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 ?
9251	9*2^321336-7	96733	Lelio R Paula	08/2014
9252	(209*10^96722-17)/3	96724	Robert Price	05/2017
9253	(54163^20431-1)/54162	96710	Serge Batalov	06/2022
9254	2^321237-4615	96702	Yves Minet	05/2019
9255	(27273^21799-1)/27272	96691	Serge Batalov	06/2022
9256	2^321187-1159	96687	Yves Minet	11/2012
9257	2^321182-1850081	96686	Enzo Doria	08/2015
9259	23359^13768+13768^23359	96680	Hans Havermann	06/2020
9258	(65630^20071-1)/65629	96680	Serge Batalov	06/2022
9260	2^321116-112829	96666	Enzo Doria	06/2014
9261	2^321108-109499	96664	Enzo Doria	04/2014
9262	2^321098+2793859	96661	Enzo Doria	03/2016
9263	(2^321100+1170)/2	96661	Stefano Morozzi	09/2020
9264	2^321057+4097	96648	Lelio R Paula	06/2016
9265	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
9266	22743^17750+17750^22743	96640	Hans Havermann	04/2020
9267	22882^16679+16679^22882	96612	Hans Havermann	02/2020
9268	23452^13163+13163^23452	96608	Hans Havermann	02/2020
9269	(1042^32009-1)/1041	96596	Serge Batalov	06/2022
9270	(85*10^96594-373)/9	96595	Robert Price	05/2021
9271	(2^320863+666)/2	96590	Stefano Morozzi	09/2020
9272	p(19849)#/2-64	96581	Robert Price	04/2017
9273	2^320817+189	96576	Lelio R Paula	12/2012
9274	2^320816-4685	96576	Yves Minet	05/2019
9276	(361*10^96567-163)/9	96569	Robert Price	10/2017
9275	(19*10^96568+137)/3	96569	Robert Price	03/2022
9277	2^320788-110327	96567	Enzo Doria	05/2014
9278	(3065^27697-1)/3064	96561	Serge Batalov	06/2022
9279	2^320764+793	96560	Lelio R Paula	02/2013
9280	(2^320752+1842)/2	96556	Stefano Morozzi	02/2021
9281	(48331^20611-1)/48330	96542	Serge Batalov	06/2022
9282	(50595^20521-1)/50594	96529	Serge Batalov	06/2022
9283	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
9284	23288^13947+13947^23288	96517	Hans Havermann	07/2020
9286	2^320616-78795	96516	Lelio R Paula	03/2016
9285	(19*10^96520+287)/9/109/409	96516	Alfred Reich	11/2022
9287	2^320612-461939	96514	Enzo Doria	07/2015
9288	(21245^22303-1)/21244	96507	Serge Batalov	06/2022
9289	10^96504+987654321	96505	Robert Price	12/2019
9290	10^96504+71887	96505	Patrick De Geest	02/2020
9291	22654^18195+18195^22654	96505	Hans Havermann	07/2020
9292	10^96504-139277	96504	Patrick De Geest	02/2020
9293	(218^41263-1)/217	96490	Serge Batalov	06/2022
9294	(47220^20641-1)/47219	96474	Serge Batalov	06/2022
9295	5*2^320431+7	96461	Lelio R Paula	08/2014
9296	19^75431-90	96458	Lelio R Paula	06/2016
9297	(11853^23677-1)/11852	96452	Serge Batalov	06/2022
9298	(2^320386+2814)/2	96446	Stefano Morozzi	02/2021
9299	(2^320370+3)/67	96440	Lelio R Paula	10/2013
9300	3*10^96431-17	96432	Robert Price	03/2021
9301	2^320309+1871477	96423	Enzo Doria	05/2016
9302	(10412^24001-1)/10411	96421	Serge Batalov	06/2022
9303	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
9304	(29*10^96407-23)/3	96408	Robert Price	03/2022
9305	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
9306	2^320232-173	96400	Lelio R Paula	12/2012
9307	175^42975-2	96395	Lelio R Paula	10/2017
9308	(2^320170+2718)/2	96381	Stefano Morozzi	09/2020
9309	10^96377+199911	96378	Patrick De Geest	12/2016
9310	10^96377-20001	96377	Robert Price	11/2016
9311	(18079^22639-1)/18078	96374	Serge Batalov	06/2022
9313	2^320124-2790449	96367	Enzo Doria	03/2016
9312	10^96366+19197	96367	Patrick De Geest	08/2021
9315	10^96366-10000000001	96366	Robert Price	04/2021
9314	10^96366-287367	96366	Patrick De Geest	08/2021
9316	(26351^21799-1)/26350	96365	Serge Batalov	06/2022
9317	22488^19255+19255^22488	96351	Hans Havermann	11/2019
9318	23248^13939+13939^23248	96346	Hans Havermann	11/2019
9319	(5928^25537-1)/5927	96345	Serge Batalov	06/2022
9321	2^320043-108775	96343	Enzo Doria	04/2014
9320	24989^7168+7168^24989	96343	Hans Havermann	11/2019
9322	10^96338+424939	96339	Patrick De Geest	03/2016
9323	10^96338-9281	96338	Robert Price	09/2015
9324	(8527^24509-1)/8526	96336	Serge Batalov	06/2022
9325	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
9326	(2444^28433-1)/2443	96331	Serge Batalov	06/2022
9327	(48690^20551-1)/48689	96327	Serge Batalov	06/2022
9328	(61935^20101-1)/61934	96318	Serge Batalov	06/2022
9329	25699^5596+5596^25699	96317	Hans Havermann	07/2020
9330	(7*10^96312+83)/9	96312	Tyler Busby	01/2023
9331	(11*10^96298+529)/9	96299	Robert Price	09/2021
9333	26502^4297+4297^26502	96287	Hans Havermann	07/2020
9332	(54180^20341-1)/54179	96287	Serge Batalov	06/2022
9334	2^319838+4257	96281	Lelio R Paula	03/2016
9335	2^319830-16995	96279	Lelio R Paula	03/2016
9336	6^123713+143	96268	Lelio R Paula	05/2016
9337	(28*10^96265-97)/3	96266	Robert Price	07/2016
9338	(3799^26893-1)/3798	96265	Serge Batalov	06/2022
9340	103^47825-102	96264	Norbert Schneider	10/2016
9339	(54041^20341-1)/54040	96264	Serge Batalov	06/2022
9341	(2^319777+2082)/2	96263	Stefano Morozzi	09/2020
9342	(2^319771+3686)/2	96261	Stefano Morozzi	09/2020
9343	2^319713-81	96244	Lelio R Paula	11/2012
9344	2^319711+213413	96243	Enzo Doria	09/2023
9345	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
9346	22834^16393+16393^22834	96238	Hans Havermann	05/2020
9347	8*10^96236+27	96237	Robert Price	09/2021
9348	12^89153-43	96213	Lelio R Paula	06/2016
9349	(25048^21871-1)/25047	96202	Serge Batalov	06/2022
9351	(2*10^96195-59)/3	96195	Robert Price	05/2017
9350	9*10^96194-77	96195	Robert Price	08/2020
9352	2^319545+147	96193	Lelio R Paula	11/2012
9353	23357^13128+13128^23357	96189	Hans Havermann	02/2020
9354	(19838^22381-1)/19837	96179	Serge Batalov	06/2022
9355	(221^41023-1)/220	96172	Serge Batalov	06/2022
9356	25952^5073+5073^25952	96160	Hans Havermann	12/2019
9357	(50891^20431-1)/50890	96157	Serge Batalov	06/2022
9358	(50^56597+1)/51	96155	Robert Price	03/2014
9359	22313^20374+20374^22313	96149	Hans Havermann	12/2019
9360	22279^20668+20668^22279	96141	Hans Havermann	11/2019
9361	(41*10^96137-59)/9	96138	Robert Price	10/2017
9362	2^319353-110343	96135	Enzo Doria	05/2014
9363	11^92309-42	96130	Lelio R Paula	05/2016
9364	(21675^22171-1)/21674	96129	Serge Batalov	06/2022
9365	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
9366	(7*10^96112+143)/3	96113	Robert Price	04/2016
9367	26731^3940+3940^26731	96112	Hans Havermann	07/2020
9368	22640^17583+17583^22640	96109	Hans Havermann	07/2020
9369	(19178^22441-1)/19177	96107	Serge Batalov	06/2022
9370	2^319237+65835	96100	Lelio R Paula	03/2016
9371	2^319194-1841	96087	Yves Minet	03/2013
9372	23949^10280+10280^23949	96084	Hans Havermann	07/2020
9373	(1927^29251-1)/1926	96083	Serge Batalov	06/2022
9374	20^73847-31	96078	Lelio R Paula	05/2016
9375	(60229^20101-1)/60228	96075	Serge Batalov	06/2022
9376	(28044^21601-1)/28043	96074	Serge Batalov	06/2022
9377	50^56543-49	96065	Norbert Schneider	09/2018
9378	2^319107-109555	96061	Enzo Doria	04/2014
9379	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
9380	2^319098-112157	96059	Enzo Doria	06/2014
9381	15^81673+94	96055	Lelio R Paula	07/2016
9382	(85761^19471-1)/85760	96052	Serge Batalov	06/2022
9383	2^319074+1871749	96051	Enzo Doria	05/2016
9384	25670^5517+5517^25670	96050	Hans Havermann	06/2020
9385	6*10^96037+19	96038	Robert Price	11/2021
9386	2^319007-112111	96031	Enzo Doria	06/2014
9387	(57987^20161-1)/57986	96029	Serge Batalov	06/2022
9389	2^318946-1421	96013	Yves Minet	01/2013
9388	(68310^19861-1)/68309	96013	Serge Batalov	06/2022
9390	(20294^22291-1)/20293	96012	Serge Batalov	06/2022
9391	(304^38669-1)/303	96008	Serge Batalov	06/2022
9392	(1840^29401-1)/1839	95986	Serge Batalov	06/2022
9393	22830^16003+16003^22830	95982	Hans Havermann	02/2020
9394	2^318834-110411	95979	Enzo Doria	05/2014
9395	2^318831-1965	95978	Lelio R Paula	03/2016
9396	(5*10^95976+7)/3	95977	Erik Branger	03/2014
9397	(12797^23369-1)/12796	95975	Serge Batalov	06/2022
9398	(10534^23857-1)/10533	95963	Serge Batalov	06/2022
9399	22871^15696+15696^22871	95962	Hans Havermann	01/2020
9400	(2^318760+858)/2	95957	Stefano Morozzi	02/2021
9401	23167^13860+13860^23167	95953	Hans Havermann	01/2020
9402	(823^32911-1)/822	95946	Serge Batalov	06/2022
9404	5*3^201089-8	95945	Lelio R Paula	08/2014
9403	(81783^19531-1)/81782	95945	Serge Batalov	06/2022
9405	2^318711-139	95942	Lelio R Paula	11/2012
9406	2^318635-1167	95919	Lelio R Paula	03/2016
9407	15^81555+16	95917	Lelio R Paula	07/2016
9408	(37*10^95895+377)/9	95896	Robert Price	10/2017
9409	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
9410	2^318496-97305	95877	Lelio R Paula	03/2016
9411	22129^21496+21496^22129	95871	Hans Havermann	07/2020
9413	2^318466+15015	95868	Lelio R Paula	03/2016
9412	24847^7216+7216^24847	95868	Hans Havermann	07/2020
9414	23706^11065+11065^23706	95866	Hans Havermann	07/2020
9415	(2863^27733-1)/2862	95865	Serge Batalov	06/2022
9416	6^123187-173129	95859	Mike Oakes	04/2011
9417	2^318423-487	95855	Yves Minet	03/2012
9418	10^95848+443709	95849	Patrick De Geest	10/2022
9419	10^95848-5000000001	95848	Robert Price	09/2022
9420	10^95848-61971	95848	Patrick De Geest	10/2022
9421	(2^318359+678)/2	95836	Stefano Morozzi	09/2020
9422	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
9423	(8060^24533-1)/8059	95831	Serge Batalov	06/2022
9424	(9853^23993-1)/9852	95814	Serge Batalov	06/2022
9426	(2^318267+2550)/2	95808	Stefano Morozzi	09/2020
9425	(5048^25873-1)/5047	95808	Serge Batalov	06/2022
9428	4*10^95799+13	95800	Robert Price	02/2021
9427	(65533^19891-1)/65532	95800	Serge Batalov	06/2022
9429	2^318203+211343	95789	Enzo Doria	08/2023
9430	45369!2+1024	95787	Robert Price	02/2015
9431	3^200758-86	95786	Lelio R Paula	05/2016
9432	(2^318271+1)/(346031404238891654090604244843)	95781	Gord Palameta	12/2018
9433	(2^318171+2030)/2	95779	Stefano Morozzi	09/2020
9434	3*10^95776-59	95777	Robert Price	10/2017
9435	(82970^19471-1)/82969	95772	Serge Batalov	06/2022
9436	193^41901-2	95768	Lelio R Paula	10/2017
9437	(2^318124+2502)/2	95765	Stefano Morozzi	09/2020
9438	(12900^23297-1)/12899	95761	Serge Batalov	06/2022
9439	4*10^95752-71	95753	Robert Price	11/2017
9440	(16955^22639-1)/16954	95743	Serge Batalov	06/2022
9441	(81795^19489-1)/81794	95740	Serge Batalov	06/2022
9442	(2742^27847-1)/2741	95737	Serge Batalov	06/2022
9443	(6072^25303-1)/6071	95726	Serge Batalov	06/2022
9444	23640^11197+11197^23640	95721	Hans Havermann	12/2019
9445	10^95712+89329	95713	Patrick De Geest	09/2022
9447	10^95712-4000001	95712	Robert Price	07/2021
9446	10^95712-989313	95712	Patrick De Geest	09/2022
9448	(60657^20011-1)/60656	95706	Serge Batalov	06/2022
9449	((10^47850-1)10000/9+6421)10^47850+(10^47850-1)/9	95704	Hans Havermann	05/2019
9450	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
9451	(26161^21661-1)/26160	95687	Serge Batalov	06/2022
9452	(2^317853+1086)/2	95683	Stefano Morozzi	09/2020
9453	4*10^95672+91	95673	Robert Price	11/2017
9454	6*10^95665+43	95666	Robert Price	07/2020
9455	(20819^22153-1)/20818	95663	Serge Batalov	06/2022
9456	(64464^19891-1)/64463	95658	Serge Batalov	06/2022
9457	(934^32203-1)/933	95652	Serge Batalov	06/2022
9458	(11*10^95641-113)/3	95642	Robert Price	01/2017
9459	(72330^19681-1)/72329	95632	Serge Batalov	06/2022
9460	(13224^23203-1)/13223	95624	Serge Batalov	06/2022
9461	(18211^22441-1)/18210	95602	Serge Batalov	06/2022
9462	(71975^19681-1)/71974	95590	Serge Batalov	06/2022
9463	(13*10^95588+11)/3	95589	Robert Price	05/2015
9464	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
9465	(13368^23167-1)/13367	95585	Serge Batalov	06/2022
9466	(25874^21661-1)/25873	95583	Serge Batalov	06/2022
9467	3^200325+70	95580	Lelio R Paula	05/2016
9468	(25*10^95574-7)/9	95575	Robert Price	12/2014
9469	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
9470	2^317464+31	95567	Lelio R Paula	11/2012
9471	(2^317451+2114)/2	95562	Stefano Morozzi	09/2020
9472	7^113073+82	95558	Lelio R Paula	04/2016
9473	(24728^21751-1)/24727	95552	Serge Batalov	06/2022
9474	(49764^20341-1)/49763	95536	Serge Batalov	06/2022
9475	(36155^20959-1)/36154	95531	Serge Batalov	06/2022
9476	(7725^24571-1)/7724	95526	Serge Batalov	06/2022
9477	(20546^22147-1)/20545	95510	Serge Batalov	06/2022
9478	2^317251+465	95503	Lelio R Paula	03/2016
9479	19^74684+58	95503	Lelio R Paula	06/2016
9480	(2^317250-7)/339	95500	Lelio R Paula	07/2013
9481	5*10^95498-21	95499	Robert Price	12/2021
9482	(21615^22031-1)/21614	95495	Serge Batalov	06/2022
9483	6^122718-79	95494	Lelio R Paula	05/2016
9484	22168^20291+20291^22168	95485	Hans Havermann	10/2019
9485	(77427^19531-1)/77426	95481	Serge Batalov	06/2022
9486	(13026^23203-1)/13025	95472	Serge Batalov	06/2022
9487	2^317141-110491	95469	Enzo Doria	05/2014
9488	(2^317097+3014)/2	95456	Stefano Morozzi	09/2020
9489	2^317094+76309	95455	Enzo Doria	05/2016
9490	2^317085+95	95453	Lelio R Paula	11/2012
9491	(17*10^95451-377)/9	95452	Robert Price	11/2017
9492	2^317057-109551	95444	Enzo Doria	04/2014
9493	3^200026+28	95437	Lelio R Paula	05/2016
9494	2^317024+93	95434	Donovan Johnson	06/2008
9495	(86*10^95428-437)/9	95429	Robert Price	03/2021
9496	10^95427+192591	95428	Patrick De Geest	05/2021
9499	2^316999+1605	95427	Lelio R Paula	03/2016
9498	(2^317000+3210)/2	95427	Stefano Morozzi	09/2020
9497	10^95427-10001	95427	Robert Price	02/2021
9500	2^316995-110427	95426	Enzo Doria	05/2014

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