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	2^1386321+60299	417325	Enzo Doria	02/2018
252	2^1386320+184531	417324	Enzo Doria	09/2017
253	2^1382074+1883587	416046	Enzo Doria	01/2017
254	2^1379907+1885223	415394	Enzo Doria	03/2017
255	2^1375574+1886719	414090	Enzo Doria	04/2017
256	2^1373111+1884833	413348	Enzo Doria	02/2017
257	2^1368632+1889731	412000	Enzo Doria	10/2017
258	(89*10^411590+1)/9	411591	Serge Batalov	09/2014
259	F(1968721)	411439	Henri Lifchitz	11/2009
260	2^1366066+683749	411227	Enzo Doria	02/2017
261	2^1355790+1888939	408134	Enzo Doria	07/2017
262	2^1355635+1884203	408087	Enzo Doria	01/2017
263	(88^208739+1)/89	405888	Paul Bourdelais	12/2020
264	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
265	2^1347744-3	405712	Paul Bourdelais	07/2019
266	10^400000+1415223	400001	Patrick De Geest	10/2020
267	10^400000-339233	400000	Patrick De Geest	10/2020
268	Tau(863^24630)	397727	Nik Lygeros / Olivier Rozier	01/2016
269	2^1319770+1884949	397291	Enzo Doria	06/2017
270	2^1313062+1888849	395272	Enzo Doria	08/2017
271	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
272	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
273	2^1311618+783529	394837	Enzo Doria	01/2017
274	2^1308000+1883521	393748	Enzo Doria	02/2017
275	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
276	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
277	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
278	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
279	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
280	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
281	2^1303102+1866409	392273	Enzo Doria	09/2017
282	2^1302818+283429	392188	Enzo Doria	01/2017
283	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
284	2^1299181+1886867	391093	Enzo Doria	04/2017
285	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
286	2^1298304+1882891	390829	Enzo Doria	01/2017
287	95196^12497+12497^95196	390000	Hans Havermann	12/2021
288	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
289	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
290	80565^62824+62824^80565	386561	Hans Havermann	08/2021
291	83747^41272+41272^83747	386548	Hans Havermann	08/2021
292	15^328574+328574^15	386434	Serge Batalov	05/2014
293	2^1280078+1885099	385342	Enzo Doria	08/2017
294	2^1274941+1880717	383796	Enzo Doria	10/2016
295	2^1272632+383431	383101	Enzo Doria	01/2017
296	2^1271346+1889839	382714	Enzo Doria	08/2017
297	(10^380976-7)/3	380976	Leonid Durman	01/2012
298	2^1257787+1447761	378632	Makoto Morimoto	10/2013
299	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
300	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
301	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
302	F(1803059)	376817	Henri Lifchitz	06/2009
303	7^442674+4	374103	Paul Bourdelais	02/2021
304	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
305	10^371696+7	371697	Alfred Reich	05/2021
306	2^1234709+883127	371685	Enzo Doria	12/2016
307	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
308	2^1231466+283819	370709	Enzo Doria	07/2017
309	2^1220335+1881263	367358	Enzo Doria	11/2016
310	2^1216694+1884769	366262	Enzo Doria	02/2017
311	2^1215889-3	366020	Paul Bourdelais	06/2019
312	2^1215296+1885441	365841	Enzo Doria	03/2017
313	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
314	2^1214307+1888115	365543	Enzo Doria	05/2017
315	2^1213815+3	365395	Paul Bourdelais	06/2019
316	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
317	2^1207345+1882577	363448	Enzo Doria	12/2016
318	2^1207073+883727	363366	Enzo Doria	03/2017
319	3^761457-2	363308	Ryan Propper	07/2015
320	(10^363030+7)/337/443	363025	Alfred Reich	12/2021
321	(2^1200924+324730)/2	361514	Stefano Morozzi	06/2021
322	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
323	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
324	2^1200861+198521	361495	Stefano Morozzi	11/2021
325	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
326	(2^1200853+372822)/2	361493	Stefano Morozzi	06/2021
327	2^1200812+324178)/2	361481	Stefano Morozzi	06/2021
328	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
329	(2^1200741+293402)/2	361459	Stefano Morozzi	07/2021
330	2^1200672+1880881	361439	Enzo Doria	10/2016
331	2^1200660+198555	361435	Stefano Morozzi	12/2021
332	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
333	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
334	2^1200550+139297	361402	Stefano Morozzi	10/2021
335	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
336	2^1200416+164065	361362	Stefano Morozzi	01/2022
337	2^1200331+155429	361336	Stefano Morozzi	10/2021
338	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
339	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
340	2^1200252+194535	361312	Stefano Morozzi	11/2021
341	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
342	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
343	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
344	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
345	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021
346	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
347	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
348	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
349	(59^203309+1)/60	360029	Paul Bourdelais	09/2021
350	2^1195093+1882577	359759	Enzo Doria	12/2016
351	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
352	2^1191375+8543	358640	Phil Moore	06/2008
353	2^1190972+1880191	358519	Enzo Doria	11/2016
354	(45^216551-1)/44	358004	Paul Bourdelais	08/2020
355	(50^210319-1)/49	357324	Paul Bourdelais	08/2020
356	(531^131072+25^131072)/2	357184	Kellen Shenton	03/2021
357	2^1179836+1885021	355167	Enzo Doria	02/2017
358	20^271951+3	353817	Paul Bourdelais	01/2021
359	(63^195893-1)/62	352477	Paul Bourdelais	08/2020
360	numbpart(100000135540)	352269	Serge Batalov	04/2017
361	(10^352237-1)/9/10567111/950335427	352221	Maksym Voznyy	01/2015
362	2^1168554+783529	351770	Enzo Doria	01/2017
363	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
364	2^1166152+1882411	351047	Enzo Doria	12/2016
365	10^350071+7	350072	Alfred Reich	05/2021
366	2^1162154+1890207	349844	Enzo Doria	08/2017
367	(7*10^348724-61)/9	348724	Erik Branger	09/2016
368	(127^165601-1)/126	348390	Alexander Zhirkov	09/2015
369	2^1153083+1883693	347113	Enzo Doria	04/2017
370	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
371	2^1145882+80779	344945	Enzo Doria	09/2016
372	2^1136462+1887289	342110	Enzo Doria	05/2017
373	F(1636007)	341905	Henri Lifchitz	03/2009
374	2^1133678+782569	341272	Enzo Doria	11/2016
375	(11^327001+1)/12	340536	Paul Bourdelais	09/2013
376	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
377	Tau(907^20848)	339132	Nik Lygeros / Olivier Rozier	01/2016
378	2^1126380-3	339075	Paul Bourdelais	06/2019
379	2^1125446+1885099	338794	Enzo Doria	08/2017
380	(63^188147+1)/64	338539	Paul Bourdelais	12/2020
381	2^1124549+143807	338523	Enzo Doria	10/2016
382	2^1121187+1886783	337511	Enzo Doria	04/2017
383	(48^200443-1)/47	336992	Paul Bourdelais	08/2020
384	(94^170371-1)/93	336162	Paul Bourdelais	09/2020
385	2^1116184+1883521	336005	Enzo Doria	02/2017
386	2^1114517+1880087	335504	Enzo Doria	10/2016
387	(101^166849+1)/102	334418	Paul Bourdelais	12/2020
388	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
389	2^1104408-114539	332460	Enzo Doria	03/2015
390	2^1101921+82085	331712	Enzo Doria	10/2016
391	2^1100655+683513	331331	Enzo Doria	01/2017
392	(10^330906+71)/9	330906	Serge Batalov	07/2015
393	2^1098346+482899	330636	Enzo Doria	11/2016
394	2^1095679+1878713	329833	Enzo Doria	09/2016
395	2^1094740-1851539	329550	Enzo Doria	08/2015
396	2^1091469-379369	328565	Enzo Doria	03/2014
397	(69^178093-1)/68	327485	Paul Bourdelais	08/2020
398	(10^326884+7)/421	326882	Alfred Reich	12/2021
399	2^1085750+582349	326844	Enzo Doria	11/2016
400	2^1083596+483061	326195	Enzo Doria	12/2016
401	(2^541456-1)*10^162995+2^541455-1	325990	paolo galliani	01/2019
402	2^1082908+583561	325988	Enzo Doria	05/2017
403	30^220411-29^220411	325574	Jean-Louis Charton	10/2018
404	2^1078242+1881649	324584	Enzo Doria	11/2016
405	2^1077737+1880117	324432	Enzo Doria	10/2016
406	2^1075425+1880117	323736	Enzo Doria	10/2016
407	(28^223381+1)/29	323267	Paul Bourdelais	12/2020
408	10^322999+187071	323000	Stefano Morozzi	03/2019
409	10^322999-143151	322999	Patrick De Geest	05/2020
410	2^1072146+1886869	322749	Enzo Doria	04/2017
411	2^1072118-7321953	322740	Enzo Doria	02/2015
412	2^1071026+1886869	322411	Enzo Doria	04/2017
413	2^1070539+1880633	322265	Enzo Doria	10/2016
414	2^1069293-1147195	321890	Enzo Doria	05/2015
415	2^1065968+1880941	320889	Enzo Doria	10/2016
416	2^1065897-1147195	320867	Enzo Doria	05/2015
417	2^1063427+1882103	320124	Enzo Doria	12/2016
418	2^1061095-1061095	319422	Henri Lifchitz	10/2013
419	2^1060950+653119	319378	Enzo Doria	12/2016
420	2^1060363+782753	319202	Enzo Doria	11/2016
421	(71^172259-1)/70	318895	Paul Bourdelais	08/2020
422	2^1054736+483061	317508	Enzo Doria	12/2016
423	2^1053965+1879667	317276	Enzo Doria	10/2016
424	(43^194119-1)/42	317086	Paul Bourdelais	08/2020
425	2^1052186-458165	316740	Enzo Doria	03/2015
426	2^1046613-114685	315062	Enzo Doria	04/2015
427	2^1045625-459373	314765	Enzo Doria	06/2015
428	(7*10^314564-61)/9	314564	Erik Branger	09/2016
429	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
430	(53^181981-1)/52	313784	Paul Bourdelais	08/2020
431	2^1041944+283051	313657	Enzo Doria	12/2016
432	2^1041153-114391	313419	Enzo Doria	02/2015
433	(74^167311+1)/75	312742	Paul Bourdelais	12/2020
434	2^1038871+1866983	312732	Enzo Doria	04/2016
435	(55^179573-1)/54	312521	Paul Bourdelais	08/2020
436	2^1037647+1881263	312363	Enzo Doria	11/2016
437	2^1037226+1879699	312237	Enzo Doria	10/2016
438	2^1036867+1865843	312129	Enzo Doria	02/2016
439	(76^165947+1)/77	312114	Paul Bourdelais	01/2021
440	2^1036020-114539	311874	Enzo Doria	02/2015
441	(90^159463-1)/89	311628	Paul Bourdelais	08/2020
442	2^1032240+1883431	310736	Enzo Doria	01/2017
443	2^1030352+1870021	310167	Enzo Doria	06/2016
444	2^1030046+1882843	310075	Enzo Doria	11/2016
445	3^648872+16	309591	Robert Price	04/2020
446	5^442281+2	309142	Paul Bourdelais	01/2021
447	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
448	(67^167449-1)/66	305773	Paul Bourdelais	08/2020
449	(62^170539+1)/63	305671	Paul Bourdelais	12/2020
450	2^1015321-1015321	305643	Henri Lifchitz	08/2013
451	2^1014224-2791229	305312	Enzo Doria	01/2016
452	(10^304986+7)/673	304984	Alfred Reich	11/2021
453	2^1010751-107709	304267	Enzo Doria	03/2014
454	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
455	77842^8039+8039^77842	303989	Hans Havermann	01/2022
456	2^1009577+1869587	303913	Enzo Doria	06/2016
457	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
458	80766^5771+5771^80766	303782	Hans Havermann	01/2022
459	78390^7459+7459^78390	303580	Hans Havermann	01/2022
460	2^1008301+1869377	303529	Enzo Doria	06/2016
461	(2^1007838+5)/3	303389	Serge Batalov	08/2015
462	6^389756+5	303290	Paul Bourdelais	02/2021
463	71016^18649+18649^71016	303285	Hans Havermann	01/2022
464	80160^6047+6047^80160	303129	Hans Havermann	01/2022
465	71790^16553+16553^71790	302874	Hans Havermann	11/2021
466	65208^44129+44129^65208	302874	Hans Havermann	11/2021
467	84181^3960+3960^84181	302858	Hans Havermann	11/2021
468	71956^16087+16087^71956	302682	Hans Havermann	11/2021
469	2^1005326+383059	302634	Enzo Doria	12/2016
470	2^1004929+1877567	302514	Enzo Doria	08/2016
471	69341^22978+22978^69341	302418	Hans Havermann	12/2021
472	111443^516+516^111443	302306	Hans Havermann	12/2021
473	67638^29387+29387^67638	302218	Hans Havermann	11/2021
474	2^1003494+1874899	302082	Enzo Doria	06/2016
475	75189^10400+10400^75189	302037	Hans Havermann	12/2021
476	67237^31042+31042^67237	302026	Hans Havermann	12/2021
477	64540^47791+47791^64540	302005	Hans Havermann	11/2021
478	2^1003046+60529	301947	Enzo Doria	04/2016
479	83278^4209+4209^83278	301815	Hans Havermann	09/2021
480	64431^48250+48250^64431	301763	Hans Havermann	09/2021
481	67237^30714+30714^67237	301716	Hans Havermann	09/2021
482	64641^46288+46288^64641	301581	Hans Havermann	09/2021
483	71513^16482+16482^71513	301572	Hans Havermann	10/2021
484	72017^15396+15396^72017	301565	Hans Havermann	09/2021
485	65534^39927+39927^65534	301540	Hans Havermann	10/2021
486	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
487	63169^59152+59152^63169	301441	Hans Havermann	09/2021
488	75055^10348+10348^75055	301336	Hans Havermann	09/2021
489	2^1000647+1881353	301225	Enzo Doria	11/2016
490	83686^3961+3961^83686	301086	Hans Havermann	10/2021
491	68529^24742+24742^68529	301078	Hans Havermann	09/2021
492	65207^41416+41416^65207	301072	Hans Havermann	10/2021
493	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
494	90762^2071+2071^90762	300984	Hans Havermann	06/2021
495	63909^51142+51142^63909	300934	Hans Havermann	08/2021
496	2^999646+1874029	300924	Enzo Doria	06/2016
497	66280^34607+34607^66280	300856	Hans Havermann	06/2021
498	65534^38925+38925^65534	300817	Hans Havermann	07/2021
499	63296^56517+56517^63296	300794	Hans Havermann	06/2021
500	110610^523+523^110610	300694	Hans Havermann	06/2021

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Probable Primes Top 10000

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