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	15^328574+328574^15	386434	Serge Batalov	05/2014
252	2^1280078+1885099	385342	Enzo Doria	08/2017
253	2^1274941+1880717	383796	Enzo Doria	10/2016
254	2^1272632+383431	383101	Enzo Doria	01/2017
255	2^1271346+1889839	382714	Enzo Doria	08/2017
256	(10^380976-7)/3	380976	Leonid Durman	01/2012
257	2^1257787+1447761	378632	Makoto Morimoto	10/2013
258	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
259	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
260	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
261	F(1803059)	376817	Henri Lifchitz	06/2009
262	7^442674+4	374103	Paul Bourdelais	02/2021
263	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
264	2^1234709+883127	371685	Enzo Doria	12/2016
265	2^1231466+283819	370709	Enzo Doria	07/2017
266	2^1220335+1881263	367358	Enzo Doria	11/2016
267	2^1216694+1884769	366262	Enzo Doria	02/2017
268	2^1215889-3	366020	Paul Bourdelais	06/2019
269	2^1215296+1885441	365841	Enzo Doria	03/2017
270	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
271	2^1214307+1888115	365543	Enzo Doria	05/2017
272	2^1213815+3	365395	Paul Bourdelais	06/2019
273	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
274	2^1207345+1882577	363448	Enzo Doria	12/2016
275	2^1207073+883727	363366	Enzo Doria	03/2017
276	3^761457-2	363308	Ryan Propper	07/2015
277	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
278	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
279	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
280	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
281	2^1200672+1880881	361439	Enzo Doria	10/2016
282	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
283	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
284	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
285	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
286	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
287	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
288	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
289	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
290	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
291	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021
292	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
293	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
294	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
295	2^1195093+1882577	359759	Enzo Doria	12/2016
296	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
297	2^1191375+8543	358640	Phil Moore	06/2008
298	2^1190972+1880191	358519	Enzo Doria	11/2016
299	(45^216551-1)/44	358004	Paul Bourdelais	08/2020
300	(50^210319-1)/49	357324	Paul Bourdelais	08/2020
301	(531^131072+25^131072)/2	357184	Kellen Shenton	03/2021
302	2^1179836+1885021	355167	Enzo Doria	02/2017
303	20^271951+3	353817	Paul Bourdelais	01/2021
304	(63^195893-1)/62	352477	Paul Bourdelais	08/2020
305	numbpart(100000135540)	352269	Serge Batalov	04/2017
306	(10^352237-1)/9/10567111/950335427	352221	Maksym Voznyy	01/2015
307	2^1168554+783529	351770	Enzo Doria	01/2017
308	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
309	2^1166152+1882411	351047	Enzo Doria	12/2016
310	2^1162154+1890207	349844	Enzo Doria	08/2017
311	(7*10^348724-61)/9	348724	Erik Branger	09/2016
312	(127^165601-1)/126	348390	Alexander Zhirkov	09/2015
313	2^1153083+1883693	347113	Enzo Doria	04/2017
314	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
315	2^1145882+80779	344945	Enzo Doria	09/2016
316	2^1136462+1887289	342110	Enzo Doria	05/2017
317	F(1636007)	341905	Henri Lifchitz	03/2009
318	2^1133678+782569	341272	Enzo Doria	11/2016
319	(11^327001+1)/12	340536	Paul Bourdelais	09/2013
320	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
321	Tau(907^20848)	339132	Nik Lygeros / Olivier Rozier	01/2016
322	2^1126380-3	339075	Paul Bourdelais	06/2019
323	2^1125446+1885099	338794	Enzo Doria	08/2017
324	(63^188147+1)/64	338539	Paul Bourdelais	12/2020
325	2^1124549+143807	338523	Enzo Doria	10/2016
326	2^1121187+1886783	337511	Enzo Doria	04/2017
327	(48^200443-1)/47	336992	Paul Bourdelais	08/2020
328	(94^170371-1)/93	336162	Paul Bourdelais	09/2020
329	2^1116184+1883521	336005	Enzo Doria	02/2017
330	2^1114517+1880087	335504	Enzo Doria	10/2016
331	(101^166849+1)/102	334418	Paul Bourdelais	12/2020
332	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
333	2^1104408-114539	332460	Enzo Doria	03/2015
334	2^1101921+82085	331712	Enzo Doria	10/2016
335	2^1100655+683513	331331	Enzo Doria	01/2017
336	(10^330906+71)/9	330906	Serge Batalov	07/2015
337	2^1098346+482899	330636	Enzo Doria	11/2016
338	2^1095679+1878713	329833	Enzo Doria	09/2016
339	2^1094740-1851539	329550	Enzo Doria	08/2015
340	2^1091469-379369	328565	Enzo Doria	03/2014
341	(69^178093-1)/68	327485	Paul Bourdelais	08/2020
342	2^1085750+582349	326844	Enzo Doria	11/2016
343	2^1083596+483061	326195	Enzo Doria	12/2016
344	(2^541456-1)*10^162995+2^541455-1	325990	paolo galliani	01/2019
345	2^1082908+583561	325988	Enzo Doria	05/2017
346	30^220411-29^220411	325574	Jean-Louis Charton	10/2018
347	2^1078242+1881649	324584	Enzo Doria	11/2016
348	2^1077737+1880117	324432	Enzo Doria	10/2016
349	2^1075425+1880117	323736	Enzo Doria	10/2016
350	(28^223381+1)/29	323267	Paul Bourdelais	12/2020
351	10^322999+187071	323000	Stefano Morozzi	03/2019
352	10^322999-143151	322999	Patrick De Geest	05/2020
353	2^1072146+1886869	322749	Enzo Doria	04/2017
354	2^1072118-7321953	322740	Enzo Doria	02/2015
355	2^1071026+1886869	322411	Enzo Doria	04/2017
356	2^1070539+1880633	322265	Enzo Doria	10/2016
357	2^1069293-1147195	321890	Enzo Doria	05/2015
358	2^1065968+1880941	320889	Enzo Doria	10/2016
359	2^1065897-1147195	320867	Enzo Doria	05/2015
360	2^1063427+1882103	320124	Enzo Doria	12/2016
361	2^1061095-1061095	319422	Henri Lifchitz	10/2013
362	2^1060950+653119	319378	Enzo Doria	12/2016
363	2^1060363+782753	319202	Enzo Doria	11/2016
364	(71^172259-1)/70	318895	Paul Bourdelais	08/2020
365	2^1054736+483061	317508	Enzo Doria	12/2016
366	2^1053965+1879667	317276	Enzo Doria	10/2016
367	(43^194119-1)/42	317086	Paul Bourdelais	08/2020
368	2^1052186-458165	316740	Enzo Doria	03/2015
369	2^1046613-114685	315062	Enzo Doria	04/2015
370	2^1045625-459373	314765	Enzo Doria	06/2015
371	(7*10^314564-61)/9	314564	Erik Branger	09/2016
372	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
373	(53^181981-1)/52	313784	Paul Bourdelais	08/2020
374	2^1041944+283051	313657	Enzo Doria	12/2016
375	2^1041153-114391	313419	Enzo Doria	02/2015
376	(74^167311+1)/75	312742	Paul Bourdelais	12/2020
377	2^1038871+1866983	312732	Enzo Doria	04/2016
378	(55^179573-1)/54	312521	Paul Bourdelais	08/2020
379	2^1037647+1881263	312363	Enzo Doria	11/2016
380	2^1037226+1879699	312237	Enzo Doria	10/2016
381	2^1036867+1865843	312129	Enzo Doria	02/2016
382	(76^165947+1)/77	312114	Paul Bourdelais	01/2021
383	2^1036020-114539	311874	Enzo Doria	02/2015
384	(90^159463-1)/89	311628	Paul Bourdelais	08/2020
385	2^1032240+1883431	310736	Enzo Doria	01/2017
386	2^1030352+1870021	310167	Enzo Doria	06/2016
387	2^1030046+1882843	310075	Enzo Doria	11/2016
388	3^648872+16	309591	Robert Price	04/2020
389	5^442281+2	309142	Paul Bourdelais	01/2021
390	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
391	(67^167449-1)/66	305773	Paul Bourdelais	08/2020
392	(62^170539+1)/63	305671	Paul Bourdelais	12/2020
393	2^1015321-1015321	305643	Henri Lifchitz	08/2013
394	2^1014224-2791229	305312	Enzo Doria	01/2016
395	2^1010751-107709	304267	Enzo Doria	03/2014
396	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
397	2^1009577+1869587	303913	Enzo Doria	06/2016
398	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
399	2^1008301+1869377	303529	Enzo Doria	06/2016
400	(2^1007838+5)/3	303389	Serge Batalov	08/2015
401	6^389756+5	303290	Paul Bourdelais	02/2021
402	2^1005326+383059	302634	Enzo Doria	12/2016
403	2^1004929+1877567	302514	Enzo Doria	08/2016
404	2^1003494+1874899	302082	Enzo Doria	06/2016
405	2^1003046+60529	301947	Enzo Doria	04/2016
406	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
407	2^1000647+1881353	301225	Enzo Doria	11/2016
408	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
409	2^999646+1874029	300924	Enzo Doria	06/2016
410	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
411	10^300476+3	300477	Ed Trice	10/2012
412	10^300476-530913	300476	Patrick De Geest	03/2016
413	2^998053+1879667	300444	Enzo Doria	09/2016
414	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
415	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
416	10^300000+287389	300001	Patrick De Geest	10/2019
417	10^300000-83657	300000	Patrick De Geest	10/2019
418	numbpart(72526161452)	299999	Serge Batalov	04/2017
419	2^996182-114431	299881	Enzo Doria	02/2015
420	2^995214-2788361	299590	Enzo Doria	12/2015
421	2^994791-114319	299462	Enzo Doria	01/2015
422	2^994490-1863791	299372	Enzo Doria	01/2016
423	2^993322+1885729	299020	Enzo Doria	03/2017
424	2^992711-2788807	298836	Enzo Doria	12/2015
425	2^992525-114199	298780	Enzo Doria	12/2014
426	2^992329+1884707	298721	Enzo Doria	02/2017
427	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
428	2^985217-114553	296580	Enzo Doria	03/2015
429	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
430	2^984131-1828009	296253	Enzo Doria	01/2015
431	2^983620+60451	296100	Phil Moore	03/2008
432	2^982721-2683	295829	Yves Minet	02/2016
433	2^981298-2788421	295401	Enzo Doria	12/2015
434	2^981163-2790967	295360	Enzo Doria	12/2015
435	2^979594+1865839	294888	Enzo Doria	02/2016
436	2^976760+1885021	294035	Enzo Doria	02/2017
437	2^974441+1878407	293336	Enzo Doria	08/2016
438	2^974180+1876831	293258	Enzo Doria	07/2016
439	2^974170+453319	293255	Enzo Doria	01/2017
440	2^972744-114419	292826	Enzo Doria	03/2015
441	11^281143+6	292781	Paul Bourdelais	03/2021
442	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
443	2^970911+1873373	292274	Enzo Doria	07/2016
444	2^970670+383059	292201	Enzo Doria	12/2016
445	2^970141-100363	292042	Enzo Doria	02/2014
446	2^969945+1874717	291983	Enzo Doria	06/2016
447	2^969384+1880701	291814	Enzo Doria	10/2016
448	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
449	2^962194+60139	289650	Enzo Doria	02/2016
450	2^959307-1861507	288781	Enzo Doria	11/2015
451	14^251797-3	288592	Paul Bourdelais	12/2020
452	2^957372+283531	288198	Enzo Doria	02/2017
453	2^957192-1864049	288144	Enzo Doria	01/2016
454	2^956446+1875199	287919	Enzo Doria	06/2016
455	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
456	2^955178+1883587	287538	Enzo Doria	12/2016
457	2^954127-954127^2	287221	Henri Lifchitz	01/2021
458	2^954001+1875257	287183	Enzo Doria	07/2016
459	(23891^65536+1)/2	286932	Serge Batalov	03/2018
460	2^952268+1878601	286662	Enzo Doria	09/2016
461	2^950801+81557	286220	Enzo Doria	08/2016
462	22845^65536+22844^65536	285658	Kellen Shenton	03/2021
463	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
464	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
465	2^948510+782569	285530	Enzo Doria	10/2016
466	2^948374-114137	285490	Enzo Doria	01/2015
467	2^947739+1872923	285298	Enzo Doria	06/2016
468	2^942533+82067	283731	Enzo Doria	09/2016
469	2^940950+1874989	283255	Enzo Doria	06/2016
470	2^940426-2786141	283097	Enzo Doria	11/2015
471	2^939881-114115	282933	Enzo Doria	12/2014
472	10^282493+632551	282494	Patrick De Geest	02/2017
474	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
473	10^282493-132327	282493	Patrick De Geest	02/2017
475	3^591827-2^591827	282374	Mike Oakes	08/2009
476	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
477	2^936716-1835519	281980	Enzo Doria	04/2015
478	2^936588+79411	281942	Enzo Doria	06/2016
479	2^936047+1877423	281779	Enzo Doria	08/2016
480	2^935713+1869377	281678	Enzo Doria	05/2016
481	2^933082+1877059	280886	Enzo Doria	08/2016
482	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
483	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
484	(10^279978+11)/3	279978	Serge Batalov	07/2015
485	2^929524-1864829	279815	Enzo Doria	01/2016
486	2^929152+60181	279703	Enzo Doria	02/2016
487	2^928621-2787883	279543	Enzo Doria	11/2015
488	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
489	2^927429+1882277	279184	Enzo Doria	12/2016
490	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
491	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
492	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
493	2^925330-1301	278553	Yves Minet	06/2015
494	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
495	2^923261-69175	277930	Enzo Doria	11/2015
496	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
497	((((((((((((((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
498	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
499	2^920318+2792299	277044	Enzo Doria	02/2016
500	2^918596-2786939	276525	Enzo Doria	11/2015

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