## PRP Records

### Probable Primes Top 10000

#### (293510 PRPs in the top)

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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See the Latest PRPs
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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 (14^441697-1)/13 506241 Paul Bourdelais 12/2014 252 101645^94522+94522^101645 505739 Gabor Levai 02/2023 253 3^1059503-2^1059503 505512 Mike Oakes 04/2012 254 101542^92885+92885^101542 504465 Gabor Levai 04/2022 255 105273^60238+60238^105273 503192 Miklos Levai 09/2023 256 105098^61113+61113^105098 503014 Miklos Levai 09/2022 257 2^1670703+60293 502932 Enzo Doria 11/2017 258 (2^1669219-2^834610+1)/5 502485 Borys Jaworski 01/2011 259 101311^90816+90816^101311 502317 Gabor Levai 12/2021 260 101643^87368+87368^101643 502254 Gabor Levai 11/2022 261 101863^84922+84922^101863 502085 Gabor Levai 10/2022 262 2^1666440+212671 501649 Enzo Doria 09/2023 263 100207^99856+99856^100207 500973 Gabor Levai 11/2021 264 101839^83028+83028^101839 500969 Gabor Levai 11/2022 265 100263^98600+98600^100263 500702 Gabor Levai 09/2021 266 101761^82168+82168^101761 500126 Gabor Levai 03/2022 267 2^1661176+336631 500064 Tony Prest / Never Odd Or Even 09/2019 268 101070^88579+88579^101070 500027 Gabor Levai 01/2022 269 (85^259159-1)/84 500025 Paul Bourdelais 11/2021 270 2^1660973+368139 500003 Tony Prest / Never Odd Or Even 08/2020 271 2^1660964-382425 500000 Tony Prest / Never Odd Or Even 05/2020 272 (87^257689-1)/86 499791 Paul Bourdelais 01/2021 273 (64*10^499210+53)/9 499211 Serge Batalov 03/2015 274 Tau(631^32370) 498503 Nik Lygeros / Olivier Rozier 05/2015 275 29^339887-28^339887 497051 Jean-Louis Charton 05/2019 276 2^1650267+193743 496780 Stefano Morozzi 09/2023 277 2^1650196+191835 496759 Stefano Morozzi 07/2023 278 2^1650190+185733 496757 Stefano Morozzi 07/2023 279 2^1650141+189525 496742 Stefano Morozzi 07/2023 280 2^1650103+189519 496731 Stefano Morozzi 05/2023 281 2^1631030+73519 490989 Enzo Doria 08/2023 282 (2^1629469-1)/644908484660139264379223 490496 Gord Palameta 11/2017 283 10^487291+7 487292 Alfred Reich 06/2021 284 2^1617579+1889543 486940 Enzo Doria 09/2017 285 L(2316773) 484177 Serge Batalov 06/2017 286 (57^275669-1)/56 484039 Paul Bourdelais 04/2021 287 2^1599624+20011 481535 Enzo Doria 07/2023 288 2^1599120-5 481384 Stefano Morozzi 12/2022 289 10^480684-3 480684 Paul Bourdelais 01/2021 290 2^1595483+184133 480289 Enzo Doria 07/2017 291 2^1594947+3 480127 Paul Bourdelais 07/2019 292 (94^241993-1)/93 477482 Paul Bourdelais 09/2020 293 2^1585195+1888373 477192 Enzo Doria 08/2017 294 (33^313553+1)/34 476134 Paul Bourdelais 02/2021 295 3^994536+16 474515 Robert Price 10/2020 296 2^1575391+71483 474240 Enzo Doria 04/2018 297 (2^1572882+5)/3 473485 Serge Batalov 08/2015 298 (6^608099-1)/5 473193 Paul Bourdelais 05/2010 299 2^1569708+20371 472530 Enzo Doria 09/2023 300 3^989124+16 471933 Robert Price 10/2020 301 2^1567006+1888099 471716 Enzo Doria 05/2017 302 2^1563067+1889813 470531 Enzo Doria 08/2017 303 2^1549797+60197 466536 Enzo Doria 02/2018 304 2^1549030+1887619 466305 Enzo Doria 05/2017 305 416^177481-415^177481 464840 Jean-Louis Charton 12/2016 306 (78^245183-1)/77 463908 Paul Bourdelais 02/2021 307 2^1534770+20809 462012 Enzo Doria 08/2023 308 10^459480-11 459480 Mischa Rodermond 04/2023 309 (5^656657-2^656657)/3 458984 Jon Grantham 08/2023 310 2^1522569+71657 458339 Enzo Doria 04/2018 311 2^1518191+75353 457022 Ben Maloney / Five or Bust 01/2009 312 6^584279-5 454658 Paul Bourdelais 02/2021 313 2^1509037-13 454266 Stefano Morozzi 12/2022 314 (52^264697-1)/51 454220 Paul Bourdelais 10/2021 315 2^1506029+1890167 453360 Enzo Doria 02/2018 316 (34^294277+1)/35 450678 Paul Bourdelais 06/2018 317 2^1495434+1890439 450171 Enzo Doria 12/2017 318 2^1494634+7 449930 Stefano Morozzi 10/2022 319 2^1493170+784129 449489 Enzo Doria 08/2017 320 2^1489873+1888277 448497 Enzo Doria 06/2017 321 2^1485203+71663 447091 Enzo Doria 09/2023 322 2^1484671+1888463 446931 Enzo Doria 06/2017 323 2^1482867+1886783 446388 Enzo Doria 04/2017 324 2^1482148+284011 446172 Enzo Doria 04/2017 325 2^1479356+1888291 445331 Enzo Doria 06/2017 326 2^1473184+212671 443473 Enzo Doria 09/2023 327 2^1466432+20371 441441 Enzo Doria 08/2023 328 14^384558+3 440753 Paul Bourdelais 01/2021 329 2^1461244+784531 439879 Enzo Doria 10/2017 330 3^919094+5*2^919094 438520 Jon Grantham 08/2023 331 (67^239053+1)/68 436527 Paul Bourdelais 09/2021 332 2^1448122+74209 435929 Enzo Doria 08/2023 333 2^1446263+74333 435369 Enzo Doria 08/2023 334 (80^228419+1)/81 434701 Paul Bourdelais 02/2021 335 2^1443089+60227 434414 Enzo Doria 10/2017 336 (21^328129-1)/20 433858 Paul Bourdelais 06/2014 337 (35^280979+1)/36 433850 Paul Bourdelais 09/2021 338 2^1434400+3 431798 Paul Bourdelais 06/2019 339 2^1432308+1888801 431168 Enzo Doria 10/2017 340 (2^1430131+1)/(3*356468732537*36519993971459) 430487 Gord Palameta 12/2018 341 (7^508867-2^508867)/5 430042 Jon Grantham 08/2023 342 2^1425483+1886813 429114 Enzo Doria 04/2017 343 (63^238481+1)/64 429107 Paul Bourdelais 12/2020 344 (17^348259+1)/18 428514 Paul Bourdelais 05/2014 345 (10^427912+89)/9 427912 Serge Batalov 12/2014 346 2^1421089+1890167 427791 Enzo Doria 09/2017 347 20^326600+3 424917 Paul Bourdelais 01/2021 348 (10^424861-7)/3 424861 Leonid Durman 01/2012 349 10^424821-11 424821 Mischa Rodermond 04/2023 350 (2^1411200+13)/7 424813 Stefano Morozzi 09/2022 351 1+3^605376+5^605376 423140 Jon Grantham 08/2023 352 2^1404213+184217 422711 Enzo Doria 09/2017 353 2^1401872+1884385 422006 Enzo Doria 04/2017 354 2^1401257+6077 421821 Enzo Doria 09/2017 355 138^196873-137^196873 421285 Jean-Louis Charton 12/2009 356 2^1398726+7 421059 Stefano Morozzi 10/2022 357 2^1398269+131595 420921 Makoto Morimoto 10/2013 358 2^1397071+684443 420561 Enzo Doria 07/2017 359 953^141023-952^141023 420121 Jean-Louis Charton 10/2016 360 2^1393111+1867211 419369 Enzo Doria 09/2023 361 (3^877843-1)/2 418838 Paul Bourdelais 07/2010 362 2^1386321+60299 417325 Enzo Doria 02/2018 363 2^1386320+184531 417324 Enzo Doria 09/2017 364 2^1382074+1883587 416046 Enzo Doria 01/2017 365 2^1379907+1885223 415394 Enzo Doria 03/2017 366 2^1375574+1886719 414090 Enzo Doria 04/2017 367 2^1373111+1884833 413348 Enzo Doria 02/2017 368 2^1372996+15 413313 Stefano Morozzi 10/2022 369 2^1368632+1889731 412000 Enzo Doria 10/2017 370 (89*10^411590+1)/9 411591 Serge Batalov 09/2014 371 F(1968721) 411439 Henri Lifchitz 11/2009 372 2^1366066+683749 411227 Enzo Doria 02/2017 373 2^1355826+15 408145 Stefano Morozzi 10/2022 374 2^1355790+1888939 408134 Enzo Doria 07/2017 375 2^1355635+1884203 408087 Enzo Doria 01/2017 376 (88^208739+1)/89 405888 Paul Bourdelais 12/2020 377 (2^1347781-2^673891+1)/5 405722 Borys Jaworski 10/2008 378 2^1347744-3 405712 Paul Bourdelais 07/2019 379 9*10^404644-11 404645 Mischa Rodermond 04/2023 380 1215^131072+242^131072 404302 Kellen Shenton 08/2022 381 1196^131072+595^131072 403405 Kellen Shenton 08/2022 382 10^400000+1415223 400001 Patrick De Geest 10/2020 383 10^400000-339233 400000 Patrick De Geest 10/2020 384 Tau(863^24630) 397727 Nik Lygeros / Olivier Rozier 01/2016 385 2^1320057+211517 397377 Enzo Doria 08/2023 386 2^1319770+1884949 397291 Enzo Doria 06/2017 387 2^1313062+1888849 395272 Enzo Doria 08/2017 388 (1073516^81920+1)/(1073516^16384+1) 395236 Serge Batalov 01/2017 389 (1059995^81920+1)/(1059995^16384+1) 394875 Serge Batalov 01/2017 390 2^1311618+783529 394837 Enzo Doria 01/2017 391 2^1308000+1883521 393748 Enzo Doria 02/2017 392 (1009565^81920+1)/(1009565^16384+1) 393487 Serge Batalov 01/2017 393 (995042^81920+1)/(995042^16384+1) 393075 Serge Batalov 01/2017 394 (988945^81920+1)/(988945^16384+1) 392900 Serge Batalov 01/2017 395 (988823^81920+1)/(988823^16384+1) 392897 Serge Batalov 01/2017 396 (2^1304983-1)/52199321 392832 Tony Prest / Never Odd Or Even 03/2014 397 (978970^81920+1)/(978970^16384+1) 392612 Serge Batalov 01/2017 398 2^1303102+1866409 392273 Enzo Doria 09/2017 399 2^1302818+283429 392188 Enzo Doria 01/2017 400 (934422^81920+1)/(934422^16384+1) 391286 Serge Batalov 01/2017 401 2^1299181+1886867 391093 Enzo Doria 04/2017 402 (37^249341-1)/36 391016 Paul Bourdelais 08/2020 403 2^1298304+1882891 390829 Enzo Doria 01/2017 404 95196^12497+12497^95196 390000 Hans Havermann 12/2021 405 86206^33381+33381^86206 389953 Hans Havermann 05/2023 406 (874207^81920+1)/(874207^16384+1) 389390 Serge Batalov 01/2017 407 (7^457871-5^457871)/2 386946 Jon Grantham 08/2023 408 79455^73828+73828^79455 386805 Hans Havermann 03/2023 409 81650^54369+54369^81650 386642 Yusuf AttarBashi 06/2021 410 80565^62824+62824^80565 386561 Hans Havermann 08/2021 411 83747^41272+41272^83747 386548 Hans Havermann 08/2021 412 15^328574+328574^15 386434 Serge Batalov 05/2014 413 2^1280078+1885099 385342 Enzo Doria 08/2017 414 2^1279921+17 385295 Stefano Morozzi 10/2022 415 2^1276977+71657 384409 Enzo Doria 08/2023 416 2^1274941+1880717 383796 Enzo Doria 10/2016 417 2^1272632+383431 383101 Enzo Doria 01/2017 418 2^1271346+1889839 382714 Enzo Doria 08/2017 419 5*3^798534-2^798534 380999 Jon Grantham 08/2023 420 (10^380976-7)/3 380976 Leonid Durman 01/2012 421 (4*10^380056+11)/3 380057 Tyler Busby 03/2023 422 2^1257787+1447761 378632 Makoto Morimoto 10/2013 423 (2^1257787+32270)/(2*233*281*2207*3011) 378620 Makoto Morimoto 12/2016 424 2^1257728+20851 378614 Enzo Doria 08/2023 425 (77^200657-1)/76 378536 Paul Bourdelais 08/2020 426 (98^189619+1)/99 377573 Paul Bourdelais 02/2021 427 F(1803059) 376817 Henri Lifchitz 06/2009 428 (10^376417-3^376417)/7 376417 Jon Grantham 08/2023 429 2^1245230+19 374852 Stefano Morozzi 10/2022 430 7^442674+4 374103 Paul Bourdelais 02/2021 431 (97^187393-1)/96 372306 Paul Bourdelais 09/2020 432 10^371696+7 371697 Alfred Reich 05/2021 433 2^1234709+883127 371685 Enzo Doria 12/2016 434 2^1234119+21803 371507 Enzo Doria 09/2023 435 (67^203431+1)/68 371479 Paul Bourdelais 09/2021 436 2^1231466+283819 370709 Enzo Doria 07/2017 437 73^197880+197880 368715 Kellen Shenton 06/2023 438 5*3^771723-2^771723 368207 Jon Grantham 08/2023 439 (2^1222097+19)/3 367888 Stefano Morozzi 09/2022 440 2^1220335+1881263 367358 Enzo Doria 11/2016 441 2^1216694+1884769 366262 Enzo Doria 02/2017 442 2^1215889-3 366020 Paul Bourdelais 06/2019 443 2^1215296+1885441 365841 Enzo Doria 03/2017 444 (80^192133+1)/81 365645 Paul Bourdelais 01/2021 445 2^1214307+1888115 365543 Enzo Doria 05/2017 446 2^1213815+3 365395 Paul Bourdelais 06/2019 447 (80^191953+1)/81 365302 Paul Bourdelais 01/2021 448 2^1208276+22201 363728 Enzo Doria 09/2023 449 2^1207345+1882577 363448 Enzo Doria 12/2016 450 2^1207073+883727 363366 Enzo Doria 03/2017 451 3^761457-2 363308 Ryan Propper 07/2015 452 (10^363030+7)/337/443 363025 Alfred Reich 12/2021 453 2^1200972+141811 361529 Stefano Morozzi 10/2022 454 (2^1200924+324730)/2 361514 Stefano Morozzi 06/2021 455 (2^1200912+274110)/2 361511 Stefano Morozzi 01/2021 456 2^1200906+165249 361509 Stefano Morozzi 07/2022 457 2^1200890+166339 361504 Stefano Morozzi 01/2023 458 (2^1200887+344126)/2 361503 Stefano Morozzi 10/2020 459 2^1200877+186755 361500 Stefano Morozzi 09/2022 460 2^1200861+198521 361495 Stefano Morozzi 11/2021 461 (2^1200856+305790)/2 361494 Stefano Morozzi 10/2020 462 (2^1200853+372822)/2 361493 Stefano Morozzi 06/2021 463 2^1200812+324178)/2 361481 Stefano Morozzi 06/2021 464 (2^1200768+380458)/2 361467 Stefano Morozzi 01/2021 465 2^1200756+140917 361464 Stefano Morozzi 05/2022 466 2^1200741+184781 361460 Stefano Morozzi 09/2022 467 (2^1200741+293402)/2 361459 Stefano Morozzi 07/2021 468 2^1200734+142653 361457 Stefano Morozzi 02/2023 470 2^1200672+1880881 361439 Enzo Doria 10/2016 469 2^1200672+141535 361439 Stefano Morozzi 09/2022 471 2^1200669+178805 361438 Stefano Morozzi 11/2022 472 2^1200660+198555 361435 Stefano Morozzi 12/2021 473 2^1200657+164837 361434 Stefano Morozzi 05/2022 474 2^1200631+166431 361426 Stefano Morozzi 02/2023 475 2^1200627+150669 361425 Stefano Morozzi 02/2023 476 (2^1200603+356030)/2 361418 Stefano Morozzi 10/2020 477 (2^1200590+275854)/2 361414 Stefano Morozzi 03/2021 478 2^1200550+139297 361402 Stefano Morozzi 10/2021 479 2^1200486+172855 361383 Stefano Morozzi 01/2023 480 (2^1200456+320526)/2 361373 Stefano Morozzi 10/2020 481 2^1200443+142121 361370 Stefano Morozzi 01/2023 482 2^1200416+164065 361362 Stefano Morozzi 01/2022 483 2^1200331+155429 361336 Stefano Morozzi 10/2021 485 (2^1200289+348366)/2 361323 Stefano Morozzi 10/2020 484 2^1200289+141885 361323 Stefano Morozzi 11/2022 486 (2^1200284+273162)/2 361322 Stefano Morozzi 10/2020 487 2^1200252+194535 361312 Stefano Morozzi 11/2021 488 (2^1200250+364230)/2 361311 Stefano Morozzi 10/2020 489 2^1200227+156881 361305 Stefano Morozzi 05/2022 490 (2^1200209+305990)/2 361299 Stefano Morozzi 10/2020 491 (2^1200210+376278)/2 361299 Stefano Morozzi 10/2020 492 (2^1200182+274462)/2 361291 Stefano Morozzi 01/2021 493 2^1200178+149193 361290 Stefano Morozzi 07/2022 494 2^1200168+140403 361287 Stefano Morozzi 03/2022 495 (2^1200162+275910)/2 361285 Stefano Morozzi 03/2021 496 2^1200157+168927 361284 Stefano Morozzi 02/2023 497 2^1200134+141385 361277 Stefano Morozzi 08/2022 498 (2^1200131+360150)/2 361276 Stefano Morozzi 10/2020 499 (2^1200118+290718)/2 361272 Stefano Morozzi 01/2021 500 2^1200022+192777 361243 Stefano Morozzi 09/2022

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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