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 ?
5501	2^422515-114997	127190	Enzo Doria	06/2015
5502	5*10^127179-3	127180	Robert Price	07/2015
5503	31678^10343+10343^31678	127176	Hans Havermann	03/2021
5504	(44*10^127169-233)/9	127170	Robert Price	01/2019
5505	34947^4352+4352^34947	127162	Hans Havermann	03/2021
5506	6*10^127158+19	127159	Robert Price	11/2021
5507	30469^14902+14902^30469	127155	Hans Havermann	03/2021
5508	5*10^127153+77	127154	Robert Price	12/2018
5509	29941^17620+17620^29941	127130	Hans Havermann	02/2021
5510	31607^10516+10516^31607	127119	Hans Havermann	03/2021
5511	(19*10^127118-97)/3	127119	Robert Price	10/2021
5512	(29*10^127111+691)/9	127112	Robert Price	08/2021
5513	736^44335+44335^736	127104	Norbert Schneider	07/2019
5514	33040^7023+7023^33040	127090	Hans Havermann	03/2021
5515	(4*10^127081+167)/9	127081	Robert Price	03/2022
5516	29748^18661+18661^29748	127052	Hans Havermann	03/2021
5517	27905^28578-28578^27905	127049	Frank Doornink	03/2024
5518	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
5519	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
5520	(14*10^127014-137)/3	127015	Robert Price	04/2021
5521	31436^10965+10965^31436	127002	Hans Havermann	03/2021
5522	28905^24758+24758^28905	127001	Hans Havermann	03/2021
5523	2^421860-113285	126993	Enzo Doria	07/2014
5524	(10^127030+7)/81234833/9230384921/6092460488946445358851	126991	Alfred Reich	07/2021
5525	(2^421827-7)/11	126982	Lelio R Paula	05/2015
5526	26268^28729-28729^26268	126966	Frank Doornink	03/2024
5527	11^121910-840	126957	Enzo Doria	12/2012
5528	(56*10^126935+187)/9	126936	Robert Price	10/2021
5529	28915^24538+24538^28915	126933	Hans Havermann	03/2021
5530	(29*10^126928-77)/3	126929	Robert Price	02/2020
5531	(259*10^126919-1)/3	126921	Robert Price	12/2020
5532	10^126919+204567	126920	Patrick De Geest	05/2021
5533	(2^421617+100280245065)	126920	Paul Bourdelais	05/2022
5534	10^126919-100001	126919	Robert Price	07/2020
5535	28340^28503+28503^28340	126907	Norbert Schneider	02/2021
5536	2^421534-3001935	126895	Paul Bourdelais	07/2023
5537	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
5538	(5*10^126871-119)/3	126872	Robert Price	03/2018
5539	331^50339-10004	126846	Enzo Doria	07/2012
5540	2^421363-2790757	126843	Enzo Doria	03/2016
5541	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
5542	37938^2203+2203^37938	126828	Hans Havermann	03/2021
5543	(13*10^126819+77)/9	126820	Robert Price	07/2022
5544	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
5546	(14*10^126784-83)/3	126785	Robert Price	12/2018
5545	2^421169-3001935	126785	Paul Bourdelais	07/2023
5547	2^421161-286183	126783	Enzo Doria	06/2015
5548	26733^28628-28628^26733	126738	Frank Doornink	03/2024
5549	(106*10^126726+17)/3	126728	Robert Price	04/2021
5550	30718^13347+13347^30718	126724	Hans Havermann	03/2021
5551	2^420939-113935	126716	Enzo Doria	10/2014
5552	11*23^93048+356	126708	Eric Chen	08/2023
5553	177^56363-2	126703	Lelio R Paula	10/2017
5554	2^420741-113659	126656	Enzo Doria	08/2014
5555	2^420694-21	126642	Lelio R Paula	05/2017
5556	(13*10^126638+437)/9	126639	Robert Price	04/2018
5557	(167*10^126637-17)/3	126639	Robert Price	03/2020
5558	4*10^126625+87	126626	Robert Price	08/2018
5559	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
5560	7*10^126600-99	126601	Robert Price	06/2019
5561	U(655247)/250330563881/206066063082749	126596	Serge Batalov	07/2024
5562	2^420424-59189	126561	Enzo Doria	10/2015
5563	28717^25534+25534^28717	126560	Hans Havermann	03/2021
5564	(86*10^126542+103)/9	126543	Robert Price	12/2021
5565	(19*10^126517-7)/3	126518	Robert Price	12/2023
5566	28922^23655+23655^28922	126503	Hans Havermann	03/2021
5567	2^420126+71893	126471	Enzo Doria	04/2016
5568	25982^28643-28643^25982	126450	Frank Doornink	03/2024
5569	(43*10^126441+47)/9	126442	Robert Price	12/2018
5570	8*10^126408+71	126409	Robert Price	05/2022
5571	2^419866+1877059	126393	Enzo Doria	07/2016
5572	29315^20484+20484^29315	126390	Hans Havermann	03/2021
5573	29433^19676+19676^29433	126384	Hans Havermann	03/2021
5574	F(604711)	126377	Henri Lifchitz	02/2005
5575	2^419757+72707	126360	Enzo Doria	04/2016
5576	2^419720-21569	126349	Enzo Doria	07/2013
5577	2^419637+29	126324	Henri Lifchitz	02/2006
5578	31004^11865+11865^31004	126319	Hans Havermann	03/2021
5579	2^419612+1876741	126316	Enzo Doria	07/2016
5580	2^419520+2793271	126289	Enzo Doria	03/2016
5581	(2^419447-5)/369	126264	Lelio R Paula	05/2014
5582	2^419328-1859939	126231	Enzo Doria	03/2016
5583	2^419282-1851507	126217	Enzo Doria	08/2015
5584	(133*10^126212+17)/3	126214	Robert Price	11/2021
5585	2^419251+1866143	126208	Enzo Doria	03/2016
5586	11^121185+2	126202	Robert Price	05/2014
5587	28203^28352+28352^28203	126175	Norbert Schneider	01/2021
5588	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
5589	2^418851+23	126087	Robert Price	09/2015
5590	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
5591	2^418829+167	126081	Lelio R Paula	01/2012
5592	31037^11530+11530^31037	126067	Hans Havermann	03/2021
5593	4*10^126064-69	126065	Robert Price	01/2022
5594	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
5595	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
5596	(35*10^126048-323)/9	126049	Robert Price	10/2021
5597	33016^6551+6551^33016	126000	Hans Havermann	03/2021
5598	2^418548-111546435	125996	Paul Bourdelais	10/2021
5599	25134^28625-28625^25134	125958	Frank Doornink	12/2023
5600	34736^4227+4227^34736	125954	Hans Havermann	03/2021
5601	(23*35^81566-144013)/34	125944	Eric Chen	05/2025
5602	26197^28502-28502^26197	125930	Frank Doornink	03/2024
5603	2^418319-109501	125927	Enzo Doria	04/2014
5604	2^418316-112373	125926	Enzo Doria	06/2014
5605	40398^1309+1309^40398	125919	Hans Havermann	03/2021
5606	(8*10^125894-29)/3	125895	Robert Price	07/2018
5607	(26*10^125886-413)/9	125887	Robert Price	05/2018
5608	10^(262938+1)-710^62938-1	125877	Robert Price	07/2023
5609	55*10^125847+9	125849	Robert Price	03/2022
5610	4*10^125832+57	125833	Robert Price	05/2022
5611	2^417968+1869811	125821	Enzo Doria	06/2016
5612	2^417902+63	125802	Lelio R Paula	09/2015
5613	(10^125792-91)/9	125792	Serge Batalov	12/2014
5614	30438^13573+13573^30438	125791	Hans Havermann	03/2021
5615	32867^6714+6714^32867	125782	Hans Havermann	03/2021
5616	31155^10892+10892^31155	125777	Hans Havermann	03/2021
5617	(35*10^125754-593)/9	125755	Robert Price	07/2018
5618	30455^13464+13464^30455	125754	Hans Havermann	03/2021
5619	(32*10^125751-77)/9	125752	Robert Price	06/2018
5620	2^417704+77011	125742	Enzo Doria	05/2016
5621	29755^16816+16816^29755	125737	Hans Havermann	03/2021
5622	(22*10^125734+203)/9	125735	Robert Price	10/2021
5623	29918^15915+15915^29918	125710	Hans Havermann	03/2021
5624	(10^125706+149)/3	125706	Serge Batalov	12/2014
5625	28531^25368+25368^28531	125659	Hans Havermann	03/2021
5626	2^417419-115309	125656	Enzo Doria	07/2015
5627	(46*10^125642+593)/9	125643	Robert Price	04/2022
5628	2^417315+213953	125625	Enzo Doria	10/2023
5629	2^417300+77281	125620	Enzo Doria	05/2016
5630	30638^12537+12537^30638	125561	Hans Havermann	03/2021
5631	2^417095-1657	125559	Yves Minet	07/2014
5632	30162^14525+14525^30162	125538	Hans Havermann	03/2021
5633	(56*10^125535+583)/9	125536	Robert Price	08/2021
5634	(23*10^125517-179)/3	125518	Robert Price	06/2022
5635	9*10^125516+29	125517	Robert Price	03/2022
5636	404*35^81280+23	125505	Eric Chen	05/2025
5637	(88*10^125492-637)/9	125493	Robert Price	11/2020
5638	28958^21525+21525^28958	125474	Hans Havermann	02/2021
5641	2^416773-25	125462	Lelio R Paula	09/2015
5639	(10^125482+7)/162685667/1639829194459	125462	Alfred Reich	07/2021
5640	26078^28409-28409^26078	125462	Frank Doornink	03/2024
5642	33889^5032+5032^33889	125449	Hans Havermann	03/2021
5643	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
5644	(2861^36481+1)/(2861^191+1)	125438	Martin Hopf	12/2023
5645	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
5646	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
5647	2^416641-2*416641+1	125422	Robert Price	05/2018
5648	33392^5697+5697^33392	125409	Hans Havermann	03/2021
5649	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
5650	2^416530+1870429	125389	Enzo Doria	05/2016
5651	(56*10^125385+691)/9	125386	Robert Price	05/2019
5652	27953^28198+28198^27953	125381	Norbert Schneider	01/2021
5653	31074^10837+10837^31074	125381	Hans Havermann	03/2021
5654	33745^5194+5194^33745	125380	Hans Havermann	03/2021
5655	2^416490+1875109	125376	Enzo Doria	09/2016
5656	28360^26331+26331^28360	125365	Hans Havermann	03/2021
5657	2^416416-114929	125354	Enzo Doria	05/2015
5658	25805^28412-28412^25805	125346	Frank Doornink	03/2024
5659	(77*10^125330-293)/9	125331	Robert Price	09/2019
5660	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
5661	2^416134+1865899	125269	Enzo Doria	03/2016
5662	153^57337-152	125264	Norbert Schneider	12/2018
5663	(599*10^125224+13)/9	125226	Robert Price	02/2022
5664	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
5665	30054^14657+14657^30054	125207	Hans Havermann	03/2021
5666	(23^91943-1)/22	125201	Robert Price	01/2012
5667	2^415884-933075	125194	Paul Bourdelais	06/2021
5668	43125^27010-106	125185	Enzo Doria	08/2012
5669	(38*10^125166+349)/9	125167	Robert Price	10/2018
5670	10^125166-5001	125166	Robert Price	12/2021
5671	2^415765-112603	125158	Enzo Doria	06/2014
5672	8*10^125088-13	125089	Robert Price	08/2019
5673	(25*10^125076-13)/3	125077	Robert Price	09/2019
5674	(11*10^125054+73)/3	125055	Robert Price	08/2021
5675	(101^62383-1)/17542099700	125026	Paul Vanderveen	06/2025
5676	(29*10^125021-113)/3	125022	Robert Price	10/2019
5677	2^415290-113591	125015	Enzo Doria	08/2014
5678	2^415276-460919	125011	Enzo Doria	06/2015
5679	2^415259+77243	125006	Enzo Doria	05/2016
5680	(67*10^124990+77)/9	124991	Robert Price	10/2021
5681	2^415144-3683	124971	Yves Minet	10/2011
5682	2^415092+111546435	124956	Paul Bourdelais	10/2021
5683	31936^8173+8173^31936	124946	Hans Havermann	03/2021
5684	27458^28145-28145^27458	124927	Frank Doornink	03/2024
5685	5^178715-4	124917	Tyler NeSmith	07/2021
5686	29767^15700+15700^29767	124900	Hans Havermann	03/2021
5687	(310^50131-1)/309	124892	Tom Wu	07/2024
5688	2^414874+79	124890	Lelio R Paula	01/2015
5689	25292^28361-28361^25292	124874	Frank Doornink	01/2024
5690	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
5691	2^414618+79459	124813	Enzo Doria	06/2016
5692	(61*10^124809-1)/3	124811	Robert Price	01/2020
5693	(235*29^85334+129)/28	124794	Eric Chen	06/2025
5694	(29*10^124765-71)/3	124766	Robert Price	07/2021
5695	2^414432-1846709	124757	Enzo Doria	07/2015
5696	2*10^124751-51	124752	Robert Price	04/2018
5697	(56*10^124735+367)/9	124736	Robert Price	06/2019
5698	27362^28111-28111^27362	124733	Frank Doornink	03/2024
5699	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
5700	(23*10^124690+37)/3	124691	Robert Price	02/2022
5701	p(25046)#-p(25046+1)	124675	Henri Lifchitz	11/2024
5702	56*10^124656-3	124658	Robert Price	03/2020
5703	(7*10^124648+197)/3	124649	Robert Price	07/2018
5705	2^414032-5	124637	Henri Lifchitz	07/2006
5704	2^414032+1872331	124637	Enzo Doria	05/2016
5706	37373^2158+2158^37373	124604	Hans Havermann	03/2021
5707	29811^15112+15112^29811	124590	Hans Havermann	03/2021
5708	(22^92791-3^92791)/19	124564	Robert Price	02/2025
5709	F(596093)/36870605281541	124563	Serge Batalov	07/2024
5710	2^413781-2023	124561	Riley Fisher	09/2023
5711	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
5712	29757^15296+15296^29757	124521	Hans Havermann	03/2021
5713	35056^3561+3561^35056	124504	Hans Havermann	03/2021
5714	40588^1167+1167^40588	124487	Hans Havermann	02/2021
5715	(85*10^124485-49)/9	124486	Robert Price	12/2020
5716	64^68909-63^68909	124463	Robert Price	07/2013
5717	35016^3581+3581^35016	124448	Hans Havermann	03/2021
5718	2^413387+76253	124442	Enzo Doria	04/2016
5719	28749^21298+21298^28749	124436	Hans Havermann	03/2021
5720	2^413352+524287	124432	Paul Underwood	09/2018
5721	287117#+391613	124424	Nicolas PALAU	01/2017
5722	(4*10^124420+83)/3	124421	Robert Price	02/2018
5723	34578^3965+3965^34578	124421	Hans Havermann	03/2021
5724	(68*10^124392-329)/9	124393	Robert Price	03/2021
5725	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
5726	10^124383+58407	124384	Patrick De Geest	08/2021
5728	10^124383-8000001	124383	Robert Price	04/2021
5727	10^124383-5801	124383	Patrick De Geest	08/2021
5729	26091^28154-28154^26091	124342	Frank Doornink	03/2024
5730	(41*10^124335-383)/9	124336	Robert Price	11/2018
5731	(304*10^124329-43)/9	124331	Robert Price	02/2020
5732	34716^3811+3811^34716	124320	Hans Havermann	03/2021
5733	26892^28063-28063^26892	124309	Frank Doornink	03/2024
5734	2^412868-120599	124286	Paul Bourdelais	02/2012
5735	10^124248+899089	124249	Patrick De Geest	05/2021
5737	10^124248-1000001	124248	Robert Price	08/2020
5736	10^124248-501903	124248	Patrick De Geest	05/2021
5738	45^75145-2	124231	Lelio R Paula	08/2015
5739	29901^14272+14272^29901	124224	Hans Havermann	03/2021
5740	2^412645-112213	124219	Enzo Doria	06/2014
5741	29837^14500+14500^29837	124163	Hans Havermann	03/2021
5742	28074^26455+26455^28074	124158	Hans Havermann	03/2021
5743	954^41669-41669^954	124155	Norman Luhn	10/2024
5744	432^47093-47093^432	124113	Norman Luhn	10/2024
5745	2^412285+213317	124111	Enzo Doria	09/2023
5746	(12^115001-1)/2530033	124101	Paul Vanderveen	06/2025
5747	2^412248+74611	124100	Enzo Doria	04/2016
5748	(22*10^124096-13)/9	124097	Robert Price	06/2018
5749	(455*10^124093+31)/9	124095	Robert Price	06/2021
5750	2^412192-3329	124083	Yves Minet	12/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301723 PRPs in the top)