzo Doria	07/2014
3376	2^350868-19725	105622	Enzo Doria	06/2013
3377	2^350858-59291	105619	Enzo Doria	10/2015
3378	2^350851+135	105617	Lelio R Paula	10/2011
3379	2^350841-741	105614	Lelio R Paula	01/2017
3380	3*10^105582+77	105583	Robert Price	09/2018
3381	8*10^105571+3	105572	Robert Price	08/2015
3382	2^350674-78557	105564	Jorge Menendez	03/2018
3383	2*5^151026-3	105563	Lelio R Paula	11/2014
3384	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
3385	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
3386	3^221211+236	105545	Lelio R Paula	11/2016
3387	(32*10^105530-77)/9	105531	Robert Price	06/2018
3388	10^105515+33	105516	Lelio R Paula	11/2016
3389	10^105515-41033	105515	Patrick De Geest	12/2016
3390	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
3391	17^85732-72	105489	Lelio R Paula	01/2017
3392	2^350307-110329	105453	Enzo Doria	05/2014
3393	2^350253-20365	105437	Enzo Doria	06/2013
3394	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
3395	2^350139-109009	105403	Enzo Doria	04/2014
3396	3*5^150763+4	105380	Lelio R Paula	11/2014
3397	12^97643+91	105375	Lelio R Paula	02/2017
3398	6*5^150744-7	105367	Lelio R Paula	11/2014
3399	2^349996-112169	105360	Enzo Doria	06/2014
3400	(418*10^105343+23)/9	105345	Robert Price	02/2020
3401	11^101142-1080	105329	Enzo Doria	12/2012
3402	(68*10^105320-41)/9	105321	Robert Price	10/2013
3403	3^220712-9934	105307	Enzo Doria	05/2014
3404	7*10^105296+9	105297	Robert Price	09/2015
3405	2^349739+1873373	105282	Enzo Doria	06/2016
3406	7^124574+24	105278	Lelio R Paula	11/2016
3407	2^349708-20957	105273	Enzo Doria	06/2013
3408	2^349649-20469	105255	Enzo Doria	06/2013
3409	2^349607-20109	105243	Enzo Doria	06/2013
3410	(85*10^105242+473)/9	105243	Robert Price	01/2020
3411	2^349594-19085	105239	Enzo Doria	05/2013
3412	2^349530+1874479	105220	Enzo Doria	06/2016
3413	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
3414	3^220464-112852	105189	Enzo Doria	07/2014
3415	2^349419-17349	105186	Enzo Doria	05/2013
3416	2^349400-2579	105180	Yves Minet	07/2014
3417	8*5^150471+3	105176	Lelio R Paula	11/2014
3418	655^37342+37342^655	105165	Norbert Schneider	08/2018
3419	13^94403+94	105160	Lelio R Paula	12/2016
3420	2^349301-112309	105151	Enzo Doria	06/2014
3421	9*2^349220+5	105127	Lelio R Paula	09/2014
3422	7*3^220317+8	105119	Lelio R Paula	09/2014
3423	7^124386+88	105119	Lelio R Paula	11/2016
3424	2^349171-19657	105111	Enzo Doria	06/2013
3425	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
3426	(2^349111-5)/3	105093	Lelio R Paula	12/2013
3427	675^37142+37142^675	105087	Norbert Schneider	08/2018
3428	2^348981-2797573	105054	Enzo Doria	04/2016
3429	2^348869-6555	105021	Lelio R Paula	01/2017
3430	5^150217+78	104998	Lelio R Paula	11/2016
3431	(28*10^104972+149)/3	104973	Robert Price	12/2019
3432	2^348703-113005	104971	Enzo Doria	06/2014
3434	2^348612-809	104943	Yves Minet	05/2013
3433	(73*10^104942-1)/9	104943	Robert Price	01/2015
3435	2^348583-350407	104934	Enzo Doria	06/2015
3436	2^348531-949	104919	Yves Minet	05/2012
3437	20^80636-59	104910	Lelio R Paula	12/2016
3438	8*10^104893-13	104894	Robert Price	08/2019
3439	2^348437+35	104890	Lelio R Paula	09/2011
3440	2^348348+135	104864	Lelio R Paula	09/2011
3441	(2^348284+9)/25	104843	Lelio R Paula	12/2013
3442	75^55914-74	104843	Norbert Schneider	01/2015
3443	2^348268+255255	104840	Lelio R Paula	01/2017
3444	5^149985-52	104836	Lelio R Paula	11/2016
3445	2^348224-20249	104826	Enzo Doria	06/2013
3446	2^348212-20105	104823	Enzo Doria	06/2013
3447	20^80562+19	104814	Lelio R Paula	12/2016
3448	2*10^104811-87	104812	Robert Price	04/2018
3449	2^348149-20053	104804	Enzo Doria	06/2013
3450	2^348095-171	104788	Lelio R Paula	09/2011
3451	2^348003-20377	104760	Enzo Doria	06/2013
3452	2^347994-741	104757	Lelio R Paula	12/2016
3453	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
3454	2^347910-109937	104732	Enzo Doria	04/2014
3455	5^149794+28	104702	Lelio R Paula	11/2016
3456	105^51800-2	104698	Lelio R Paula	10/2017
3457	(16^86939+3^86939)/19	104684	Robert Price	06/2013
3458	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
3459	2^347731-18609	104678	Enzo Doria	05/2013
3460	4*6^134519+7	104677	Lelio R Paula	11/2014
3461	2^347612-18545	104642	Enzo Doria	05/2013
3462	6^134465+95	104635	Lelio R Paula	11/2016
3463	2^347517-17301	104614	Enzo Doria	05/2013
3464	3^219222-310	104596	Lelio R Paula	11/2016
3465	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
3466	2^347372-17853	104570	Enzo Doria	05/2013
3467	2^347314+99	104552	Lelio R Paula	09/2011
3468	2^347300-22233	104548	Enzo Doria	06/2013
3469	2^347287-19845	104544	Enzo Doria	06/2013
3470	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
3471	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
3472	7*2^347239-3	104531	Lelio R Paula	09/2014
3473	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
3474	5*3^219047+8	104513	Lelio R Paula	09/2014
3475	2^347148-109073	104502	Enzo Doria	04/2014
3476	2^347129-20145	104497	Enzo Doria	06/2013
3477	4*10^104461-57	104462	Robert Price	10/2018
3478	2^346923-19585	104435	Enzo Doria	05/2013
3479	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
3480	2^346854+346854^2+1	104414	Robert Price	06/2014
3481	2^346834+11715	104408	Lelio R Paula	04/2015
3482	79^55009+78	104387	Norbert Schneider	02/2015
3483	3^218744+58	104368	Lelio R Paula	11/2016
3484	9*10^104361+89	104362	Robert Price	11/2019
3485	2^346649+65	104352	Lelio R Paula	09/2011
3486	2^346638-17265	104349	Enzo Doria	05/2013
3487	5*10^104326+77	104327	Robert Price	12/2018
3489	2^346527-111817	104316	Enzo Doria	05/2014
3488	6^134055+101	104316	Lelio R Paula	11/2016
3490	92105!4+8	104312	Robert Price	09/2019
3491	6^134013+163	104283	Lelio R Paula	11/2016
3492	18^83049-89	104250	Lelio R Paula	01/2017
3493	2^346213+484049	104221	Enzo Doria	04/2017
3494	18^83021-91	104214	Lelio R Paula	01/2017
3495	10^104212+128779	104213	Patrick De Geest	05/2016
3496	10^104212+237447	104213	Patrick De Geest	05/2016
3497	10^104212+242139	104213	Patrick De Geest	05/2016
3498	10^104212+269199	104213	Patrick De Geest	05/2016
3499	(10^104212-71)/1	104212	Serge Batalov	12/2014
3500	23678^23821-23821^23678	104202	Norbert Schneider	01/2020

Find by discoverer :

PRP Records

Probable Primes Top 10000

(259919 PRPs in the top)