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 (> 30000)	Who ?	When ?
3251	2^337267-19	101528	Lelio R Paula	07/2011
3252	2^337183-19989	101503	Enzo Doria	06/2013
3253	2^337149+72425	101492	Enzo Doria	04/2016
3254	2^337101-20241	101478	Enzo Doria	06/2013
3255	2^337035-20001	101458	Enzo Doria	06/2013
3256	2^337017-16995	101453	Lelio R Paula	09/2016
3257	2^336979-115315	101441	Enzo Doria	06/2015
3258	2^336970-20885	101439	Enzo Doria	06/2013
3259	2^336958+79	101435	Lelio R Paula	10/2009
3260	2^336942+169	101430	Lelio R Paula	10/2009
3261	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
3262	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
3263	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
3264	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
3265	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
3266	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
3267	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
3268	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
3269	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
3270	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
3271	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
3272	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
3273	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
3274	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
3275	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
3276	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
3277	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
3278	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
3279	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
3280	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3281	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
3282	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3283	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
3284	2^336842+94065	101400	Lelio R Paula	09/2016
3285	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
3286	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
3287	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
3288	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
3289	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
3290	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
3291	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
3292	10^101369+203811	101370	Patrick De Geest	11/2016
3293	10^101369-99	101369	Lelio R Paula	09/2016
3294	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
3295	2^336701-113563	101358	Enzo Doria	08/2014
3296	2^336644-109023	101340	Enzo Doria	04/2014
3297	2^336601-21081	101327	Enzo Doria	06/2013
3298	20^77869+63	101310	Lelio R Paula	09/2016
3299	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
3300	6^130179-137	101299	Lelio R Paula	10/2016
3301	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
3302	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
3303	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
3304	2^336369-19753	101258	Enzo Doria	05/2013
3305	2^336350-344291	101252	Enzo Doria	07/2015
3306	2^336243-108777	101220	Enzo Doria	03/2014
3307	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
3308	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
3309	2^336150-20393	101192	Enzo Doria	06/2013
3310	2^336112-1865249	101180	Enzo Doria	03/2016
3311	2^336103-109015	101178	Enzo Doria	04/2014
3312	13^90809-96	101157	Lelio R Paula	10/2016
3313	19^79098-30	101147	Lelio R Paula	10/2016
3314	19^79095+88	101144	Lelio R Paula	10/2016
3315	15^85976+32	101116	Lelio R Paula	10/2016
3316	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
3317	(4^167933+17)/3	101106	Robert Price	02/2017
3318	2^335858+153	101104	Lelio R Paula	10/2009
3319	6^129918-35	101096	Lelio R Paula	10/2016
3320	3^211885-70	101095	Lelio R Paula	09/2016
3321	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
3322	2^335818-20033	101092	Enzo Doria	06/2013
3323	2^335813-110083	101090	Enzo Doria	04/2014
3324	2^335804+2155	101088	Lelio R Paula	09/2016
3325	2^335784-16145	101082	Enzo Doria	04/2013
3326	11^97051+62	101069	Lelio R Paula	10/2016
3327	3*10^101065+11	101066	Robert Price	07/2018
3328	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
3329	2^335658-94395	101044	Lelio R Paula	09/2016
3330	2^335586+169	101022	Lelio R Paula	10/2009
3331	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
3332	(19*10^100997+737)/9	100998	Robert Price	07/2018
3333	47599!2+1024	100991	Robert Price	02/2015
3334	2^335468-18629	100986	Enzo Doria	05/2013
3335	2^335454-20961	100982	Enzo Doria	06/2013
3336	10^100978+61	100979	Lelio R Paula	09/2016
3337	10^100978-156437	100978	Patrick De Geest	11/2016
3338	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
3339	2^335403-1859167	100967	Enzo Doria	03/2016
3340	23599^18976+18976^23599	100962	Hans Havermann	10/2018
3341	9*2^335364-5	100956	Lelio R Paula	08/2014
3342	2^335349+72287	100951	Enzo Doria	04/2016
3343	2^335329+16095	100945	Lelio R Paula	09/2016
3344	232823#+233663	100937	Makoto Morimoto	10/2017
3345	2^335237-20893	100917	Enzo Doria	06/2013
3346	2^335222-19337	100912	Enzo Doria	05/2013
3347	2^335222-109985	100912	Enzo Doria	04/2014
3348	2^335182-17237	100900	Enzo Doria	05/2013
3349	2^335043-16737	100858	Enzo Doria	05/2013
3350	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
3351	2^335038-20633	100857	Enzo Doria	06/2013
3352	2^335031+1873373	100855	Enzo Doria	06/2016
3353	23489^19650+19650^23489	100847	Hans Havermann	10/2018
3354	3^211354-8816	100842	Enzo Doria	05/2014
3355	2^334984-112757	100841	Enzo Doria	06/2014
3356	29451^2648+2648^29451	100809	Hans Havermann	09/2018
3357	25583^8716+8716^25583	100806	Hans Havermann	08/2018
3358	2^334857+48527	100803	Lelio R Paula	08/2011
3359	12^93406+29	100803	Lelio R Paula	10/2016
3360	28780^3179+3179^28780	100796	Hans Havermann	09/2018
3361	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
3362	2^334809-13	100788	Lelio R Paula	04/2011
3363	(82*10^100780-1)/9	100781	Robert Price	12/2014
3364	31395^1622+1622^31395	100780	Hans Havermann	09/2018
3365	(2^334779+47)/5	100778	Lelio R Paula	12/2013
3366	2^334751+2049	100771	Lelio R Paula	09/2016
3367	13^90443-98	100749	Lelio R Paula	10/2016
3368	(7*10^100737+71)/3	100738	Robert Price	05/2018
3369	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
3370	15^85639-28	100720	Lelio R Paula	10/2016
3371	27068^5259+5259^27068	100718	Hans Havermann	08/2018
3372	2^334562+577294575	100711	Lelio R Paula	09/2016
3373	4*3^211077-5	100710	Lelio R Paula	08/2014
3374	2^334524+145	100702	Lelio R Paula	07/2009
3375	27648^4375+4375^27648	100666	Hans Havermann	09/2018
3376	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
3377	2^334294-113111	100633	Enzo Doria	07/2014
3378	25581^8582+8582^25581	100626	Hans Havermann	08/2018
3379	6^129308-17723	100622	Enzo Doria	03/2013
3380	6^129305+95	100619	Lelio R Paula	10/2016
3381	2^334244-1167	100618	Lelio R Paula	09/2016
3382	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
3383	24885^10984+10984^24885	100555	Hans Havermann	07/2018
3384	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
3385	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
3386	23578^18367+18367^23578	100538	Hans Havermann	07/2018
3387	13^90251+24	100535	Lelio R Paula	10/2016
3388	2^333963+789	100533	Lelio R Paula	08/2011
3389	2^333919-1840087	100520	Enzo Doria	06/2015
3390	2^333911+72623	100518	Enzo Doria	04/2016
3391	24605^12168+12168^24605	100517	Hans Havermann	08/2018
3392	18^80064-67	100503	Lelio R Paula	10/2016
3393	5^143742-48	100472	Lelio R Paula	10/2016
3394	24095^14784+14784^24095	100472	Hans Havermann	08/2018
3395	2^333757-112123	100471	Enzo Doria	06/2014
3396	27358^4693+4693^27358	100444	Hans Havermann	07/2018
3397	2^333603-108861	100425	Enzo Doria	03/2014
3398	9*7^118818-2	100414	Lelio R Paula	11/2014
3399	2^333546-17097	100408	Enzo Doria	05/2013
3400	17^81597+72	100401	Lelio R Paula	10/2016
3401	p(20559)#/2+8	100384	Robert Price	01/2017
3402	11^96390-24	100380	Lelio R Paula	10/2016
3404	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
3403	23565^18136+18136^23565	100353	Hans Havermann	07/2018
3405	2^333354+763	100350	Lelio R Paula	08/2011
3406	2^333289-109483	100330	Enzo Doria	04/2014
3407	2^333240-2790209	100316	Enzo Doria	03/2016
3408	23601^17798+17798^23601	100314	Hans Havermann	05/2018
3410	(2^333227-2^166614+1)/5	100311		11/2006
3409	2^333225+719	100311	Lelio R Paula	08/2011
3411	2^333221-2785333	100310	Enzo Doria	10/2015
3412	76^53332-75	100308	Norbert Schneider	02/2015
3413	6^128892-17573	100298	Enzo Doria	03/2013
3414	2^333105-113215	100275	Enzo Doria	07/2014
3415	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
3416	4*10^100257-83	100258	Robert Price	10/2018
3417	17^81476-74	100253	Lelio R Paula	10/2016
3418	23392^19207+19207^23392	100199	Hans Havermann	06/2018
3419	17^81417-16	100180	Theodore Burton	11/2005
3420	2^332739-113215	100165	Enzo Doria	07/2014
3421	2^332730-1865621	100162	Enzo Doria	03/2016
3422	91^51127-2	100160	Lelio R Paula	09/2013
3423	15^85159-32	100155	Lelio R Paula	10/2016
3424	6^128661+97	100118	Lelio R Paula	10/2016
3425	19^78285+40	100108	Lelio R Paula	07/2016
3426	6^128640+5	100102	Lelio R Paula	11/2014
3427	28562^3189+3189^28562	100072	Hans Havermann	05/2018
3428	6^128565-127	100044	Lelio R Paula	08/2016
3429	2^332309-133	100035	Lelio R Paula	02/2011
3430	2^332307+731	100035	Lelio R Paula	07/2011
3431	2^332301+12927	100033	Lelio R Paula	04/2013
3432	23406^18781+18781^23406	100031	Hans Havermann	04/2018
3433	12^92684-13	100023	Lelio R Paula	07/2016
3434	10^100002+236023	100003	Stefano Morozzi	05/2018
3435	10^100002+433741	100003	Stefano Morozzi	05/2018
3436	(10^100002-1)/9-10^33441	100002	Akihiko Yoshida	03/2018
3437	(10^100002-1)/9-10^44692	100002	Akihiko Yoshida	03/2018
3438	10^100002-249519	100002	Patrick De Geest	07/2018
3439	10^100001+314199	100002	Patrick De Geest	07/2018
3488	25206!+p(4114)	100001	Henri Lifchitz	09/2005
3489	25206!-p(5447)	100001	Henri Lifchitz	10/2005
3490	25206!-p(12402)	100001	Henri Lifchitz	04/2006
3491	25206!-p(16290)	100001	Henri Lifchitz	09/2006
3492	25206!-p(19647)	100001	Henri Lifchitz	02/2007
3493	2^332194+11473	100001	Henri Lifchitz	03/2007
3448	10^100000+342909	100001	Milton L. Brown	12/2007
3465	10^100000+346579	100001	Robert Price	04/2012
3466	10^100000+829767	100001	Robert Price	05/2012
3467	10^100000+871899	100001	Robert Price	05/2012
3468	10^100000+1475997	100001	Robert Price	07/2012
3481	10^100000+1751769	100001	Robert Price	08/2012
3482	10^100000+2155489	100001	Robert Price	10/2012
3483	10^100000+2483527	100001	Robert Price	12/2012
3484	10^100000+2503087	100001	Robert Price	12/2012
3485	10^100000+2686179	100001	Robert Price	12/2012
3486	10^100000+2688933	100001	Robert Price	12/2012
3487	10^100000+3667159	100001	Robert Price	08/2013
3477	10^100000+3938473	100001	Robert Price	05/2015
3478	10^100000+3979761	100001	Robert Price	05/2015
3479	10^100000+4293973	100001	Robert Price	09/2015
3449	10^100000+4858267	100001	Robert Price	12/2015
3450	10^100000+5113299	100001	Robert Price	02/2016
3451	10^100000+5169411	100001	Robert Price	02/2016
3469	10^100000+5354043	100001	Robert Price	05/2016
3470	10^100000+5717979	100001	Robert Price	05/2016
3471	10^100000+6080631	100001	Robert Price	07/2016
3472	10^100000+6308469	100001	Robert Price	07/2016
3473	10^100000+6512023	100001	Robert Price	08/2016
3474	10^100000+6596557	100001	Robert Price	08/2016
3475	10^100000+7115409	100001	Robert Price	10/2016
3476	10^100000+7235803	100001	Robert Price	10/2016
3452	10^100000+7867333	100001	Robert Price	12/2016
3453	10^100000+8743093	100001	Robert Price	02/2017
3454	10^100000+8955391	100001	Robert Price	03/2017
3455	10^100000+9180019	100001	Robert Price	03/2017
3456	10^100000+9225987	100001	Robert Price	04/2017
3457	10^100000+9265587	100001	Robert Price	04/2017
3458	10^100000+9287049	100001	Robert Price	04/2017
3459	10^100000+9425053	100001	Robert Price	05/2017
3460	10^100000+9450769	100001	Robert Price	05/2017
3461	10^100000+9528747	100001	Robert Smith	05/2017
3462	10^100000+9548071	100001	Robert Price	06/2017
3463	10^100000+10064287	100001	Robert Price	08/2017
3464	10^100000+10229569	100001	Robert Price	10/2017
3440	10^100000+11187931	100001	Robert Price	03/2018
3441	10^100000+11264721	100001	Robert Price	04/2018
3442	10^100000+11477661	100001	Robert Price	05/2018
3443	10^100000+11644653	100001	Robert Price	07/2018
3444	10^100001-431439	100001	Patrick De Geest	07/2018
3445	10^100000+11769399	100001	Robert Price	08/2018
3446	10^100000+11848159	100001	Robert Price	08/2018
3447	10^100000+11863467	100001	Robert Price	08/2018
3480	10^100000+11992051	100001	Robert Price	09/2018
3494	10^99999+309403	100000	Daniel Heuer	01/2004
3495	10^100000-260199	100000	Patrick De Geest	01/2010
3496	10^99999-59511	99999	Patrick De Geest	07/2009
3497	2^332141-113073	99985	Enzo Doria	07/2014
3499	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
3498	23827^15702+15702^23827	99978	Hans Havermann	04/2018
3500	2^332085+1865897	99968	Enzo Doria	03/2016

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PRP Records

Probable Primes Top 10000

(224660 PRPs in the top)