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 ?
251	2^1234709+883127	371685	Enzo Doria	12/2016
252	2^1231466+283819	370709	Enzo Doria	07/2017
253	2^1220335+1881263	367358	Enzo Doria	11/2016
254	2^1216694+1884769	366262	Enzo Doria	02/2017
255	2^1215889-3	366020	Paul Bourdelais	06/2019
256	2^1215296+1885441	365841	Enzo Doria	03/2017
257	2^1214307+1888115	365543	Enzo Doria	05/2017
258	2^1213815+3	365395	Paul Bourdelais	06/2019
259	2^1207345+1882577	363448	Enzo Doria	12/2016
260	2^1207073+883727	363366	Enzo Doria	03/2017
261	3^761457-2	363308	Ryan Propper	07/2015
262	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
263	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
264	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
265	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
266	2^1200672+1880881	361439	Enzo Doria	10/2016
267	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
268	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
269	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
270	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
271	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
272	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
273	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
274	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
275	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
276	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
277	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
278	2^1195093+1882577	359759	Enzo Doria	12/2016
279	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
280	2^1191375+8543	358640	Phil Moore	06/2008
281	2^1190972+1880191	358519	Enzo Doria	11/2016
282	(45^216551-1)/44	358004	Paul Bourdelais	08/2020
283	(50^210319-1)/49	357324	Paul Bourdelais	08/2020
284	2^1179836+1885021	355167	Enzo Doria	02/2017
285	20^271951+3	353817	Paul Bourdelais	01/2021
286	(63^195893-1)/62	352477	Paul Bourdelais	08/2020
287	numbpart(100000135540)	352269	Serge Batalov	04/2017
288	(10^352237-1)/9/10567111/950335427	352221	Maksym Voznyy	01/2015
289	2^1168554+783529	351770	Enzo Doria	01/2017
290	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
291	2^1166152+1882411	351047	Enzo Doria	12/2016
292	2^1162154+1890207	349844	Enzo Doria	08/2017
293	(7*10^348724-61)/9	348724	Erik Branger	09/2016
294	(127^165601-1)/126	348390	Alexander Zhirkov	09/2015
295	2^1153083+1883693	347113	Enzo Doria	04/2017
296	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
297	2^1145882+80779	344945	Enzo Doria	09/2016
298	2^1136462+1887289	342110	Enzo Doria	05/2017
299	F(1636007)	341905	Henri Lifchitz	03/2009
300	2^1133678+782569	341272	Enzo Doria	11/2016
301	(11^327001+1)/12	340536	Paul Bourdelais	09/2013
302	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
303	Tau(907^20848)	339132	Nik Lygeros / Olivier Rozier	01/2016
304	2^1126380-3	339075	Paul Bourdelais	06/2019
305	2^1125446+1885099	338794	Enzo Doria	08/2017
306	(63^188147+1)/64	338539	Paul Bourdelais	12/2020
307	2^1124549+143807	338523	Enzo Doria	10/2016
308	2^1121187+1886783	337511	Enzo Doria	04/2017
309	(48^200443-1)/47	336992	Paul Bourdelais	08/2020
310	(94^170371-1)/93	336162	Paul Bourdelais	09/2020
311	2^1116184+1883521	336005	Enzo Doria	02/2017
312	2^1114517+1880087	335504	Enzo Doria	10/2016
313	(101^166849+1)/102	334418	Paul Bourdelais	12/2020
314	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
315	2^1104408-114539	332460	Enzo Doria	03/2015
316	2^1101921+82085	331712	Enzo Doria	10/2016
317	2^1100655+683513	331331	Enzo Doria	01/2017
318	(10^330906+71)/9	330906	Serge Batalov	07/2015
319	2^1098346+482899	330636	Enzo Doria	11/2016
320	2^1095679+1878713	329833	Enzo Doria	09/2016
321	2^1094740-1851539	329550	Enzo Doria	08/2015
322	2^1091469-379369	328565	Enzo Doria	03/2014
323	(69^178093-1)/68	327485	Paul Bourdelais	08/2020
324	2^1085750+582349	326844	Enzo Doria	11/2016
325	2^1083596+483061	326195	Enzo Doria	12/2016
326	(2^541456-1)*10^162995+2^541455-1	325990	paolo galliani	01/2019
327	2^1082908+583561	325988	Enzo Doria	05/2017
328	30^220411-29^220411	325574	Jean-Louis Charton	10/2018
329	2^1078242+1881649	324584	Enzo Doria	11/2016
330	2^1077737+1880117	324432	Enzo Doria	10/2016
331	2^1075425+1880117	323736	Enzo Doria	10/2016
332	(28^223381+1)/29	323267	Paul Bourdelais	12/2020
333	10^322999+187071	323000	Stefano Morozzi	03/2019
334	10^322999-143151	322999	Patrick De Geest	05/2020
335	2^1072146+1886869	322749	Enzo Doria	04/2017
336	2^1072118-7321953	322740	Enzo Doria	02/2015
337	2^1071026+1886869	322411	Enzo Doria	04/2017
338	2^1070539+1880633	322265	Enzo Doria	10/2016
339	2^1069293-1147195	321890	Enzo Doria	05/2015
340	2^1065968+1880941	320889	Enzo Doria	10/2016
341	2^1065897-1147195	320867	Enzo Doria	05/2015
342	2^1063427+1882103	320124	Enzo Doria	12/2016
343	2^1061095-1061095	319422	Henri Lifchitz	10/2013
344	2^1060950+653119	319378	Enzo Doria	12/2016
345	2^1060363+782753	319202	Enzo Doria	11/2016
346	(71^172259-1)/70	318895	Paul Bourdelais	08/2020
347	2^1054736+483061	317508	Enzo Doria	12/2016
348	2^1053965+1879667	317276	Enzo Doria	10/2016
349	(43^194119-1)/42	317086	Paul Bourdelais	08/2020
350	2^1052186-458165	316740	Enzo Doria	03/2015
351	2^1046613-114685	315062	Enzo Doria	04/2015
352	2^1045625-459373	314765	Enzo Doria	06/2015
353	(7*10^314564-61)/9	314564	Erik Branger	09/2016
354	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
355	(53^181981-1)/52	313784	Paul Bourdelais	08/2020
356	2^1041944+283051	313657	Enzo Doria	12/2016
357	2^1041153-114391	313419	Enzo Doria	02/2015
358	(74^167311+1)/75	312742	Paul Bourdelais	12/2020
359	2^1038871+1866983	312732	Enzo Doria	04/2016
360	(55^179573-1)/54	312521	Paul Bourdelais	08/2020
361	2^1037647+1881263	312363	Enzo Doria	11/2016
362	2^1037226+1879699	312237	Enzo Doria	10/2016
363	2^1036867+1865843	312129	Enzo Doria	02/2016
364	2^1036020-114539	311874	Enzo Doria	02/2015
365	(90^159463-1)/89	311628	Paul Bourdelais	08/2020
366	2^1032240+1883431	310736	Enzo Doria	01/2017
367	2^1030352+1870021	310167	Enzo Doria	06/2016
368	2^1030046+1882843	310075	Enzo Doria	11/2016
369	3^648872+16	309591	Robert Price	04/2020
370	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
371	(67^167449-1)/66	305773	Paul Bourdelais	08/2020
372	(62^170539+1)/63	305671	Paul Bourdelais	12/2020
373	2^1015321-1015321	305643	Henri Lifchitz	08/2013
374	2^1014224-2791229	305312	Enzo Doria	01/2016
375	2^1010751-107709	304267	Enzo Doria	03/2014
376	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
377	2^1009577+1869587	303913	Enzo Doria	06/2016
378	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
379	2^1008301+1869377	303529	Enzo Doria	06/2016
380	(2^1007838+5)/3	303389	Serge Batalov	08/2015
381	2^1005326+383059	302634	Enzo Doria	12/2016
382	2^1004929+1877567	302514	Enzo Doria	08/2016
383	2^1003494+1874899	302082	Enzo Doria	06/2016
384	2^1003046+60529	301947	Enzo Doria	04/2016
385	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
386	2^1000647+1881353	301225	Enzo Doria	11/2016
387	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
388	2^999646+1874029	300924	Enzo Doria	06/2016
389	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
390	10^300476+3	300477	Ed Trice	10/2012
391	10^300476-530913	300476	Patrick De Geest	03/2016
392	2^998053+1879667	300444	Enzo Doria	09/2016
393	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
394	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
395	10^300000+287389	300001	Patrick De Geest	10/2019
396	10^300000-83657	300000	Patrick De Geest	10/2019
397	numbpart(72526161452)	299999	Serge Batalov	04/2017
398	2^996182-114431	299881	Enzo Doria	02/2015
399	2^995214-2788361	299590	Enzo Doria	12/2015
400	2^994791-114319	299462	Enzo Doria	01/2015
401	2^994490-1863791	299372	Enzo Doria	01/2016
402	2^993322+1885729	299020	Enzo Doria	03/2017
403	2^992711-2788807	298836	Enzo Doria	12/2015
404	2^992525-114199	298780	Enzo Doria	12/2014
405	2^992329+1884707	298721	Enzo Doria	02/2017
406	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
407	2^985217-114553	296580	Enzo Doria	03/2015
408	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
409	2^984131-1828009	296253	Enzo Doria	01/2015
410	2^983620+60451	296100	Phil Moore	03/2008
411	2^982721-2683	295829	Yves Minet	02/2016
412	2^981298-2788421	295401	Enzo Doria	12/2015
413	2^981163-2790967	295360	Enzo Doria	12/2015
414	2^979594+1865839	294888	Enzo Doria	02/2016
415	2^976760+1885021	294035	Enzo Doria	02/2017
416	2^974441+1878407	293336	Enzo Doria	08/2016
417	2^974180+1876831	293258	Enzo Doria	07/2016
418	2^974170+453319	293255	Enzo Doria	01/2017
419	2^972744-114419	292826	Enzo Doria	03/2015
420	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
421	2^970911+1873373	292274	Enzo Doria	07/2016
422	2^970670+383059	292201	Enzo Doria	12/2016
423	2^970141-100363	292042	Enzo Doria	02/2014
424	2^969945+1874717	291983	Enzo Doria	06/2016
425	2^969384+1880701	291814	Enzo Doria	10/2016
426	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
427	2^962194+60139	289650	Enzo Doria	02/2016
428	2^959307-1861507	288781	Enzo Doria	11/2015
429	14^251797-3	288592	Paul Bourdelais	12/2020
430	2^957372+283531	288198	Enzo Doria	02/2017
431	2^957192-1864049	288144	Enzo Doria	01/2016
432	2^956446+1875199	287919	Enzo Doria	06/2016
433	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
434	2^955178+1883587	287538	Enzo Doria	12/2016
435	2^954127-954127^2	287221	Henri Lifchitz	01/2021
436	2^954001+1875257	287183	Enzo Doria	07/2016
437	(23891^65536+1)/2	286932	Serge Batalov	03/2018
438	2^952268+1878601	286662	Enzo Doria	09/2016
439	2^950801+81557	286220	Enzo Doria	08/2016
440	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
441	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
442	2^948510+782569	285530	Enzo Doria	10/2016
443	2^948374-114137	285490	Enzo Doria	01/2015
444	2^947739+1872923	285298	Enzo Doria	06/2016
445	2^942533+82067	283731	Enzo Doria	09/2016
446	2^940950+1874989	283255	Enzo Doria	06/2016
447	2^940426-2786141	283097	Enzo Doria	11/2015
448	2^939881-114115	282933	Enzo Doria	12/2014
449	10^282493+632551	282494	Patrick De Geest	02/2017
451	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
450	10^282493-132327	282493	Patrick De Geest	02/2017
452	3^591827-2^591827	282374	Mike Oakes	08/2009
453	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
454	2^936716-1835519	281980	Enzo Doria	04/2015
455	2^936588+79411	281942	Enzo Doria	06/2016
456	2^936047+1877423	281779	Enzo Doria	08/2016
457	2^935713+1869377	281678	Enzo Doria	05/2016
458	2^933082+1877059	280886	Enzo Doria	08/2016
459	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
460	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
461	(10^279978+11)/3	279978	Serge Batalov	07/2015
462	2^929524-1864829	279815	Enzo Doria	01/2016
463	2^929152+60181	279703	Enzo Doria	02/2016
464	2^928621-2787883	279543	Enzo Doria	11/2015
465	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
466	2^927429+1882277	279184	Enzo Doria	12/2016
467	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
468	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
469	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
470	2^925330-1301	278553	Yves Minet	06/2015
471	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
472	2^923261-69175	277930	Enzo Doria	11/2015
473	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
474	((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	277369	Serge Batalov	07/2016
475	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
476	2^920318+2792299	277044	Enzo Doria	02/2016
477	2^918596-2786939	276525	Enzo Doria	11/2015
478	2^916639+60563	275936	Enzo Doria	04/2016
479	2^916385-2786383	275860	Enzo Doria	11/2015
480	2^915928+82081	275722	Enzo Doria	09/2016
481	2^915576-114137	275616	Enzo Doria	01/2015
482	2^914828+1876741	275391	Enzo Doria	07/2016
483	2^914757-2203	275370	Yves Minet	12/2015
484	2^911900+1871245	274510	Enzo Doria	05/2016
485	2^910490+283429	274085	Enzo Doria	01/2017
486	2^909988-1862249	273934	Enzo Doria	12/2015
487	2^909297+1879157	273726	Enzo Doria	08/2016
488	2^909257-1864423	273714	Enzo Doria	01/2016
489	2^908579-1861747	273510	Enzo Doria	12/2015
490	2^907635-2791597	273226	Enzo Doria	01/2016
491	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
492	2^906594-113201	272912	Enzo Doria	08/2014
493	2^904773+1872167	272364	Enzo Doria	06/2016
494	2^904149-1862473	272176	Enzo Doria	12/2015
495	(7*10^271757-61)/9	271757	Erik Branger	03/2012
496	2^902497+1880117	271679	Enzo Doria	09/2016
497	2^901858+77689	271487	Enzo Doria	06/2016
498	2^901372+1875301	271341	Enzo Doria	06/2016
499	2^899121-115033	270663	Enzo Doria	07/2015
500	2^898900+883021	270596	Enzo Doria	12/2016

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Probable Primes Top 10000

(277034 PRPs in the top)