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 ?
8501	2^338156+167053	101796	Stefano Morozzi	09/2022
8502	2^338158+69303	101796	Stefano Morozzi	09/2022
8503	2^338158+171189	101796	Stefano Morozzi	11/2022
8504	2^338157-188989	101796	Stefano Morozzi	12/2022
8505	2^338158-188711	101796	Stefano Morozzi	12/2022
8506	2^338155+132621	101795	Stefano Morozzi	02/2022
8507	2^338155-82605	101795	Stefano Morozzi	03/2022
8508	2^338155-182631	101795	Stefano Morozzi	03/2022
8509	2^338155+187755	101795	Stefano Morozzi	04/2022
8510	2^338154-83975	101795	Stefano Morozzi	04/2022
8511	2^338154+163759	101795	Stefano Morozzi	05/2022
8512	2^338152-25767	101794	Stefano Morozzi	12/2021
8513	2^338152+181927	101794	Stefano Morozzi	02/2022
8514	2^338151+60779	101794	Stefano Morozzi	03/2022
8515	2^338151+189149	101794	Stefano Morozzi	05/2022
8516	2^338152+45567	101794	Stefano Morozzi	11/2022
8517	2^338147+29343	101793	Stefano Morozzi	01/2022
8518	2^338148+130803	101793	Stefano Morozzi	01/2022
8519	2^338146+166167	101793	Stefano Morozzi	06/2022
8520	2^338149-185073	101793	Stefano Morozzi	06/2022
8521	2^338149+41757	101793	Stefano Morozzi	09/2022
8522	2^338149+125015	101793	Stefano Morozzi	02/2023
8523	2^338144+180697	101792	Stefano Morozzi	01/2022
8524	2^338143+8589	101792	Stefano Morozzi	02/2022
8525	2^338143-55611	101792	Stefano Morozzi	02/2022
8526	2^338143+60623	101792	Stefano Morozzi	03/2022
8527	2^338145-63609	101792	Stefano Morozzi	12/2022
8528	2^338141-77301	101791	Stefano Morozzi	12/2021
8529	2^338141+157145	101791	Stefano Morozzi	02/2022
8530	2^338140+84745	101791	Stefano Morozzi	03/2022
8531	2^338140+90073	101791	Stefano Morozzi	05/2022
8532	2^338142+96583	101791	Stefano Morozzi	11/2022
8533	2^338139-134719	101790	Stefano Morozzi	04/2022
8534	2^338138+95443	101790	Stefano Morozzi	11/2022
8535	2^338133+1445	101789	Stefano Morozzi	12/2021
8536	2^338133+172469	101789	Stefano Morozzi	11/2022
8537	2^338134+23235	101789	Stefano Morozzi	11/2022
8538	2^338132+105643	101788	Stefano Morozzi	01/2022
8539	2^338131+181871	101788	Stefano Morozzi	02/2022
8540	2^338132-184539	101788	Stefano Morozzi	04/2022
8541	2^338130+22383	101788	Stefano Morozzi	11/2022
8542	2^338132+170143	101788	Stefano Morozzi	11/2022
8543	2^338131-62599	101788	Stefano Morozzi	12/2022
8544	2^338128+128953	101787	Stefano Morozzi	01/2022
8545	2^338127+11021	101787	Stefano Morozzi	03/2022
8546	2^338127+192935	101787	Stefano Morozzi	09/2022
8547	2^338127+98621	101787	Stefano Morozzi	11/2022
8548	2^338128+98853	101787	Stefano Morozzi	02/2023
8549	2^338123-25959	101786	Stefano Morozzi	12/2021
8550	2^338124-180765	101786	Stefano Morozzi	02/2022
8551	2^338125-7129	101786	Stefano Morozzi	03/2022
8552	2^338125-40071	101786	Stefano Morozzi	01/2023
8556	2^338122-20117	101785	Enzo Doria	06/2013
8557	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
8553	2^338122+32799	101785	Stefano Morozzi	02/2022
8554	2^338120+166411	101785	Stefano Morozzi	06/2022
8555	2^338122+90705	101785	Stefano Morozzi	06/2022
8558	2^338117+103761	101784	Stefano Morozzi	01/2022
8559	2^338118+53817	101784	Stefano Morozzi	01/2022
8560	2^338116+82585	101784	Stefano Morozzi	02/2022
8561	2^338118+39483	101784	Stefano Morozzi	05/2022
8562	2^338119+96659	101784	Stefano Morozzi	11/2022
8563	2^338115+61083	101783	Stefano Morozzi	03/2022
8564	2^338114+173287	101783	Stefano Morozzi	11/2022
8565	2^338113-139681	101783	Stefano Morozzi	01/2023
8566	2^338110-175365	101782	Stefano Morozzi	12/2021
8567	2^338110-3963	101782	Stefano Morozzi	01/2022
8568	2^338112+155061	101782	Stefano Morozzi	01/2022
8569	2^338112+137335	101782	Stefano Morozzi	04/2022
8570	2^338111-85627	101782	Stefano Morozzi	06/2022
8571	2^338111-90145	101782	Stefano Morozzi	01/2023
8580	35^65917-7092	101781	Enzo Doria	03/2013
8572	2^338107-1221	101781	Stefano Morozzi	12/2021
8573	2^338109+108539	101781	Stefano Morozzi	03/2022
8574	2^338109-7261	101781	Stefano Morozzi	03/2022
8575	2^338109-131961	101781	Stefano Morozzi	03/2022
8576	2^338108+39585	101781	Stefano Morozzi	05/2022
8577	2^338109+38147	101781	Stefano Morozzi	05/2022
8578	2^338108+17301	101781	Stefano Morozzi	09/2022
8579	2^338108-65859	101781	Stefano Morozzi	01/2023
8581	2^338105+79599	101780	Stefano Morozzi	01/2022
8582	2^338103-180675	101780	Stefano Morozzi	02/2022
8583	2^338103+19499	101780	Stefano Morozzi	09/2022
8584	2^338103-165319	101780	Stefano Morozzi	01/2023
8585	2^338100-100389	101779	Stefano Morozzi	12/2021
8586	2^338100+27595	101779	Stefano Morozzi	12/2021
8587	2^338101+101139	101779	Stefano Morozzi	12/2021
8588	2^338101+134985	101779	Stefano Morozzi	03/2022
8589	2^338102+186135	101779	Stefano Morozzi	03/2022
8590	2^338100+36885	101779	Stefano Morozzi	04/2022
8591	2^338102-8151	101779	Stefano Morozzi	04/2022
8592	2^338100+90637	101779	Stefano Morozzi	06/2022
8593	2^338101+68505	101779	Stefano Morozzi	09/2022
8594	2^338100-42867	101779	Stefano Morozzi	02/2023
8595	2^338097+100229	101778	Stefano Morozzi	11/2021
8596	2^338097-25695	101778	Stefano Morozzi	12/2021
8597	2^338098-110043	101778	Stefano Morozzi	06/2022
8598	2^338099-191389	101778	Stefano Morozzi	01/2023
8599	2^338093-128403	101777	Stefano Morozzi	01/2022
8600	2^338093+33051	101777	Stefano Morozzi	02/2022
8601	2^338094+135555	101777	Stefano Morozzi	03/2022
8602	2^338095-32395	101777	Stefano Morozzi	03/2022
8603	2^338090-175353	101776	Stefano Morozzi	12/2021
8604	2^338090+33277	101776	Stefano Morozzi	02/2022
8605	2^338091-105601	101776	Stefano Morozzi	02/2022
8606	2^338091-32127	101776	Stefano Morozzi	03/2022
8607	2^338092+12873	101776	Stefano Morozzi	04/2022
8608	2^338091-58485	101776	Stefano Morozzi	04/2022
8609	2^338086+177643	101775	Stefano Morozzi	12/2021
8610	2^338089+82905	101775	Stefano Morozzi	02/2022
8611	2^338088+87565	101775	Stefano Morozzi	04/2022
8612	2^338088-166205	101775	Stefano Morozzi	01/2023
8613	2^338089-140053	101775	Stefano Morozzi	01/2023
8614	2^338087+124935	101775	Stefano Morozzi	02/2023
8615	2^338085-3301	101774	Stefano Morozzi	01/2022
8616	2^338084+108691	101774	Stefano Morozzi	03/2022
8617	2^338083+164369	101774	Stefano Morozzi	05/2022
8618	2^338080+107521	101773	Stefano Morozzi	02/2022
8619	2^338080-156917	101773	Stefano Morozzi	03/2022
8620	2^338081+199775	101773	Stefano Morozzi	02/2023
8621	2^338076+62311	101772	Stefano Morozzi	04/2022
8622	2^338079+161745	101772	Stefano Morozzi	04/2022
8623	2^338078-60075	101772	Stefano Morozzi	06/2022
8624	2^338079+167079	101772	Stefano Morozzi	09/2022
8625	2^338076+122535	101772	Stefano Morozzi	11/2022
8626	2^338077+95619	101772	Stefano Morozzi	11/2022
8627	2^338078+20539	101772	Stefano Morozzi	11/2022
8628	2^338076-36813	101772	Stefano Morozzi	12/2022
8629	2^338078-64911	101772	Stefano Morozzi	01/2023
8630	2^338073-77971	101771	Stefano Morozzi	01/2022
8631	2^338074+55579	101771	Stefano Morozzi	01/2022
8632	2^338073-81813	101771	Stefano Morozzi	03/2022
8633	2^338073+138645	101771	Stefano Morozzi	05/2022
8634	2^338075+148043	101771	Stefano Morozzi	11/2022
8635	2^338070-152607	101770	Stefano Morozzi	01/2022
8636	2^338070+138787	101770	Stefano Morozzi	05/2022
8637	2^338071+165249	101770	Stefano Morozzi	06/2022
8638	2^338070+70359	101770	Stefano Morozzi	11/2022
8639	2^338071+98573	101770	Stefano Morozzi	11/2022
8640	2^338069+79365	101769	Stefano Morozzi	01/2022
8641	2^338069+107571	101769	Stefano Morozzi	02/2022
8642	2^338068+73035	101769	Stefano Morozzi	11/2022
8643	2^338064+100087	101768	Stefano Morozzi	11/2021
8644	2^338064-83793	101768	Stefano Morozzi	04/2022
8645	2^338064+193701	101768	Stefano Morozzi	09/2022
8646	2^338065+199947	101768	Stefano Morozzi	02/2023
8647	2^338060-151047	101767	Stefano Morozzi	12/2021
8648	2^338060-130805	101767	Stefano Morozzi	02/2022
8649	2^338060-136593	101767	Stefano Morozzi	12/2022
8650	2^338062-15725	101767	Stefano Morozzi	01/2023
8651	2^338058-76415	101766	Stefano Morozzi	12/2021
8652	2^338057+83865	101766	Stefano Morozzi	03/2022
8653	2^338057+86997	101766	Stefano Morozzi	04/2022
8654	2^338058+188589	101766	Stefano Morozzi	05/2022
8655	2^338058+68089	101766	Stefano Morozzi	09/2022
8656	2^338059+121803	101766	Stefano Morozzi	11/2022
8657	2^338057-39021	101766	Stefano Morozzi	01/2023
8658	2^338056+50605	101765	Stefano Morozzi	11/2021
8659	2^338053+53231	101765	Stefano Morozzi	01/2022
8660	2^338054-180497	101765	Stefano Morozzi	02/2022
8661	2^338053+59891	101765	Stefano Morozzi	03/2022
8662	2^338056+33987	101765	Stefano Morozzi	03/2022
8663	2^338055-157779	101765	Stefano Morozzi	03/2022
8664	2^338056+90307	101765	Stefano Morozzi	06/2022
8665	2^338055+124443	101765	Stefano Morozzi	02/2023
8666	2^338052-55373	101764	Stefano Morozzi	02/2022
8667	2^338050-138281	101764	Stefano Morozzi	12/2022
8668	2^338050+148959	101764	Stefano Morozzi	02/2023
8669	2^338051-118159	101764	Stefano Morozzi	02/2023
8670	2^338048+31185	101763	Stefano Morozzi	01/2022
8671	2^338047+31935	101763	Stefano Morozzi	02/2022
8672	2^338047+108011	101763	Stefano Morozzi	02/2022
8673	2^338049+56777	101763	Stefano Morozzi	02/2022
8674	2^338049-7531	101763	Stefano Morozzi	03/2022
8675	2^338048-304019	101763	Harrison Mesh	06/2022
8676	2^338049+191291	101763	Stefano Morozzi	06/2022
8677	2^338047-187699	101763	Stefano Morozzi	12/2022
8678	2^338047-66405	101763	Stefano Morozzi	01/2023
8679	2^338049-192633	101763	Stefano Morozzi	02/2023
8680	2^338046-25841	101762	Stefano Morozzi	12/2021
8681	2^338046-2285	101762	Stefano Morozzi	12/2021
8682	2^338046-177851	101762	Stefano Morozzi	01/2022
8683	2^338043+84045	101762	Stefano Morozzi	03/2022
8684	2^338046-57573	101762	Stefano Morozzi	03/2022
8685	2^338044-8177	101762	Stefano Morozzi	04/2022
8686	2^338045-58443	101762	Stefano Morozzi	04/2022
8687	2^338044+193497	101762	Stefano Morozzi	09/2022
8688	2^338043+45701	101762	Stefano Morozzi	11/2022
8689	2^338044-114197	101762	Stefano Morozzi	01/2023
8690	2^338042+194973	101761	Stefano Morozzi	11/2022
8691	2^338040-164483	101761	Stefano Morozzi	01/2023
8692	2^338038-57887	101760	Stefano Morozzi	04/2022
8693	2^338037+139169	101760	Stefano Morozzi	05/2022
8694	2^338037+188595	101760	Stefano Morozzi	05/2022
8695	2^338038-187241	101760	Stefano Morozzi	12/2022
8696	2^338039+124035	101760	Stefano Morozzi	02/2023
8697	2^338037-42523	101760	Stefano Morozzi	02/2023
8698	2^338034+125653	101759	Stefano Morozzi	11/2021
8699	2^338034-25211	101759	Stefano Morozzi	12/2021
8700	2^338033-154099	101759	Stefano Morozzi	02/2022
8701	2^338034-31803	101759	Stefano Morozzi	03/2022
8702	2^338033+162311	101759	Stefano Morozzi	04/2022
8703	2^338033-83071	101759	Stefano Morozzi	04/2022
8704	2^338035-158095	101759	Stefano Morozzi	04/2022
8705	2^338036-34193	101759	Stefano Morozzi	04/2022
8706	2^338036+42873	101759	Stefano Morozzi	09/2022
8707	2^338036+93373	101759	Stefano Morozzi	09/2022
8708	2^338035+146129	101759	Stefano Morozzi	11/2022
8709	2^338036+23983	101759	Stefano Morozzi	11/2022
8710	2^338036+170433	101759	Stefano Morozzi	11/2022
8711	2^338031+79989	101758	Stefano Morozzi	01/2022
8712	2^338032+158073	101758	Stefano Morozzi	02/2022
8713	2^338030-54371	101758	Stefano Morozzi	02/2022
8714	2^338032-180747	101758	Stefano Morozzi	02/2022
8715	2^338029-27909	101757	Stefano Morozzi	01/2022
8716	2^338027+70475	101757	Stefano Morozzi	11/2022
8717	2^338028-38705	101757	Stefano Morozzi	12/2022
8718	2^338028-140459	101757	Stefano Morozzi	01/2023
8719	2^338024-128495	101756	Stefano Morozzi	01/2022
8720	2^338025+34785	101756	Stefano Morozzi	03/2022
8721	2^338025-181765	101756	Stefano Morozzi	03/2022
8722	2^338024+63765	101756	Stefano Morozzi	05/2022
8723	2^338023-160621	101756	Stefano Morozzi	06/2022
8724	2^338026+117553	101756	Stefano Morozzi	09/2022
8725	2^338020-52437	101755	Stefano Morozzi	12/2021
8726	2^338021+160241	101755	Stefano Morozzi	03/2022
8727	2^338022+185845	101755	Stefano Morozzi	03/2022
8728	2^338021+189587	101755	Stefano Morozzi	05/2022
8729	2^338021-85891	101755	Stefano Morozzi	06/2022
8730	2^338020-87797	101755	Stefano Morozzi	12/2022
8731	2^338018-102741	101754	Stefano Morozzi	01/2022
8732	2^338018+29937	101754	Stefano Morozzi	01/2022
8733	2^338017-29505	101754	Stefano Morozzi	02/2022
8734	2^338018-30873	101754	Stefano Morozzi	02/2022
8735	2^338018-157013	101754	Stefano Morozzi	03/2022
8736	2^338019+168929	101754	Stefano Morozzi	09/2022
8737	2^338017+172721	101754	Stefano Morozzi	11/2022
8738	2^338018-136131	101754	Stefano Morozzi	12/2022
8739	2^338016+50797	101753	Stefano Morozzi	11/2021
8740	2^338016+26707	101753	Stefano Morozzi	12/2021
8741	2^338014+104677	101753	Stefano Morozzi	01/2022
8742	2^338013+145091	101753	Stefano Morozzi	11/2022
8743	2^338016-16335	101753	Stefano Morozzi	01/2023
8746	2^338010-19833	101752	Enzo Doria	06/2013
8744	2^338011+28665	101752	Stefano Morozzi	01/2022
8745	2^338010+89505	101752	Stefano Morozzi	05/2022
8747	2^338007+58985	101751	Stefano Morozzi	03/2022
8748	2^338008+109741	101751	Stefano Morozzi	03/2022
8749	2^338009+9527	101751	Stefano Morozzi	03/2022
8750	2^338007+14511	101751	Stefano Morozzi	05/2022

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Probable Primes Top 10000

(295036 PRPs in the top)