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 ?
4501	2^371276-461267	111766	Enzo Doria	07/2015
4502	6*10^111760+43	111761	Robert Price	07/2020
4503	98079!4-1024	111747	Robert Price	11/2019
4504	(2^371186+3162)/2	111738	Stefano Morozzi	09/2020
4505	2^371098-113261	111712	Enzo Doria	07/2014
4506	(7*10^111706-61)/9	111706	Erik Branger	01/2011
4507	2^371044+1869391	111696	Enzo Doria	05/2016
4508	26310^17581+17581^26310	111688	Hans Havermann	01/2021
4509	88^57416+87	111645	Norbert Schneider	11/2015
4510	2^370829-109693	111631	Enzo Doria	04/2014
4511	15^94906-2	111619	Lelio R Paula	11/2013
4512	25835^20904+20904^25835	111614	Hans Havermann	02/2021
4513	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
4514	27758^10479+10479^27758	111597	Hans Havermann	02/2021
4515	2^370695-4627	111591	Yves Minet	05/2019
4516	7*10^111579-87	111580	Robert Price	06/2020
4517	2^370643-37	111575	Yves Minet	01/2012
4518	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
4519	2^370610-3911	111565	Yves Minet	04/2017
4520	26200^18097+18097^26200	111550	Hans Havermann	01/2021
4521	286^45405+45405^286	111532	Norbert Schneider	04/2015
4522	4*5^159563-9	111531	Lelio R Paula	11/2014
4523	5*10^111528-21	111529	Robert Price	12/2021
4524	(4^185225+23)/3	111517	Robert Price	10/2018
4525	2^370393-2797093	111500	Enzo Doria	03/2016
4526	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
4527	(2^370371+554)/2	111493	Stefano Morozzi	09/2020
4528	6^143273-5	111489	Paul Bourdelais	01/2021
4529	2^370292-2791979	111469	Enzo Doria	03/2016
4530	2^370177-461551	111435	Enzo Doria	07/2015
4531	(2^370169+1706)/2	111432	Stefano Morozzi	09/2020
4532	109^54683-108	111413	Norbert Schneider	02/2017
4533	(83*10^111406-173)/9	111407	Robert Price	04/2021
4534	(2^370043+1010)/2	111394	Stefano Morozzi	09/2020
4535	32961^2396+2396^32961	111392	Hans Havermann	10/2020
4536	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
4537	2^369974+733	111374	Lelio R Paula	05/2013
4538	121^53470+120	111367	Norbert Schneider	10/2018
4539	2^369915-286267	111356	Enzo Doria	07/2015
4540	(62*10^111347-629)/9	111348	Robert Price	07/2021
4541	2^369855-1615	111338	Lelio R Paula	05/2017
4542	7*10^111325+3	111326	Robert Price	08/2015
4543	51^65176+2	111293	Lelio R Paula	08/2013
4544	2^369643-1865767	111274	Enzo Doria	03/2016
4545	2^369603+885	111262	Lelio R Paula	05/2017
4546	25555^22564+22564^25555	111252	Hans Havermann	10/2020
4547	L(532277)	111240	Renaud Lifchitz	03/2004
4548	105^55033-2	111233	Lelio R Paula	10/2017
4549	(35*10^111232-737)/9	111233	Robert Price	07/2018
4550	26970^13307+13307^26970	111227	Hans Havermann	10/2020
4551	25419^23716+23716^25419	111210	Hans Havermann	10/2020
4552	9*10^111201-29	111202	Robert Price	09/2019
4553	2^369392+29835	111199	Lelio R Paula	05/2017
4554	3^233059+16	111198	Robert Price	03/2020
4555	2^369354-3413	111187	Yves Minet	12/2016
4556	2^369296-27	111170	Lelio R Paula	02/2013
4557	2^369239-109837	111153	Enzo Doria	05/2014
4558	2^369224-291839	111148	Enzo Doria	07/2015
4559	2^369216+2798881	111146	Enzo Doria	04/2016
4560	26842^13817+13817^26842	111137	Hans Havermann	11/2020
4561	(5*10^111119-191)/3	111120	Robert Price	05/2021
4562	10^111111+163849	111112	Patrick De Geest	03/2017
4563	10^111111-312911	111111	Patrick De Geest	03/2017
4564	2^369092-216923	111108	Enzo Doria	05/2014
4565	2^369081-55	111105	Lelio R Paula	02/2013
4566	(2^369047+3618)/2	111094	Stefano Morozzi	09/2020
4567	88^57124-87	111077	Norbert Schneider	11/2015
4568	2^368980+753	111075	Lelio R Paula	05/2013
4569	2^368946-3623	111064	Yves Minet	03/2017
4570	2^368929+29835	111059	Lelio R Paula	05/2017
4571	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
4572	111^54298+110	111057	Norbert Schneider	04/2017
4573	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
4574	35799^1262+1262^35799	111015	Hans Havermann	10/2020
4575	(298*10^111004+11)/3	111006	Robert Price	11/2020
4576	27648^10349+10349^27648	111004	Hans Havermann	11/2020
4577	28899^6932+6932^28899	110997	Hans Havermann	11/2020
4578	2^368641-460303	110972	Enzo Doria	06/2015
4579	2^368619-109087	110966	Enzo Doria	04/2014
4580	(74*10^110961+313)/9	110962	Robert Price	06/2019
4581	25258^24711+24711^25258	110956	Hans Havermann	11/2020
4582	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
4583	3*2^368489+7	110927	Lelio R Paula	09/2014
4584	(14*10^110922+61)/3	110923	Robert Price	12/2018
4585	97411!4-2	110913	Robert Price	07/2017
4586	(301*10^110903+23)/9	110905	Robert Price	06/2021
4587	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
4588	25830^19619+19619^25830	110880	Hans Havermann	10/2020
4589	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
4590	26022^18191+18191^26022	110850	Hans Havermann	10/2020
4591	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
4592	(37*10^110813+251)/9	110814	Robert Price	09/2021
4593	2^368050-64875	110795	Lelio R Paula	05/2017
4594	2^368048+25	110794	Lelio R Paula	02/2013
4595	(2^368017+2262)/2	110784	Stefano Morozzi	02/2021
4596	69^60239-2	110771	Lelio R Paula	10/2013
4597	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
4598	2^367924-69	110757	Lelio R Paula	02/2013
4599	(23*10^110738+61)/3	110739	Robert Price	01/2022
4600	(2^367779+3750)/2	110713	Stefano Morozzi	01/2021
4601	2^367709-109723	110692	Enzo Doria	04/2014
4602	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
4603	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
4604	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
4605	140^51515-139	110558	Norbert Schneider	04/2019
4606	2^367215+1879223	110543	Enzo Doria	09/2016
4607	25782^19375+19375^25782	110534	Hans Havermann	10/2020
4608	26117^17058+17058^26117	110526	Hans Havermann	10/2020
4609	2^367141+41	110521	Lelio R Paula	02/2013
4610	2^367126+29835	110516	Lelio R Paula	05/2017
4611	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
4612	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
4613	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
4614	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
4615	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
4616	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
4617	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
4618	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020
4619	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
4620	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
4621	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
4622	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
4623	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
4624	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
4625	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
4626	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
4627	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
4628	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020
4629	7(10^110503-1)/9+1(10^27685-1)/9*10^41409	110503	Makoto Morimoto	09/2020
4630	7(10^110503-1)/9+1(10^91035-1)/9*10^9734	110503	Makoto Morimoto	09/2020
4631	7(10^110503-1)/9-1(10^23717-1)/9*10^43393	110503	Makoto Morimoto	09/2020
4632	7(10^110503-1)/9-110^57906-1*10^52596	110503	Makoto Morimoto	09/2020
4633	7(10^110503-1)/9-110^72287-1*10^38215	110503	Makoto Morimoto	09/2020
4634	7(10^110503-1)/9-2(10^53823-1)/9*10^28340	110503	Makoto Morimoto	09/2020
4635	7(10^110503-1)/9-2(10^88659-1)/9*10^10922	110503	Makoto Morimoto	09/2020
4636	7(10^110503-1)/9-3(10^79921-1)/9*10^15291	110503	Makoto Morimoto	09/2020
4637	7(10^110503-1)/9-310^60024-3*10^50478	110503	Makoto Morimoto	09/2020
4638	7(10^110503-1)/9-4(10^103091-1)/9*10^3706	110503	Makoto Morimoto	09/2020
4639	7(10^110503-1)/9-410^103658-4*10^6844	110503	Makoto Morimoto	09/2020
4640	7(10^110503-1)/9-410^78188-4*10^32314	110503	Makoto Morimoto	09/2020
4641	7(10^110503-1)/9-5(10^35035-1)/9*10^37734	110503	Makoto Morimoto	09/2020
4642	7(10^110503-1)/9-6(10^67347-1)/9*10^21578	110503	Makoto Morimoto	09/2020
4643	7(10^110503-1)/9-610^60391-6*10^50111	110503	Makoto Morimoto	09/2020
4644	(10^110503-1)-4(10^96247-1)/910^7128	110503	Makoto Morimoto	09/2020
4645	(10^110503-1)-410^74037-410^36465	110503	Makoto Morimoto	09/2020
4646	(10^110503-1)-410^77787-410^32715	110503	Makoto Morimoto	09/2020
4647	(10^110503-1)-410^91179-410^19323	110503	Makoto Morimoto	09/2020
4648	(10^110503-1)-5(10^99143-1)/910^5680	110503	Makoto Morimoto	09/2020
4649	(10^110503-1)-7(10^85075-1)/910^12714	110503	Makoto Morimoto	09/2020
4650	(10^110503-1)-710^100712-710^9790	110503	Makoto Morimoto	09/2020
4651	(10^110503-1)-710^76427-710^34075	110503	Makoto Morimoto	09/2020
4652	(10^110503-1)-710^90451-710^20051	110503	Makoto Morimoto	09/2020
4653	(10^110503-1)-810^106252-810^4250	110503	Makoto Morimoto	09/2020
4654	(11*10^110496+49)/3	110497	Robert Price	07/2018
4655	25447^21958+21958^25447	110481	Hans Havermann	11/2020
4656	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
4657	7*10^110468-23	110469	Robert Price	07/2019
4658	2^366853+5711	110434	Lelio R Paula	05/2017
4659	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
4660	2^366816+315	110423	Lelio R Paula	05/2017
4661	2^366775-2787037	110411	Enzo Doria	03/2016
4662	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
4663	2^366751+2797553	110404	Enzo Doria	03/2016
4664	25276^23331+23331^25276	110404	Hans Havermann	10/2020
4665	2^366748+255	110403	Lelio R Paula	05/2017
4666	2^366738-2985	110400	Yves Minet	09/2014
4667	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
4668	(2^366722+1314)/2	110395	Stefano Morozzi	02/2021
4669	2^366716+1871791	110393	Enzo Doria	05/2016
4670	2^366649+1871687	110373	Enzo Doria	05/2016
4671	2^366629-351205	110367	Enzo Doria	06/2015
4672	(31*10^110363+257)/9	110364	Robert Price	12/2021
4674	2^366558+1874479	110345	Enzo Doria	06/2016
4673	25132^24581+24581^25132	110345	Hans Havermann	10/2020
4675	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
4676	26368^15285+15285^26368	110331	Hans Havermann	10/2020
4677	(23*10^110290+19)/3	110291	Robert Price	07/2019
4678	18^87853-4409	110280	Enzo Doria	03/2013
4679	28490^7419+7419^28490	110267	Hans Havermann	11/2020
4680	2^366218-23	110243	Lelio R Paula	02/2013
4681	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
4682	2^366178-343991	110231	Enzo Doria	07/2015
4683	25777^18798+18798^25777	110174	Hans Havermann	10/2020
4684	2^365944+1871341	110161	Enzo Doria	05/2016
4685	2^365838-461267	110129	Enzo Doria	07/2015
4686	30152^4491+4491^30152	110126	Hans Havermann	11/2020
4687	10^110111+464019	110112	Patrick De Geest	05/2021
4688	10^110111-40001	110111	Robert Price	01/2021
4689	2^365763-6555	110106	Lelio R Paula	04/2017
4690	(2^365689+2^182845+1)/5	110083		11/2006
4691	2^365666-459161	110077	Enzo Doria	05/2015
4692	3*10^110076-7	110077	Robert Price	08/2015
4693	13^98785-72	110041	Lelio R Paula	03/2017
4694	(25^78707+1)/26	110027	Robert Price	06/2013
4695	(16*10^110014-73)/3	110015	Robert Price	07/2020
4696	(7*10^110006-151)/9	110006	Robert Price	02/2018
4697	6^141361-7	110001	Lelio R Paula	11/2014
4698	20^84536+81	109984	Lelio R Paula	03/2017
4699	5*2^365347-9	109982	Lelio R Paula	09/2014
4700	9*6^141303+7	109957	Lelio R Paula	11/2014
4701	27635^9522+9522^27635	109953	Hans Havermann	11/2020
4702	78^58099+77	109929	Norbert Schneider	02/2015
4703	2*10^109928-7	109929	Robert Price	10/2015
4704	30580^3933+3933^30580	109927	Hans Havermann	11/2020
4705	26380^14689+14689^26380	109926	Hans Havermann	11/2020
4706	(2^365161+1130)/2	109925	Stefano Morozzi	09/2020
4707	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
4708	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
4709	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
4710	(2^365069+3774)/2	109897	Stefano Morozzi	02/2021
4711	29652^5083+5083^29652	109894	Mark Rodenkirch	10/2020
4712	(2^365049+722)/2	109891	Stefano Morozzi	09/2020
4713	18^87533-11	109878	Lelio R Paula	04/2017
4714	2^364982-5	109871	Henri Lifchitz	04/2006
4715	3*10^109861+59	109862	Robert Price	08/2018
4716	5*10^109860-69	109861	Robert Price	02/2021
4717	2^364936-1867979	109857	Enzo Doria	04/2016
4718	27013^11652+11652^27013	109846	Hans Havermann	10/2020
4719	2^364867-112087	109836	Enzo Doria	06/2014
4720	4^182415-85061	109825	Mike Oakes	06/2011
4721	(2^364809+1034)/2	109819	Stefano Morozzi	09/2020
4722	(52*10^109807-133)/9	109808	Robert Price	09/2021
4723	25708^18675+18675^25708	109806	Hans Havermann	10/2020
4724	(17^89227+16^89227)/33	109788	Robert Price	08/2013
4725	2^364687-187	109782	Lelio R Paula	01/2012
4726	2^364644+67	109769	Lelio R Paula	01/2012
4727	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
4728	(2^364616+5)/9	109760	Lelio R Paula	01/2014
4729	(55*10^109759+89)/9	109760	Robert Price	03/2019
4730	12^101694+73	109747	Lelio R Paula	03/2017
4731	13^98518-66	109744	Lelio R Paula	03/2017
4732	(8*10^109721-269)/9	109721	Robert Price	09/2021
4733	2^364478-113261	109719	Enzo Doria	07/2014
4734	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
4735	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
4736	27814^8777+8777^27814	109681	Hans Havermann	10/2020
4737	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
4738	3^229824+340	109654	Lelio R Paula	03/2017
4739	(2*10^109645-71)/3	109645	Robert Price	12/2017
4740	2^364169-112813	109626	Enzo Doria	06/2014
4741	28822^6359+6359^28822	109622	Hans Havermann	11/2020
4742	10^109615+21	109616	Lelio R Paula	03/2017
4743	10^109615-456267	109615	Patrick De Geest	03/2017
4744	2^364094-113	109604	Lelio R Paula	01/2012
4745	25251^21898+21898^25251	109600	Hans Havermann	11/2020
4746	(4^182026+11)/3	109591	Robert Price	02/2017
4747	2^364041-6883	109588	Lelio R Paula	09/2011
4748	12^101545+11	109586	Lelio R Paula	03/2017
4749	26536^13475+13475^26536	109582	Hans Havermann	11/2020
4750	2^363842-2787101	109528	Enzo Doria	03/2016

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Probable Primes Top 10000

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