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 (> 50000)	Who ?	When ?
3252	2^370643-37	111575	Yves Minet	01/2012
3251	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
3253	2^370610-3911	111565	Yves Minet	04/2017
3254	286^45405+45405^286	111532	Norbert Schneider	04/2015
3255	4*5^159563-9	111531	Lelio R Paula	11/2014
3256	(4^185225+23)/3	111517	Robert Price	10/2018
3257	2^370393-2797093	111500	Enzo Doria	03/2016
3258	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
3259	(2^370371+554)/2	111493	Stefano Morozzi	09/2020
3260	2^370292-2791979	111469	Enzo Doria	03/2016
3261	2^370177-461551	111435	Enzo Doria	07/2015
3262	(2^370169+1706)/2	111432	Stefano Morozzi	09/2020
3263	109^54683-108	111413	Norbert Schneider	02/2017
3264	(2^370043+1010)/2	111394	Stefano Morozzi	09/2020
3265	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
3266	2^369974+733	111374	Lelio R Paula	05/2013
3267	121^53470+120	111367	Norbert Schneider	10/2018
3268	2^369915-286267	111356	Enzo Doria	07/2015
3269	2^369855-1615	111338	Lelio R Paula	05/2017
3270	7*10^111325+3	111326	Robert Price	08/2015
3271	51^65176+2	111293	Lelio R Paula	08/2013
3272	2^369643-1865767	111274	Enzo Doria	03/2016
3273	2^369603+885	111262	Lelio R Paula	05/2017
3274	L(532277)	111240	Renaud Lifchitz	03/2004
3275	105^55033-2	111233	Lelio R Paula	10/2017
3276	(35*10^111232-737)/9	111233	Robert Price	07/2018
3277	9*10^111201-29	111202	Robert Price	09/2019
3278	2^369392+29835	111199	Lelio R Paula	05/2017
3279	3^233059+16	111198	Robert Price	03/2020
3280	2^369354-3413	111187	Yves Minet	12/2016
3281	2^369296-27	111170	Lelio R Paula	02/2013
3282	2^369239-109837	111153	Enzo Doria	05/2014
3283	2^369224-291839	111148	Enzo Doria	07/2015
3284	2^369216+2798881	111146	Enzo Doria	04/2016
3285	10^111111+163849	111112	Patrick De Geest	03/2017
3286	10^111111-312911	111111	Patrick De Geest	03/2017
3287	2^369092-216923	111108	Enzo Doria	05/2014
3288	2^369081-55	111105	Lelio R Paula	02/2013
3289	(2^369047+3618)/2	111094	Stefano Morozzi	09/2020
3290	88^57124-87	111077	Norbert Schneider	11/2015
3291	2^368980+753	111075	Lelio R Paula	05/2013
3292	2^368946-3623	111064	Yves Minet	03/2017
3293	2^368929+29835	111059	Lelio R Paula	05/2017
3294	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
3295	111^54298+110	111057	Norbert Schneider	04/2017
3296	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
3297	2^368641-460303	110972	Enzo Doria	06/2015
3298	2^368619-109087	110966	Enzo Doria	04/2014
3299	(74*10^110961+313)/9	110962	Robert Price	06/2019
3300	3*2^368489+7	110927	Lelio R Paula	09/2014
3301	(14*10^110922+61)/3	110923	Robert Price	12/2018
3302	97411!4-2	110913	Robert Price	07/2017
3303	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
3304	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
3305	2^368050-64875	110795	Lelio R Paula	05/2017
3306	2^368048+25	110794	Lelio R Paula	02/2013
3307	69^60239-2	110771	Lelio R Paula	10/2013
3308	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
3309	2^367924-69	110757	Lelio R Paula	02/2013
3310	2^367709-109723	110692	Enzo Doria	04/2014
3311	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
3312	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
3313	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
3314	140^51515-139	110558	Norbert Schneider	04/2019
3315	2^367215+1879223	110543	Enzo Doria	09/2016
3316	2^367141+41	110521	Lelio R Paula	02/2013
3317	2^367126+29835	110516	Lelio R Paula	05/2017
3332	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
3331	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
3330	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
3329	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
3328	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
3327	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
3326	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
3325	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020
3318	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
3319	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
3320	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
3321	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
3322	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
3323	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
3324	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
3334	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
3335	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
3336	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020
3350	7(10^110503-1)/9+1(10^27685-1)/9*10^41409	110503	Makoto Morimoto	09/2020
3351	7(10^110503-1)/9+1(10^91035-1)/9*10^9734	110503	Makoto Morimoto	09/2020
3352	7(10^110503-1)/9-1(10^23717-1)/9*10^43393	110503	Makoto Morimoto	09/2020
3353	7(10^110503-1)/9-110^57906-1*10^52596	110503	Makoto Morimoto	09/2020
3354	7(10^110503-1)/9-110^72287-1*10^38215	110503	Makoto Morimoto	09/2020
3355	7(10^110503-1)/9-2(10^53823-1)/9*10^28340	110503	Makoto Morimoto	09/2020
3356	7(10^110503-1)/9-2(10^88659-1)/9*10^10922	110503	Makoto Morimoto	09/2020
3357	7(10^110503-1)/9-3(10^79921-1)/9*10^15291	110503	Makoto Morimoto	09/2020
3358	7(10^110503-1)/9-310^60024-3*10^50478	110503	Makoto Morimoto	09/2020
3359	7(10^110503-1)/9-4(10^103091-1)/9*10^3706	110503	Makoto Morimoto	09/2020
3349	7(10^110503-1)/9-410^103658-4*10^6844	110503	Makoto Morimoto	09/2020
3348	7(10^110503-1)/9-410^78188-4*10^32314	110503	Makoto Morimoto	09/2020
3347	7(10^110503-1)/9-5(10^35035-1)/9*10^37734	110503	Makoto Morimoto	09/2020
3337	7(10^110503-1)/9-6(10^67347-1)/9*10^21578	110503	Makoto Morimoto	09/2020
3338	7(10^110503-1)/9-610^60391-6*10^50111	110503	Makoto Morimoto	09/2020
3339	(10^110503-1)-4(10^96247-1)/910^7128	110503	Makoto Morimoto	09/2020
3340	(10^110503-1)-410^74037-410^36465	110503	Makoto Morimoto	09/2020
3341	(10^110503-1)-410^77787-410^32715	110503	Makoto Morimoto	09/2020
3342	(10^110503-1)-410^91179-410^19323	110503	Makoto Morimoto	09/2020
3333	(10^110503-1)-5(10^99143-1)/910^5680	110503	Makoto Morimoto	09/2020
3343	(10^110503-1)-7(10^85075-1)/910^12714	110503	Makoto Morimoto	09/2020
3344	(10^110503-1)-710^100712-710^9790	110503	Makoto Morimoto	09/2020
3345	(10^110503-1)-710^76427-710^34075	110503	Makoto Morimoto	09/2020
3346	(10^110503-1)-710^90451-710^20051	110503	Makoto Morimoto	09/2020
3360	(10^110503-1)-810^106252-810^4250	110503	Makoto Morimoto	09/2020
3361	(11*10^110496+49)/3	110497	Robert Price	07/2018
3362	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
3363	7*10^110468-23	110469	Robert Price	07/2019
3364	2^366853+5711	110434	Lelio R Paula	05/2017
3365	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
3366	2^366816+315	110423	Lelio R Paula	05/2017
3367	2^366775-2787037	110411	Enzo Doria	03/2016
3368	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
3369	2^366751+2797553	110404	Enzo Doria	03/2016
3370	2^366748+255	110403	Lelio R Paula	05/2017
3371	2^366738-2985	110400	Yves Minet	09/2014
3372	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
3373	2^366716+1871791	110393	Enzo Doria	05/2016
3374	2^366649+1871687	110373	Enzo Doria	05/2016
3375	2^366629-351205	110367	Enzo Doria	06/2015
3376	2^366558+1874479	110345	Enzo Doria	06/2016
3377	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
3378	(23*10^110290+19)/3	110291	Robert Price	07/2019
3379	18^87853-4409	110280	Enzo Doria	03/2013
3380	2^366218-23	110243	Lelio R Paula	02/2013
3381	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
3382	2^366178-343991	110231	Enzo Doria	07/2015
3383	2^365944+1871341	110161	Enzo Doria	05/2016
3384	2^365838-461267	110129	Enzo Doria	07/2015
3385	2^365763-6555	110106	Lelio R Paula	04/2017
3386	(2^365689+2^182845+1)/5	110083		11/2006
3387	2^365666-459161	110077	Enzo Doria	05/2015
3388	3*10^110076-7	110077	Robert Price	08/2015
3389	13^98785-72	110041	Lelio R Paula	03/2017
3390	(25^78707+1)/26	110027	Robert Price	06/2013
3391	(16*10^110014-73)/3	110015	Robert Price	07/2020
3392	(7*10^110006-151)/9	110006	Robert Price	02/2018
3393	6^141361-7	110001	Lelio R Paula	11/2014
3394	20^84536+81	109984	Lelio R Paula	03/2017
3395	5*2^365347-9	109982	Lelio R Paula	09/2014
3396	9*6^141303+7	109957	Lelio R Paula	11/2014
3397	78^58099+77	109929	Norbert Schneider	02/2015
3398	2*10^109928-7	109929	Robert Price	10/2015
3399	(2^365161+1130)/2	109925	Stefano Morozzi	09/2020
3400	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
3401	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
3402	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
3403	(2^365049+722)/2	109891	Stefano Morozzi	09/2020
3404	18^87533-11	109878	Lelio R Paula	04/2017
3405	2^364982-5	109871	Henri Lifchitz	04/2006
3406	3*10^109861+59	109862	Robert Price	08/2018
3407	2^364936-1867979	109857	Enzo Doria	04/2016
3408	2^364867-112087	109836	Enzo Doria	06/2014
3409	4^182415-85061	109825	Mike Oakes	06/2011
3410	(2^364809+1034)/2	109819	Stefano Morozzi	09/2020
3411	(17^89227+16^89227)/33	109788	Robert Price	08/2013
3412	2^364687-187	109782	Lelio R Paula	01/2012
3413	2^364644+67	109769	Lelio R Paula	01/2012
3414	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
3415	(2^364616+5)/9	109760	Lelio R Paula	01/2014
3416	(55*10^109759+89)/9	109760	Robert Price	03/2019
3417	12^101694+73	109747	Lelio R Paula	03/2017
3418	13^98518-66	109744	Lelio R Paula	03/2017
3419	2^364478-113261	109719	Enzo Doria	07/2014
3420	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
3421	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
3422	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
3423	3^229824+340	109654	Lelio R Paula	03/2017
3424	(2*10^109645-71)/3	109645	Robert Price	12/2017
3425	2^364169-112813	109626	Enzo Doria	06/2014
3426	10^109615+21	109616	Lelio R Paula	03/2017
3427	10^109615-456267	109615	Patrick De Geest	03/2017
3428	2^364094-113	109604	Lelio R Paula	01/2012
3429	(4^182026+11)/3	109591	Robert Price	02/2017
3430	2^364041-6883	109588	Lelio R Paula	09/2011
3431	12^101545+11	109586	Lelio R Paula	03/2017
3432	2^363842-2787101	109528	Enzo Doria	03/2016
3433	(2^363812+3570)/2	109519	Stefano Morozzi	09/2020
3434	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
3435	2^363769+5711	109506	Lelio R Paula	04/2017
3436	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
3437	p(22245)#/2-8	109462	Robert Price	01/2017
3438	2^363556+55	109442	Lelio R Paula	01/2012
3439	(2^363437+1682)/2	109406	Stefano Morozzi	09/2020
3440	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
3441	2^363406+1871569	109397	Enzo Doria	05/2016
3442	(2^363349+7)/9	109378	Lelio R Paula	01/2014
3443	3^229236+100	109374	Lelio R Paula	03/2017
3444	2^363268-58695	109355	Lelio R Paula	04/2017
3445	2^363191-112321	109332	Enzo Doria	06/2014
3446	4*10^109316-63	109317	Robert Price	10/2018
3447	2^363120+3	109311	Donovan Johnson	04/2006
3448	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
3449	2^363042-114641	109287	Enzo Doria	04/2015
3450	2^363020-112793	109280	Enzo Doria	06/2014
3451	(85*10^109253+203)/9	109254	Robert Price	09/2020
3452	(2^362746+3738)/2	109198	Stefano Morozzi	09/2020
3453	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
3454	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
3455	5^156181+38	109166	Lelio R Paula	02/2017
3456	(2^362623+3618)/2	109161	Stefano Morozzi	09/2020
3457	4*10^109142+91	109143	Robert Price	08/2018
3458	3^228750+68	109142	Lelio R Paula	03/2017
3459	(2^362561+786)/2	109142	Stefano Morozzi	09/2020
3460	2*10^109100-49	109101	Robert Price	09/2020
3461	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
3462	65^60167-64^60167	109078	Robert Price	08/2013
3463	7*3^228589-2	109066	Lelio R Paula	09/2014
3464	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
3465	2*7^129008+9	109025	Lelio R Paula	11/2014
3466	88*10^109022+7	109024	Robert Price	03/2020
3467	(5*10^108960+91)/3	108961	Robert Price	04/2018
3468	2^361957+76367	108960	Enzo Doria	05/2016
3469	2^361873-1411	108935	Yves Minet	01/2013
3470	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
3471	115^52842-114	108892	Norbert Schneider	07/2018
3472	13^97745-24	108883	Lelio R Paula	03/2017
3473	(2^361696+2562)/2	108882	Stefano Morozzi	09/2020
3474	17^88475+8	108864	Lelio R Paula	04/2017
3475	2^361567+51	108843	Lelio R Paula	01/2012
3476	2^361563-109501	108842	Enzo Doria	04/2014
3477	12^100852+83	108838	Lelio R Paula	03/2017
3478	2^361497+767	108822	Lelio R Paula	01/2012
3479	2^361280-112349	108757	Enzo Doria	06/2014
3480	2^361271-5955	108754	Lelio R Paula	04/2017
3481	12^100757+19	108736	Lelio R Paula	03/2017
3482	(2^361195+3618)/2	108731	Stefano Morozzi	09/2020
3483	14^94849-61	108710	Lelio R Paula	05/2017
3484	(19^85009-5^85009)/14	108705	Robert Price	07/2013
3485	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
3486	2^360973+1299	108664	Lelio R Paula	04/2017
3487	2^360959-109101	108660	Enzo Doria	04/2014
3488	6*5^155454+7	108659	Lelio R Paula	11/2014
3489	10^108656+79	108657	Lelio R Paula	02/2017
3490	10^108656-50001	108656	Patrick De Geest	03/2017
3491	2^360918-35	108648	Lelio R Paula	01/2012
3492	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
3493	3*10^108624-49	108625	Robert Price	07/2018
3494	(2^360831+666)/2	108621	Stefano Morozzi	09/2020
3495	(134*10^108610+7)/3	108612	Robert Price	02/2020
3496	(2^360742+3222)/2	108594	Stefano Morozzi	09/2020
3497	2^360706-458903	108584	Enzo Doria	04/2015
3498	2^360641-113185	108564	Enzo Doria	07/2014
3499	2^360618+75019	108557	Enzo Doria	04/2016
3500	(14*10^108545-221)/9	108546	Robert Price	04/2018

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