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) !!!
Submit your PRPs
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See the Latest PRPs
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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 |