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 ?
3251	29863^24790+24790^29863	131227	Hans Havermann	03/2021
3252	(5*10^131223-29)/3	131224	Robert Price	03/2018
3253	29524^27825+27825^29524	131218	Hans Havermann	03/2021
3254	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
3255	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
3256	30639^19136+19136^30639	131192	Hans Havermann	04/2021
3257	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
3258	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
3259	2^435773+1875557	131181	Enzo Doria	06/2016
3261	(16*10^131180+167)/3	131181	Robert Price	06/2019
3260	(26*10^131180-77)/3	131181	Robert Price	11/2019
3262	(25*10^131144-7)/9	131145	Robert Price	05/2018
3263	29299^29358-29358^29299	131138	Norbert Schneider	03/2022
3264	2^435612-2789939	131133	Enzo Doria	12/2015
3265	33976^7231+7231^33976	131121	Hans Havermann	03/2021
3266	33715^7746+7746^33715	131121	Hans Havermann	03/2021
3267	66^72047-65^72047	131093	Robert Price	09/2013
3268	(5*10^131090+37)/3	131091	Robert Price	03/2018
3269	2^435468+75631	131089	Enzo Doria	04/2016
3270	37^83588-2	131083	Lelio R Paula	08/2015
3271	(4^217720+11)/3	131081	Robert Price	02/2017
3272	30407^20448+20448^30407	131074	Hans Havermann	04/2021
3273	(22*10^131070+179)/3	131071	Robert Price	02/2022
3274	29487^27836+27836^29487	131059	Hans Havermann	04/2021
3275	29962^23615+23615^29962	131030	Hans Havermann	03/2021
3276	2^435202-113193	131009	Enzo Doria	07/2014
3277	41705^1384+1384^41705	131002	Hans Havermann	04/2021
3278	9*10^130998-19	130999	Robert Price	07/2019
3279	36243^4108+4108^36243	130969	Hans Havermann	04/2021
3280	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
3281	2^434835-111937	130899	Enzo Doria	05/2014
3282	(62*10^130895-629)/9	130896	Robert Price	07/2021
3283	2^434685+72257	130854	Enzo Doria	04/2016
3284	(7*10^130825+113)/3	130826	Robert Price	02/2018
3285	2^434539-29317	130810	Enzo Doria	07/2015
3286	(74*10^130791+637)/9	130792	Robert Price	01/2022
3287	2^434469-114259	130789	Enzo Doria	01/2015
3288	(5*10^130763+103)/9	130763	Robert Price	04/2022
3289	2^434246+33	130722	Robert Price	11/2015
3290	30156^21599+21599^30156	130710	Hans Havermann	04/2021
3291	(17*10^130695-161)/9	130695	Robert Price	02/2021
3292	30513^19148+19148^30513	130661	Hans Havermann	03/2021
3293	29736^24761+24761^29736	130654	Hans Havermann	04/2021
3294	9*10^130638+41	130639	Robert Price	08/2020
3295	2^433911-91	130621	Lelio R Paula	06/2017
3296	30786^17449+17449^30786	130588	Hans Havermann	03/2021
3297	2^433744-114419	130570	Enzo Doria	02/2015
3299	2^433708+1869451	130560	Enzo Doria	05/2016
3298	2^433710+93	130560	Lelio R Paula	06/2017
3300	(9629^32768+1)/120501441265666	130520	Kellen Shenton	05/2021
3301	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
3302	3^273521+10	130503	Tyler NeSmith	01/2021
3303	41659^1356+1356^41659	130487	Hans Havermann	03/2021
3304	4*10^130480+9	130481	Robert Price	05/2015
3305	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
3306	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
3307	(31*10^130414-49)/9	130415	Robert Price	11/2021
3308	33481^7848+7848^33481	130401	Hans Havermann	03/2021
3309	(22*10^130392+203)/9	130393	Robert Price	10/2021
3310	29773^23950+23950^29773	130386	Hans Havermann	04/2021
3311	2^433023-113497	130353	Enzo Doria	08/2014
3312	31175^15178+15178^31175	130350	Hans Havermann	04/2021
3313	2^433002+1179379	130347	Enzo Doria	06/2016
3314	2^432974+19	130339	Robert Price	08/2015
3315	31903^12168+12168^31903	130331	Hans Havermann	04/2021
3316	29387^27112+27112^29387	130278	Hans Havermann	04/2021
3317	29577^25370+25370^29577	130267	Hans Havermann	04/2021
3318	31738^12685+12685^31738	130231	Hans Havermann	03/2021
3319	44235^878+878^44235	130206	Hans Havermann	04/2021
3320	32160^11171+11171^32160	130187	Hans Havermann	04/2021
3321	29489^25956+25956^29489	130172	Hans Havermann	04/2021
3322	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
3323	33005^8766+8766^33005	130133	Hans Havermann	04/2021
3324	(35*10^130132-611)/9	130133	Robert Price	02/2022
3325	2^432217+41	130111	Lelio R Paula	06/2017
3326	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
3327	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
3328	97^65480-2	130094	Lelio R Paula	05/2017
3329	36007^4102+4102^36007	130094	Hans Havermann	04/2021
3330	4*10^130088-89	130089	Robert Price	11/2018
3331	2^432117-113215	130081	Enzo Doria	07/2014
3332	2^431804+72511	129986	Enzo Doria	04/2016
3333	(13*10^129896+137)/3	129897	Robert Price	06/2021
3334	(13*10^129890+71)/3	129891	Robert Price	06/2021
3335	29048^29101-29101^29048	129882	Norbert Schneider	03/2022
3336	37832^2709+2709^37832	129871	Hans Havermann	04/2021
3337	31055^15184+15184^31055	129853	Hans Havermann	04/2021
3338	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
3339	31385^13702+13702^31385	129833	Hans Havermann	04/2021
3340	28901^29102-29102^28901	129822	Norbert Schneider	03/2022
3341	(47*10^129789-119)/9	129790	Robert Price	05/2019
3342	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
3343	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
3344	2^430807+1869563	129686	Enzo Doria	05/2016
3345	2^430721-21429	129660	Enzo Doria	07/2013
3346	(4*10^129618+89)/3	129619	Robert Price	08/2021
3347	2^430415-276271	129568	Enzo Doria	07/2015
3348	32282^10311+10311^32282	129558	Hans Havermann	04/2021
3349	29486^24741+24741^29486	129545	Hans Havermann	04/2021
3350	(29*10^129543+313)/9	129544	Robert Price	04/2021
3351	37095^3104+3104^37095	129533	Hans Havermann	04/2021
3352	31132^14459+14459^31132	129514	Hans Havermann	04/2021
3353	32582^9435+9435^32582	129506	Hans Havermann	03/2021
3354	30442^17953+17953^30442	129505	Hans Havermann	03/2021
3355	(199*10^129487-7)/3	129489	Robert Price	05/2020
3356	2^430142-2791721	129486	Enzo Doria	03/2016
3357	(7*10^129472-13)/3	129473	Robert Price	07/2018
3358	(8*10^129469+79)/3	129470	Robert Price	10/2020
3359	31678^12213+12213^31678	129463	Hans Havermann	04/2021
3360	(772*10^129406-7)/9	129408	Robert Price	06/2022
3361	31100^14439+14439^31100	129362	Hans Havermann	04/2021
3362	33009^8288+8288^33009	129345	Hans Havermann	04/2021
3363	29675^22804+22804^29675	129324	Hans Havermann	04/2021
3364	29068^28099+28099^29068	129315	Hans Havermann	04/2021
3365	2^429568-21017	129313	Enzo Doria	07/2013
3366	(10^129295+83)/3	129295	Robert Price	08/2021
3367	(853*10^129274-7)/9	129276	Robert Price	07/2021
3368	30958^14961+14961^30958	129249	Hans Havermann	04/2021
3369	(11*10^129239-179)/3	129240	Robert Price	09/2018
3370	28659^28988+28988^28659	129208	Norbert Schneider	02/2021
3371	29423^24616+24616^29423	129203	Hans Havermann	03/2021
3372	2^429194-112685	129201	Enzo Doria	06/2014
3373	2^429145-2780449	129186	Enzo Doria	04/2016
3374	32500^9427+9427^32500	129168	Hans Havermann	04/2021
3375	33577^7014+7014^33577	129136	Hans Havermann	03/2021
3376	2^428892-113453	129110	Enzo Doria	07/2014
3377	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
3378	2^428727-113959	129060	Enzo Doria	10/2014
3379	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
3380	(10^129051-31)/3	129051	Serge Batalov	12/2014
3381	(134*10^129038+7)/3	129040	Robert Price	02/2020
3382	2^428564+71161	129011	Enzo Doria	04/2016
3383	28781^28930+28930^28781	129002	Norbert Schneider	02/2021
3384	29065^27424+27424^29065	128995	Hans Havermann	04/2021
3385	2^428502-113285	128992	Enzo Doria	07/2014
3386	2^428421-21373	128968	Enzo Doria	06/2013
3387	L(616787)	128901	Henri Lifchitz	09/2008
3388	20^99055-3	128874	Paul Bourdelais	12/2020
3389	91^65772-2	128851	Lelio R Paula	05/2017
3390	2^428022+43	128848	Lelio R Paula	05/2017
3391	2^427999-459397	128841	Enzo Doria	05/2015
3392	2^427993+76847	128839	Enzo Doria	05/2016
3393	31059^14060+14060^31059	128833	Hans Havermann	03/2021
3394	10^128805+152871	128806	Patrick De Geest	05/2021
3395	10^128805-10001	128805	Robert Price	02/2021
3396	2^427824-1851507	128788	Enzo Doria	08/2015
3397	2^427807-21469	128783	Enzo Doria	07/2013
3398	29082^26783+26783^29082	128772	Hans Havermann	04/2021
3399	40055^1638+1638^40055	128750	Hans Havermann	04/2021
3400	11^123594-240	128710	Enzo Doria	09/2012
3401	2^427504-21503	128692	Enzo Doria	07/2013
3402	37727^2574+2574^37727	128673	Hans Havermann	04/2021
3403	29686^21591+21591^29686	128668	Hans Havermann	04/2021
3404	10^128668-70000000001	128668	Robert Price	08/2021
3405	2^427420+91	128667	Lelio R Paula	05/2017
3406	8*10^128651-37	128652	Robert Price	03/2022
3407	(68*10^128645-257)/9	128646	Robert Price	07/2019
3408	2^427269-113635	128621	Enzo Doria	08/2014
3409	2^427130+1877569	128579	Enzo Doria	08/2016
3410	2^427016-115349	128545	Enzo Doria	07/2015
3411	(4*10^128510+137)/3	128511	Robert Price	03/2018
3412	2^426889-112879	128507	Enzo Doria	06/2014
3413	2^426804+1869931	128481	Enzo Doria	05/2016
3414	2^426750+77635	128465	Enzo Doria	05/2016
3415	36988^2969+2969^36988	128445	Hans Havermann	03/2021
3416	36664^3185+3185^36664	128439	Hans Havermann	03/2021
3417	32618^8649+8649^32618	128416	Hans Havermann	04/2021
3418	28883^27874+27874^28883	128391	Hans Havermann	04/2021
3419	2^426425-91	128367	Lelio R Paula	05/2017
3420	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
3421	2^426352+74971	128345	Enzo Doria	04/2016
3422	(199*10^128343-7)/3	128345	Robert Price	05/2020
3423	4*10^128343-21	128344	Robert Price	09/2018
3424	(65*10^128338+493)/9	128339	Robert Price	08/2021
3425	35632^3997+3997^35632	128337	Hans Havermann	04/2021
3426	2^426300-1863689	128330	Enzo Doria	03/2016
3427	2^426293+1881017	128327	Enzo Doria	11/2016
3428	(88*10^128324-637)/9	128325	Robert Price	11/2020
3429	(491*10^128285+31)/9	128287	Robert Price	04/2022
3430	39103^1908+1908^39103	128281	Hans Havermann	04/2021
3431	2^426043+35	128252	Robert Price	11/2015
3432	(4*10^128244-19)/3	128245	Robert Price	03/2018
3433	35489^4102+4102^35489	128222	Hans Havermann	04/2021
3434	34721^4926+4926^34721	128208	Hans Havermann	04/2021
3435	(305*10^128198+1)/9	128200	Robert Price	02/2020
3436	2^425808-459959	128181	Enzo Doria	06/2015
3437	30632^15291+15291^30632	128178	Hans Havermann	04/2021
3438	35981^3648+3648^35981	128167	Hans Havermann	04/2021
3439	2^425627-113605	128127	Enzo Doria	08/2014
3440	(4*10^128109+119)/3	128110	Robert Price	12/2021
3441	(22*10^128094+53)/3	128095	Robert Price	07/2019
3442	(86*10^128086-221)/9	128087	Robert Price	09/2019
3443	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
3444	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
3445	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
3446	2^425205+4911	128000	Marek Hubal	02/2017
3447	29241^23836+23836^29241	127995	Hans Havermann	04/2021
3448	2^425118-113663	127974	Enzo Doria	08/2014
3449	(86*10^127967-329)/9	127968	Robert Price	01/2020
3450	2^425061+1869761	127957	Enzo Doria	05/2016
3451	746^44541+44541^746	127955	Norbert Schneider	07/2019
3452	30236^17043+17043^30236	127946	Hans Havermann	03/2021
3453	2^424918-21141	127914	Enzo Doria	07/2013
3454	(62*10^127903+91)/9	127904	Robert Price	07/2021
3455	2^424864-29489	127897	Enzo Doria	08/2015
3456	30438^15893+15893^30438	127877	Hans Havermann	02/2021
3457	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
3458	28929^26258+26258^28929	127845	Hans Havermann	03/2021
3459	30563^15220+15220^30563	127828	Hans Havermann	03/2021
3460	2^424632-2786639	127827	Enzo Doria	03/2016
3461	10^127821-700001	127821	Robert Price	08/2021
3462	2^424577-113755	127811	Enzo Doria	09/2014
3463	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
3464	(56*10^127752+691)/9	127753	Robert Price	05/2019
3465	11^122629-720	127705	Enzo Doria	11/2012
3466	22*10^127645+3	127647	Robert Price	01/2020
3467	28715^27844+27844^28715	127631	Hans Havermann	03/2021
3468	(56*10^127612+187)/9	127613	Robert Price	10/2021
3469	(5*36^81995+821)/7	127609	Eric Chen	01/2021
3470	4*10^127562-39	127563	Robert Price	09/2020
3471	32595^8186+8186^32595	127547	Hans Havermann	03/2021
3472	2^423696-21429	127546	Enzo Doria	07/2013
3473	2^423664-1864559	127536	Enzo Doria	03/2016
3474	37889^2322+2322^37889	127530	Hans Havermann	03/2021
3475	37668^2429+2429^37668	127523	Hans Havermann	03/2021
3476	3^267267-4	127519	Henri Lifchitz	10/2014
3477	(103*10^127491+17)/3	127493	Robert Price	08/2020
3478	29376^21869+21869^29376	127487	Hans Havermann	03/2021
3479	31186^12241+12241^31186	127483	Hans Havermann	02/2021
3480	(19^99689+5^99689)/24	127477	Robert Price	09/2013
3481	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
3482	30594^14645+14645^30594	127446	Hans Havermann	03/2021
3483	2^423328-21537	127435	Enzo Doria	07/2013
3484	(67*10^127413-7)/3	127415	Robert Price	01/2020
3485	(2*10^127407+73)/3	127407	Robert Price	09/2020
3486	(2^423165-7)/25	127384	Lelio R Paula	05/2015
3487	(7726^32768+1)/13917994151414876602369	127379	Kellen Shenton	04/2021
3488	29512^20647+20647^29512	127341	Hans Havermann	03/2021
3489	(112*10^127324+17)/3	127326	Robert Price	03/2020
3490	29565^20252+20252^29565	127321	Hans Havermann	03/2021
3492	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
3491	(5^182099-3^182099)/2	127282	Kellen Shenton	05/2022
3493	(16*10^127259+197)/3	127260	Robert Price	04/2019
3494	(26*10^127240+61)/3	127241	Robert Price	10/2019
3495	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
3496	2^422515-114997	127190	Enzo Doria	06/2015
3497	5*10^127179-3	127180	Robert Price	07/2015
3498	31678^10343+10343^31678	127176	Hans Havermann	03/2021
3499	(44*10^127169-233)/9	127170	Robert Price	01/2019
3500	34947^4352+4352^34947	127162	Hans Havermann	03/2021

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Probable Primes Top 10000

(290751 PRPs in the top)