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 ?
3501	(5*10^131090+37)/3	131091	Robert Price	03/2018
3502	2^435468+75631	131089	Enzo Doria	04/2016
3503	37^83588-2	131083	Lelio R Paula	08/2015
3504	(4^217720+11)/3	131081	Robert Price	02/2017
3505	30407^20448+20448^30407	131074	Hans Havermann	04/2021
3506	(22*10^131070+179)/3	131071	Robert Price	02/2022
3507	29487^27836+27836^29487	131059	Hans Havermann	04/2021
3508	29962^23615+23615^29962	131030	Hans Havermann	03/2021
3509	2^435202-113193	131009	Enzo Doria	07/2014
3510	41705^1384+1384^41705	131002	Hans Havermann	04/2021
3511	9*10^130998-19	130999	Robert Price	07/2019
3512	36243^4108+4108^36243	130969	Hans Havermann	04/2021
3513	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
3514	2^434835-111937	130899	Enzo Doria	05/2014
3515	(62*10^130895-629)/9	130896	Robert Price	07/2021
3516	2^434685+72257	130854	Enzo Doria	04/2016
3517	(7*10^130825+113)/3	130826	Robert Price	02/2018
3518	2^434539-29317	130810	Enzo Doria	07/2015
3519	(74*10^130791+637)/9	130792	Robert Price	01/2022
3520	2^434469-114259	130789	Enzo Doria	01/2015
3521	(5*10^130763+103)/9	130763	Robert Price	04/2022
3522	2^434246+33	130722	Robert Price	11/2015
3523	30156^21599+21599^30156	130710	Hans Havermann	04/2021
3524	(17*10^130695-161)/9	130695	Robert Price	02/2021
3525	30513^19148+19148^30513	130661	Hans Havermann	03/2021
3526	29736^24761+24761^29736	130654	Hans Havermann	04/2021
3527	9*10^130638+41	130639	Robert Price	08/2020
3528	2^433911-91	130621	Lelio R Paula	06/2017
3529	30786^17449+17449^30786	130588	Hans Havermann	03/2021
3530	2^433744-114419	130570	Enzo Doria	02/2015
3532	2^433708+1869451	130560	Enzo Doria	05/2016
3531	2^433710+93	130560	Lelio R Paula	06/2017
3533	7*10^130535-27	130536	Robert Price	11/2022
3534	(9629^32768+1)/120501441265666	130520	Kellen Shenton	05/2021
3535	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
3536	3^273521+10	130503	Tyler NeSmith	01/2021
3537	41659^1356+1356^41659	130487	Hans Havermann	03/2021
3538	4*10^130480+9	130481	Robert Price	05/2015
3539	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
3540	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
3541	(31*10^130414-49)/9	130415	Robert Price	11/2021
3542	33481^7848+7848^33481	130401	Hans Havermann	03/2021
3543	(22*10^130392+203)/9	130393	Robert Price	10/2021
3544	29773^23950+23950^29773	130386	Hans Havermann	04/2021
3545	2^433023-113497	130353	Enzo Doria	08/2014
3546	31175^15178+15178^31175	130350	Hans Havermann	04/2021
3547	2^433002+1179379	130347	Enzo Doria	06/2016
3548	2^432974+19	130339	Robert Price	08/2015
3549	31903^12168+12168^31903	130331	Hans Havermann	04/2021
3550	29387^27112+27112^29387	130278	Hans Havermann	04/2021
3551	29577^25370+25370^29577	130267	Hans Havermann	04/2021
3552	31738^12685+12685^31738	130231	Hans Havermann	03/2021
3553	44235^878+878^44235	130206	Hans Havermann	04/2021
3554	32160^11171+11171^32160	130187	Hans Havermann	04/2021
3555	29489^25956+25956^29489	130172	Hans Havermann	04/2021
3556	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
3557	33005^8766+8766^33005	130133	Hans Havermann	04/2021
3558	(35*10^130132-611)/9	130133	Robert Price	02/2022
3559	2^432217+41	130111	Lelio R Paula	06/2017
3560	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
3561	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
3562	97^65480-2	130094	Lelio R Paula	05/2017
3563	36007^4102+4102^36007	130094	Hans Havermann	04/2021
3564	4*10^130088-89	130089	Robert Price	11/2018
3565	2^432117-113215	130081	Enzo Doria	07/2014
3566	(4*10^130080+41)/9	130080	Serge Batalov	11/2022
3567	2^431804+72511	129986	Enzo Doria	04/2016
3568	(13*10^129896+137)/3	129897	Robert Price	06/2021
3569	(13*10^129890+71)/3	129891	Robert Price	06/2021
3570	29048^29101-29101^29048	129882	Norbert Schneider	03/2022
3571	37832^2709+2709^37832	129871	Hans Havermann	04/2021
3572	31055^15184+15184^31055	129853	Hans Havermann	04/2021
3573	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
3574	31385^13702+13702^31385	129833	Hans Havermann	04/2021
3575	28901^29102-29102^28901	129822	Norbert Schneider	03/2022
3576	(47*10^129789-119)/9	129790	Robert Price	05/2019
3577	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
3578	(166*10^129712+17)/3	129714	Robert Price	07/2022
3579	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
3580	2^430807+1869563	129686	Enzo Doria	05/2016
3581	2^430721-21429	129660	Enzo Doria	07/2013
3582	(4*10^129618+89)/3	129619	Robert Price	08/2021
3583	2^430415-276271	129568	Enzo Doria	07/2015
3584	32282^10311+10311^32282	129558	Hans Havermann	04/2021
3585	29486^24741+24741^29486	129545	Hans Havermann	04/2021
3586	(29*10^129543+313)/9	129544	Robert Price	04/2021
3587	37095^3104+3104^37095	129533	Hans Havermann	04/2021
3588	31132^14459+14459^31132	129514	Hans Havermann	04/2021
3589	32582^9435+9435^32582	129506	Hans Havermann	03/2021
3590	30442^17953+17953^30442	129505	Hans Havermann	03/2021
3591	(199*10^129487-7)/3	129489	Robert Price	05/2020
3592	2^430142-2791721	129486	Enzo Doria	03/2016
3593	(7*10^129472-13)/3	129473	Robert Price	07/2018
3594	(8*10^129469+79)/3	129470	Robert Price	10/2020
3595	31678^12213+12213^31678	129463	Hans Havermann	04/2021
3596	(772*10^129406-7)/9	129408	Robert Price	06/2022
3597	31100^14439+14439^31100	129362	Hans Havermann	04/2021
3598	33009^8288+8288^33009	129345	Hans Havermann	04/2021
3599	29675^22804+22804^29675	129324	Hans Havermann	04/2021
3600	29068^28099+28099^29068	129315	Hans Havermann	04/2021
3601	2^429568-21017	129313	Enzo Doria	07/2013
3602	(10^129295+83)/3	129295	Robert Price	08/2021
3603	(853*10^129274-7)/9	129276	Robert Price	07/2021
3604	30958^14961+14961^30958	129249	Hans Havermann	04/2021
3605	(11*10^129239-179)/3	129240	Robert Price	09/2018
3606	28659^28988+28988^28659	129208	Norbert Schneider	02/2021
3607	29423^24616+24616^29423	129203	Hans Havermann	03/2021
3608	2^429194-112685	129201	Enzo Doria	06/2014
3609	2^429145-2780449	129186	Enzo Doria	04/2016
3610	32500^9427+9427^32500	129168	Hans Havermann	04/2021
3611	33577^7014+7014^33577	129136	Hans Havermann	03/2021
3612	2^428892-113453	129110	Enzo Doria	07/2014
3613	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
3614	2^428727-113959	129060	Enzo Doria	10/2014
3615	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
3616	(10^129051-31)/3	129051	Serge Batalov	12/2014
3617	(134*10^129038+7)/3	129040	Robert Price	02/2020
3618	2^428564+71161	129011	Enzo Doria	04/2016
3619	28781^28930+28930^28781	129002	Norbert Schneider	02/2021
3620	29065^27424+27424^29065	128995	Hans Havermann	04/2021
3621	2^428502-113285	128992	Enzo Doria	07/2014
3622	2^428421-21373	128968	Enzo Doria	06/2013
3623	L(616787)	128901	Henri Lifchitz	09/2008
3624	20^99055-3	128874	Paul Bourdelais	12/2020
3625	91^65772-2	128851	Lelio R Paula	05/2017
3626	2^428022+43	128848	Lelio R Paula	05/2017
3627	2^427999-459397	128841	Enzo Doria	05/2015
3628	2^427993+76847	128839	Enzo Doria	05/2016
3629	31059^14060+14060^31059	128833	Hans Havermann	03/2021
3630	10^128805+152871	128806	Patrick De Geest	05/2021
3631	10^128805-10001	128805	Robert Price	02/2021
3632	2^427824-1851507	128788	Enzo Doria	08/2015
3633	2^427807-21469	128783	Enzo Doria	07/2013
3634	29082^26783+26783^29082	128772	Hans Havermann	04/2021
3635	40055^1638+1638^40055	128750	Hans Havermann	04/2021
3636	11^123594-240	128710	Enzo Doria	09/2012
3637	2^427504-21503	128692	Enzo Doria	07/2013
3638	37727^2574+2574^37727	128673	Hans Havermann	04/2021
3639	29686^21591+21591^29686	128668	Hans Havermann	04/2021
3640	10^128668-70000000001	128668	Robert Price	08/2021
3641	2^427420+91	128667	Lelio R Paula	05/2017
3642	8*10^128651-37	128652	Robert Price	03/2022
3643	(68*10^128645-257)/9	128646	Robert Price	07/2019
3644	2^427269-113635	128621	Enzo Doria	08/2014
3645	2^427130+1877569	128579	Enzo Doria	08/2016
3646	2^427016-115349	128545	Enzo Doria	07/2015
3647	(4*10^128510+137)/3	128511	Robert Price	03/2018
3648	2^426889-112879	128507	Enzo Doria	06/2014
3649	2^426804+1869931	128481	Enzo Doria	05/2016
3650	2^426750+77635	128465	Enzo Doria	05/2016
3651	36988^2969+2969^36988	128445	Hans Havermann	03/2021
3652	36664^3185+3185^36664	128439	Hans Havermann	03/2021
3653	32618^8649+8649^32618	128416	Hans Havermann	04/2021
3654	28883^27874+27874^28883	128391	Hans Havermann	04/2021
3655	2^426425-91	128367	Lelio R Paula	05/2017
3656	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
3657	2^426352+74971	128345	Enzo Doria	04/2016
3658	(199*10^128343-7)/3	128345	Robert Price	05/2020
3659	4*10^128343-21	128344	Robert Price	09/2018
3660	(65*10^128338+493)/9	128339	Robert Price	08/2021
3661	35632^3997+3997^35632	128337	Hans Havermann	04/2021
3662	2^426300-1863689	128330	Enzo Doria	03/2016
3663	2^426293+1881017	128327	Enzo Doria	11/2016
3664	(88*10^128324-637)/9	128325	Robert Price	11/2020
3665	(491*10^128285+31)/9	128287	Robert Price	04/2022
3666	39103^1908+1908^39103	128281	Hans Havermann	04/2021
3667	2^426043+35	128252	Robert Price	11/2015
3668	(4*10^128244-19)/3	128245	Robert Price	03/2018
3669	35489^4102+4102^35489	128222	Hans Havermann	04/2021
3670	34721^4926+4926^34721	128208	Hans Havermann	04/2021
3671	(305*10^128198+1)/9	128200	Robert Price	02/2020
3672	2^425808-459959	128181	Enzo Doria	06/2015
3673	30632^15291+15291^30632	128178	Hans Havermann	04/2021
3674	35981^3648+3648^35981	128167	Hans Havermann	04/2021
3675	2^425627-113605	128127	Enzo Doria	08/2014
3676	(4*10^128109+119)/3	128110	Robert Price	12/2021
3677	(22*10^128094+53)/3	128095	Robert Price	07/2019
3678	(86*10^128086-221)/9	128087	Robert Price	09/2019
3679	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
3680	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
3681	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
3682	Phi(149401,10)/30037901719561	128003	Makoto Kamada	07/2022
3683	2^425205+4911	128000	Marek Hubal	02/2017
3684	29241^23836+23836^29241	127995	Hans Havermann	04/2021
3685	2^425118-113663	127974	Enzo Doria	08/2014
3686	(86*10^127967-329)/9	127968	Robert Price	01/2020
3687	2^425061+1869761	127957	Enzo Doria	05/2016
3688	746^44541+44541^746	127955	Norbert Schneider	07/2019
3689	30236^17043+17043^30236	127946	Hans Havermann	03/2021
3690	2^424918-21141	127914	Enzo Doria	07/2013
3691	(62*10^127903+91)/9	127904	Robert Price	07/2021
3692	2^424864-29489	127897	Enzo Doria	08/2015
3693	30438^15893+15893^30438	127877	Hans Havermann	02/2021
3694	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
3695	28929^26258+26258^28929	127845	Hans Havermann	03/2021
3696	30563^15220+15220^30563	127828	Hans Havermann	03/2021
3697	2^424632-2786639	127827	Enzo Doria	03/2016
3698	10^127821-700001	127821	Robert Price	08/2021
3699	2^424577-113755	127811	Enzo Doria	09/2014
3700	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
3701	(56*10^127752+691)/9	127753	Robert Price	05/2019
3702	11^122629-720	127705	Enzo Doria	11/2012
3703	22*10^127645+3	127647	Robert Price	01/2020
3704	28715^27844+27844^28715	127631	Hans Havermann	03/2021
3705	(56*10^127612+187)/9	127613	Robert Price	10/2021
3706	(5*36^81995+821)/7	127609	Eric Chen	01/2021
3707	4*10^127562-39	127563	Robert Price	09/2020
3708	32595^8186+8186^32595	127547	Hans Havermann	03/2021
3709	2^423696-21429	127546	Enzo Doria	07/2013
3710	2^423664-1864559	127536	Enzo Doria	03/2016
3711	37889^2322+2322^37889	127530	Hans Havermann	03/2021
3712	37668^2429+2429^37668	127523	Hans Havermann	03/2021
3713	3^267267-4	127519	Henri Lifchitz	10/2014
3714	(103*10^127491+17)/3	127493	Robert Price	08/2020
3715	29376^21869+21869^29376	127487	Hans Havermann	03/2021
3716	31186^12241+12241^31186	127483	Hans Havermann	02/2021
3717	(19^99689+5^99689)/24	127477	Robert Price	09/2013
3718	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
3719	30594^14645+14645^30594	127446	Hans Havermann	03/2021
3720	2^423328-21537	127435	Enzo Doria	07/2013
3721	(67*10^127413-7)/3	127415	Robert Price	01/2020
3722	(2*10^127407+73)/3	127407	Robert Price	09/2020
3723	(2^423165-7)/25	127384	Lelio R Paula	05/2015
3724	(7726^32768+1)/13917994151414876602369	127379	Kellen Shenton	04/2021
3725	(4*10^127349+17)/3	127350	Tyler Busby	01/2023
3726	29512^20647+20647^29512	127341	Hans Havermann	03/2021
3727	(112*10^127324+17)/3	127326	Robert Price	03/2020
3728	29565^20252+20252^29565	127321	Hans Havermann	03/2021
3730	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
3729	(5^182099-3^182099)/2	127282	Kellen Shenton	05/2022
3731	(16*10^127259+197)/3	127260	Robert Price	04/2019
3732	(26*10^127240+61)/3	127241	Robert Price	10/2019
3733	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
3734	2^422515-114997	127190	Enzo Doria	06/2015
3735	5*10^127179-3	127180	Robert Price	07/2015
3736	31678^10343+10343^31678	127176	Hans Havermann	03/2021
3737	(44*10^127169-233)/9	127170	Robert Price	01/2019
3738	34947^4352+4352^34947	127162	Hans Havermann	03/2021
3739	6*10^127158+19	127159	Robert Price	11/2021
3740	30469^14902+14902^30469	127155	Hans Havermann	03/2021
3741	5*10^127153+77	127154	Robert Price	12/2018
3742	29941^17620+17620^29941	127130	Hans Havermann	02/2021
3743	31607^10516+10516^31607	127119	Hans Havermann	03/2021
3744	(19*10^127118-97)/3	127119	Robert Price	10/2021
3745	(29*10^127111+691)/9	127112	Robert Price	08/2021
3746	736^44335+44335^736	127104	Norbert Schneider	07/2019
3747	33040^7023+7023^33040	127090	Hans Havermann	03/2021
3748	(4*10^127081+167)/9	127081	Robert Price	03/2022
3749	29748^18661+18661^29748	127052	Hans Havermann	03/2021
3750	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017

Find by discoverer :

PRP Records

Probable Primes Top 10000

(291910 PRPs in the top)