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	2^1116184+1883521	336005	Enzo Doria	02/2017
252	2^1114517+1880087	335504	Enzo Doria	10/2016
253	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
254	2^1104408-114539	332460	Enzo Doria	03/2015
255	2^1101921+82085	331712	Enzo Doria	10/2016
256	2^1100655+683513	331331	Enzo Doria	01/2017
257	(10^330906+71)/9	330906	Serge Batalov	07/2015
258	2^1098346+482899	330636	Enzo Doria	11/2016
259	2^1095679+1878713	329833	Enzo Doria	09/2016
260	2^1094740-1851539	329550	Enzo Doria	08/2015
261	2^1091469-379369	328565	Enzo Doria	03/2014
262	2^1085750+582349	326844	Enzo Doria	11/2016
263	2^1083596+483061	326195	Enzo Doria	12/2016
264	(2^541456-1)*10^162995+2^541455-1	325990	paolo galliani	01/2019
265	2^1082908+583561	325988	Enzo Doria	05/2017
266	30^220411-29^220411	325574	Jean-Louis Charton	10/2018
267	2^1078242+1881649	324584	Enzo Doria	11/2016
268	2^1077737+1880117	324432	Enzo Doria	10/2016
269	2^1075425+1880117	323736	Enzo Doria	10/2016
270	10^322999+187071	323000	Stefano Morozzi	03/2019
271	2^1072146+1886869	322749	Enzo Doria	04/2017
272	2^1072118-7321953	322740	Enzo Doria	02/2015
273	2^1071026+1886869	322411	Enzo Doria	04/2017
274	2^1070539+1880633	322265	Enzo Doria	10/2016
275	2^1069293-1147195	321890	Enzo Doria	05/2015
276	2^1065968+1880941	320889	Enzo Doria	10/2016
277	2^1065897-1147195	320867	Enzo Doria	05/2015
278	2^1063427+1882103	320124	Enzo Doria	12/2016
279	2^1061095-1061095	319422	Henri Lifchitz	10/2013
280	2^1060950+653119	319378	Enzo Doria	12/2016
281	2^1060363+782753	319202	Enzo Doria	11/2016
282	2^1054736+483061	317508	Enzo Doria	12/2016
283	2^1053965+1879667	317276	Enzo Doria	10/2016
284	2^1052186-458165	316740	Enzo Doria	03/2015
285	2^1046613-114685	315062	Enzo Doria	04/2015
286	2^1045625-459373	314765	Enzo Doria	06/2015
287	(7*10^314564-61)/9	314564	Erik Branger	09/2016
288	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
289	2^1041944+283051	313657	Enzo Doria	12/2016
290	2^1041153-114391	313419	Enzo Doria	02/2015
291	2^1038871+1866983	312732	Enzo Doria	04/2016
292	2^1037647+1881263	312363	Enzo Doria	11/2016
293	2^1037226+1879699	312237	Enzo Doria	10/2016
294	2^1036867+1865843	312129	Enzo Doria	02/2016
295	2^1036020-114539	311874	Enzo Doria	02/2015
296	2^1032240+1883431	310736	Enzo Doria	01/2017
297	2^1030352+1870021	310167	Enzo Doria	06/2016
298	2^1030046+1882843	310075	Enzo Doria	11/2016
299	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
300	2^1015321-1015321	305643	Henri Lifchitz	08/2013
301	2^1014224-2791229	305312	Enzo Doria	01/2016
302	2^1010751-107709	304267	Enzo Doria	03/2014
303	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
304	2^1009577+1869587	303913	Enzo Doria	06/2016
305	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
306	2^1008301+1869377	303529	Enzo Doria	06/2016
307	(2^1007838+5)/3	303389	Serge Batalov	08/2015
308	2^1005326+383059	302634	Enzo Doria	12/2016
309	2^1004929+1877567	302514	Enzo Doria	08/2016
310	2^1003494+1874899	302082	Enzo Doria	06/2016
311	2^1003046+60529	301947	Enzo Doria	04/2016
312	2^1000647+1881353	301225	Enzo Doria	11/2016
313	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
314	2^999646+1874029	300924	Enzo Doria	06/2016
315	10^300476+3	300477	Ed Trice	10/2012
316	10^300476-530913	300476	Patrick De Geest	03/2016
317	2^998053+1879667	300444	Enzo Doria	09/2016
318	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
319	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
320	10^300000+287389	300001	Patrick De Geest	10/2019
321	10^300000-83657	300000	Patrick De Geest	10/2019
322	numbpart(72526161452)	299999	Serge Batalov	04/2017
323	2^996182-114431	299881	Enzo Doria	02/2015
324	2^995214-2788361	299590	Enzo Doria	12/2015
325	2^994791-114319	299462	Enzo Doria	01/2015
326	2^994490-1863791	299372	Enzo Doria	01/2016
327	2^993322+1885729	299020	Enzo Doria	03/2017
328	2^992711-2788807	298836	Enzo Doria	12/2015
329	2^992525-114199	298780	Enzo Doria	12/2014
330	2^992329+1884707	298721	Enzo Doria	02/2017
331	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
332	2^985217-114553	296580	Enzo Doria	03/2015
333	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
334	2^984131-1828009	296253	Enzo Doria	01/2015
335	2^983620+60451	296100	Phil Moore	03/2008
336	2^982721-2683	295829	Yves Minet	02/2016
337	2^981298-2788421	295401	Enzo Doria	12/2015
338	2^981163-2790967	295360	Enzo Doria	12/2015
339	2^979594+1865839	294888	Enzo Doria	02/2016
340	2^976760+1885021	294035	Enzo Doria	02/2017
341	2^974441+1878407	293336	Enzo Doria	08/2016
342	2^974180+1876831	293258	Enzo Doria	07/2016
343	2^974170+453319	293255	Enzo Doria	01/2017
344	2^972744-114419	292826	Enzo Doria	03/2015
345	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
346	2^970911+1873373	292274	Enzo Doria	07/2016
347	2^970670+383059	292201	Enzo Doria	12/2016
348	2^970141-100363	292042	Enzo Doria	02/2014
349	2^969945+1874717	291983	Enzo Doria	06/2016
350	2^969384+1880701	291814	Enzo Doria	10/2016
351	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
352	2^962194+60139	289650	Enzo Doria	02/2016
353	2^959307-1861507	288781	Enzo Doria	11/2015
354	2^957372+283531	288198	Enzo Doria	02/2017
355	2^957192-1864049	288144	Enzo Doria	01/2016
356	2^956446+1875199	287919	Enzo Doria	06/2016
357	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
358	2^955178+1883587	287538	Enzo Doria	12/2016
359	2^954001+1875257	287183	Enzo Doria	07/2016
360	(23891^65536+1)/2	286932	Serge Batalov	03/2018
361	2^952268+1878601	286662	Enzo Doria	09/2016
362	2^950801+81557	286220	Enzo Doria	08/2016
363	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
364	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
365	2^948510+782569	285530	Enzo Doria	10/2016
366	2^948374-114137	285490	Enzo Doria	01/2015
367	2^947739+1872923	285298	Enzo Doria	06/2016
368	2^942533+82067	283731	Enzo Doria	09/2016
369	2^940950+1874989	283255	Enzo Doria	06/2016
370	2^940426-2786141	283097	Enzo Doria	11/2015
371	2^939881-114115	282933	Enzo Doria	12/2014
372	10^282493+632551	282494	Patrick De Geest	02/2017
374	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
373	10^282493-132327	282493	Patrick De Geest	02/2017
375	3^591827-2^591827	282374	Mike Oakes	08/2009
376	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
377	2^936716-1835519	281980	Enzo Doria	04/2015
378	2^936588+79411	281942	Enzo Doria	06/2016
379	2^936047+1877423	281779	Enzo Doria	08/2016
380	2^935713+1869377	281678	Enzo Doria	05/2016
381	2^933082+1877059	280886	Enzo Doria	08/2016
382	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
383	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
384	(10^279978+11)/3	279978	Serge Batalov	07/2015
385	2^929524-1864829	279815	Enzo Doria	01/2016
386	2^929152+60181	279703	Enzo Doria	02/2016
387	2^928621-2787883	279543	Enzo Doria	11/2015
388	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
389	2^927429+1882277	279184	Enzo Doria	12/2016
390	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
391	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
392	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
393	2^925330-1301	278553	Yves Minet	06/2015
394	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
395	2^923261-69175	277930	Enzo Doria	11/2015
396	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
397	((((((((((((((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
398	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
399	2^920318+2792299	277044	Enzo Doria	02/2016
400	2^918596-2786939	276525	Enzo Doria	11/2015
401	2^916639+60563	275936	Enzo Doria	04/2016
402	2^916385-2786383	275860	Enzo Doria	11/2015
403	2^915928+82081	275722	Enzo Doria	09/2016
404	2^915576-114137	275616	Enzo Doria	01/2015
405	2^914828+1876741	275391	Enzo Doria	07/2016
406	2^914757-2203	275370	Yves Minet	12/2015
407	2^911900+1871245	274510	Enzo Doria	05/2016
408	2^910490+283429	274085	Enzo Doria	01/2017
409	2^909988-1862249	273934	Enzo Doria	12/2015
410	2^909297+1879157	273726	Enzo Doria	08/2016
411	2^909257-1864423	273714	Enzo Doria	01/2016
412	2^908579-1861747	273510	Enzo Doria	12/2015
413	2^907635-2791597	273226	Enzo Doria	01/2016
414	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
415	2^906594-113201	272912	Enzo Doria	08/2014
416	2^904773+1872167	272364	Enzo Doria	06/2016
417	2^904149-1862473	272176	Enzo Doria	12/2015
418	(7*10^271757-61)/9	271757	Erik Branger	03/2012
419	2^902497+1880117	271679	Enzo Doria	09/2016
420	2^901858+77689	271487	Enzo Doria	06/2016
421	2^901372+1875301	271341	Enzo Doria	06/2016
422	2^899121-115033	270663	Enzo Doria	07/2015
423	2^898900+883021	270596	Enzo Doria	12/2016
424	2^898762-251511	270555	Enzo Doria	12/2013
425	2^898589+47	270503	Lelio R Paula	03/2016
426	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
427	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
428	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
429	2^897867-3217	270285	Yves Minet	12/2016
430	2^897849-115273	270280	Enzo Doria	07/2015
431	2^896616-114179	269909	Enzo Doria	12/2014
432	2^894928+583561	269401	Enzo Doria	04/2017
433	2^894673-39343	269324	Enzo Doria	08/2015
434	F(1285607)	268676	Henri Lifchitz	11/2008
435	2^892112+187663	268553	Enzo Doria	08/2016
436	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
437	2^890957-69583	268205	Enzo Doria	12/2015
438	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
439	2^890122-351401	267954	Enzo Doria	07/2015
440	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
441	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
442	2^886324+77791	266811	Enzo Doria	06/2016
443	2^884714+1880527	266326	Enzo Doria	10/2016
444	11^255426+255426^11	265999	Serge Batalov	05/2014
445	2^883462-343421	265949	Enzo Doria	07/2015
446	2^883442+1875019	265943	Enzo Doria	06/2016
447	2^883333-291583	265910	Enzo Doria	07/2015
448	2^880411+1882673	265031	Enzo Doria	12/2016
449	2^879530-2788031	264765	Enzo Doria	12/2015
450	2^878118+2793079	264340	Enzo Doria	02/2016
451	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
452	2^875748-461129	263627	Enzo Doria	07/2015
453	2^875181-2789923	263456	Enzo Doria	12/2015
454	2^875101-350083	263432	Enzo Doria	08/2015
455	2^874684+1883587	263307	Enzo Doria	01/2017
456	2^874616+1872211	263286	Enzo Doria	05/2016
457	2^874073+2792957	263123	Enzo Doria	02/2016
458	2^873628+1878751	262989	Enzo Doria	08/2016
459	2^873288-269	262886	Yves Minet	01/2015
460	2^871146-3173	262242	Yves Minet	07/2016
461	2^869601-163	261776	Yves Minet	01/2015
462	2^869326+282859	261694	Enzo Doria	11/2016
463	2^869035-114181	261606	Enzo Doria	12/2014
464	2^865715+80303	260607	Enzo Doria	07/2016
465	2^865048+1882411	260406	Enzo Doria	12/2016
466	2^864899-113871	260361	Enzo Doria	10/2014
467	(7*10^260198-61)/9	260198	Erik Branger	11/2011
468	2^864298-2788421	260180	Enzo Doria	12/2015
469	2^864039-2791357	260102	Enzo Doria	01/2016
470	2^863621-113833	259976	Enzo Doria	10/2014
471	2^862837+75767	259740	Enzo Doria	05/2016
472	2^862637-31	259680	Jorge Menendez	05/2019
473	2^862088+1874941	259515	Enzo Doria	06/2016
474	2^861987-134557	259484	Hans Havermann	10/2018
475	2^861516-1854029	259343	Enzo Doria	09/2015
476	2^860975-1853977	259180	Enzo Doria	09/2015
477	2^860625-1858843	259074	Enzo Doria	10/2015
478	2^860110+77689	258919	Enzo Doria	05/2016
479	2^859600+1880371	258766	Enzo Doria	10/2016
480	2^859433+494711	258716	Makoto Morimoto	10/2013
481	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
482	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
483	2^859240+1875271	258658	Enzo Doria	06/2016
484	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
485	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
486	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
487	2^857016-633113	257988	Enzo Doria	12/2013
488	2^855732-113969	257602	Enzo Doria	10/2014
489	2^853682-3911	256984	Enzo Doria	05/2014
490	11^246668-90	256879	Enzo Doria	12/2012
491	2^851904-113939	256449	Enzo Doria	10/2014
492	2^851725-851725^2	256395	Henri Lifchitz	03/2019
493	11^246167-90	256357	Enzo Doria	12/2012
494	2^850700-569049	256087	Enzo Doria	11/2013
495	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
496	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
497	2^849177-114025	255628	Enzo Doria	12/2014
498	2^848502-3173	255425	Yves Minet	07/2016
499	2^848178-140291	255328	Enzo Doria	01/2014
500	2^847622-2441	255160	Yves Minet	02/2016

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PRP Records

Probable Primes Top 10000

(259919 PRPs in the top)