## PRP Records

### Probable Primes Top 10000

#### (290751 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 ? 8251 12^87212-37 94118 Lelio R Paula 06/2016 8252 11^90376+76 94117 Lelio R Paula 05/2016 8253 (6^120946-11)/5 94114 Paul Bourdelais 11/2011 8254 (2^312622+534)/2 94109 Stefano Morozzi 09/2020 8255 (10^94096+191)/3 94096 Robert Price 11/2017 8256 23794^9005+9005^23794 94093 Hans Havermann 09/2020 8257 2^312562-112685 94091 Enzo Doria 06/2014 8258 137^44026-2 94072 Lelio R Paula 10/2017 8259 s(164441) 94052 Robert Price 05/2020 8260 2^312404-869688105 94043 Lelio R Paula 09/2016 8261 2^312387+2793533 94038 Enzo Doria 03/2016 8263 10^94016+91 94017 Robert Price 04/2011 8262 (15*2^312325-1)/7201 94017 Lelio R Paula 02/2014 8264 10^94016-188963 94016 Patrick De Geest 08/2013 8265 (17*2^312315-1)/45 94016 Lelio R Paula 02/2014 8266 (401*10^94010+13)/9 94012 Robert Price 09/2021 8267 23866^8691+8691^23866 94010 Hans Havermann 08/2020 8268 6^120802+7661 94003 Mike Oakes 04/2011 8269 (67607*2^312254+1)/177 94001 Lelio R Paula 06/2014 8270 (2^312245+702)/2 93995 Stefano Morozzi 09/2020 8271 (56*10^93993+493)/9 93994 Robert Price 10/2021 8272 (11*2^312207+1)/19 93984 Lelio R Paula 09/2013 8273 2^312201+51 93982 Lelio R Paula 11/2012 8274 (4*6^120749+1)/5 93961 Serge Batalov 10/2014 8275 (781*10^93942-7)/9 93944 Robert Price 12/2021 8276 3^196892+58 93942 Lelio R Paula 05/2016 8277 2^312060+18915 93940 Lelio R Paula 03/2016 8278 42^57867-41 93933 Norbert Schneider 08/2018 8279 8*10^93921+83 93922 Robert Price 11/2021 8280 2^311992-16209 93919 Enzo Doria 04/2013 8281 (85^48677+1)/86 93917 Paul Bourdelais 08/2017 8282 2^311965-39 93911 Lelio R Paula 11/2012 8283 2^311920-111689 93898 Enzo Doria 05/2014 8284 130^44414+129 93889 Norbert Schneider 01/2019 8285 (2^311892+2730)/2 93889 Stefano Morozzi 09/2020 8286 7*10^93887-47 93888 Robert Price 02/2017 8287 9*10^93878-37 93879 Robert Price 06/2021 8288 (28*10^93874+323)/9 93875 Robert Price 10/2021 8289 (2^311778+1530)/2 93855 Stefano Morozzi 09/2020 8290 12^86965-13 93851 Lelio R Paula 06/2016 8291 24862^5953+5953^24862 93848 Hans Havermann 09/2020 8292 22299^16148+16148^22299 93837 Hans Havermann 08/2020 8293 2^311705+16095 93833 Lelio R Paula 03/2016 8294 (2^311701+3002)/2 93832 Stefano Morozzi 09/2020 8296 2^311665-81 93821 Lelio R Paula 11/2012 8295 (2^311665+2654)/2 93821 Stefano Morozzi 09/2020 8297 (2^311648+3058)/2 93816 Stefano Morozzi 09/2020 8298 (2^311639+2738)/2 93813 Stefano Morozzi 01/2021 8299 730^32761+32761^730 93806 Norbert Schneider 09/2017 8300 11^90073+92 93802 Lelio R Paula 05/2016 8301 6*10^93792+41 93793 Robert Price 01/2017 8302 10^93790+64611 93791 Patrick De Geest 04/2020 8305 (2^311580+7)/591329 93790 Lelio R Paula 06/2013 8303 10^93790-123456789 93790 Robert Price 02/2020 8304 10^93790-157517 93790 Patrick De Geest 04/2020 8306 (49*10^93782+293)/9 93783 Robert Price 03/2021 8307 12^86900-77 93781 Lelio R Paula 06/2016 8308 2^311508-109769 93774 Enzo Doria 04/2014 8309 2^311486-1859621 93767 Enzo Doria 03/2016 8310 Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831 93765 Kurt Beschorner 04/2015 8311 (10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831) 93765 Gord Palameta 10/2018 8312 2^311471+311469 93763 Renaud Lifchitz 01/2003 8313 (88*10^93760-1)/3 93762 Robert Price 10/2017 8314 2^311426+79459 93749 Enzo Doria 06/2016 8315 21537^21634+21634^21537 93745 Norbert Schneider 04/2020 8316 2^311409+111546435 93744 Paul Bourdelais 10/2021 8317 (2^311360+3078)/2 93729 Stefano Morozzi 09/2020 8318 (2^311341+2186)/2 93723 Stefano Morozzi 09/2020 8319 (2^311313+774)/2 93715 Stefano Morozzi 09/2020 8321 2^311294+5775 93709 Lelio R Paula 03/2016 8320 25155^5312+5312^25155 93709 Hans Havermann 09/2020 8322 2^311252-1017 93697 Lelio R Paula 03/2016 8323 2^311247-112041 93695 Enzo Doria 06/2014 8324 7*10^93692-83 93693 Robert Price 09/2017 8325 2^311205-109645 93683 Enzo Doria 04/2014 8326 5^134027-84 93681 Lelio R Paula 04/2016 8327 (2^311148-1017)/557 93663 Lelio R Paula 06/2013 8328 (2^311027-2^155514+1)/5 93628 11/2006 8329 26748^3161+3161^26748 93614 Hans Havermann 08/2020 8330 3^196192-28 93608 Robert Price 12/2013 8331 216091#+261433 93606 Makoto Morimoto 12/2015 8332 5^133917+68 93604 Lelio R Paula 04/2016 8333 2^310924-1709 93598 Yves Minet 03/2013 8334 24555^6476+6476^24555 93587 Hans Havermann 08/2020 8335 (2^310867+734)/2 93580 Stefano Morozzi 09/2020 8336 (266*10^93577-11)/3 93579 Robert Price 09/2016 8337 (16*10^93577+161)/3 93578 Robert Price 05/2016 8338 3^196113-56 93570 Lelio R Paula 04/2016 8339 2^310806-110345 93562 Enzo Doria 05/2014 8340 3^196093+86 93561 Lelio R Paula 04/2016 8341 2^310780-2327 93555 Yves Minet 10/2013 8342 30^63332+41 93550 Lelio R Paula 08/2012 8343 (21181*2^310707+1)/21 93536 Lelio R Paula 06/2014 8344 8*5^133807+7 93528 Lelio R Paula 10/2014 8345 2^310686+8193 93526 Lelio R Paula 03/2016 8346 22681^13282+13282^22681 93520 Hans Havermann 09/2020 8347 2^310646+63 93514 Lelio R Paula 11/2012 8348 (77*10^93508+31)/9 93509 Robert Price 10/2015 8349 (1000907^15583+1)/1000908 93499 Faysal YAtim 04/2009 8350 (2*10^93497+7)/9 93497 Erik Branger 03/2011 8351 3^195958-112852 93496 Enzo Doria 07/2014 8352 2^310583+16385 93495 Lelio R Paula 03/2016 8353 (9913*2^310557-1)/35 93490 Lelio R Paula 04/2015 8354 9*7^110614+2 93481 Lelio R Paula 11/2014 8355 (19*10^93467+83)/3 93468 Robert Price 08/2020 8356 2^310469-8295 93461 Lelio R Paula 03/2016 8357 2^310459-1159 93458 Yves Minet 11/2012 8358 6^120075-95 93437 Lelio R Paula 05/2016 8359 (2^310362+1758)/2 93428 Stefano Morozzi 09/2020 8360 148^43041-147 93411 Norbert Schneider 05/2019 8361 2^310289+98327 93407 Yves Minet 11/2010 8362 21769^19510+19510^21769 93395 Hans Havermann 08/2020 8363 2^310217-113143 93385 Enzo Doria 07/2014 8364 7^110494-68 93379 Lelio R Paula 04/2016 8365 2^310184-113093 93375 Enzo Doria 07/2014 8366 2^310180-110417 93374 Enzo Doria 05/2014 8367 gcd(V(1124905),5*F(224981)*(F(224981)-1)+1) 93372 Serge Batalov 04/2015 8368 (2^310173+3150)/2 93372 Stefano Morozzi 09/2020 8369 3^195669+68 93358 Lelio R Paula 04/2016 8370 10^93356+91 93357 Robert Price 04/2011 8371 10^93356-28313 93356 Patrick De Geest 08/2013 8372 (85*10^93346+23)/9 93347 Robert Price 11/2015 8373 (3^195648-5)/3158276 93342 Lelio R Paula 04/2013 8374 10^93333-4000001 93333 Robert Price 07/2021 8375 3^195556+8680 93304 Lelio R Paula 04/2016 8376 2^309942-109991 93302 Enzo Doria 04/2014 8377 2^309926-1867301 93298 Enzo Doria 03/2016 8378 2^309924+85951 93297 Yves Minet 03/2011 8379 2^309896-4229 93288 Yves Minet 08/2018 8380 (86*10^93263-77)/9 93264 Robert Price 05/2016 8381 6^119836-125 93251 Lelio R Paula 05/2016 8382 (77*10^93249-257)/9 93250 Robert Price 10/2017 8383 21822^18749+18749^21822 93245 Hans Havermann 09/2020 8384 3^195430-2 93244 Theodore Burton 02/2007 8385 (13*10^93236+47)/3 93237 Robert Price 01/2017 8386 (67*10^93226-7)/3 93228 Robert Price 10/2017 8387 (86*10^93217-221)/9 93218 Robert Price 06/2017 8388 2^309637-16329 93211 Enzo Doria 04/2013 8389 (41*10^93207+49)/9 93208 Robert Price 04/2016 8390 14^81312-57 93194 Lelio R Paula 06/2016 8391 41^57783-40 93192 Theodore Burton 02/2007 8392 3*10^93179-97 93180 Robert Price 08/2017 8393 5*7^110252-4 93175 Lelio R Paula 11/2014 8394 22022^16959+16959^22022 93140 Hans Havermann 08/2020 8395 83061!4-512 93137 Robert Price 11/2019 8396 25169^5016+5016^25169 93135 Hans Havermann 08/2020 8397 (483641^16384+1)/2 93135 Richard Fischer 02/2021 8398 2^309380-27 93133 Lelio R Paula 11/2012 8399 25653^4268+4268^25653 93127 Hans Havermann 08/2020 8400 (2^309355+1826)/2 93125 Stefano Morozzi 02/2021 8401 (2^309334+2710)/2 93119 Stefano Morozzi 09/2020 8402 23*10^93116-7 93118 Robert Price 03/2016 8403 (2^309270+3214)/2 93100 Stefano Morozzi 09/2020 8404 (29*10^93082+1)/3 93083 Robert Price 11/2015 8405 (2^309198+3738)/2 93078 Stefano Morozzi 09/2020 8406 (58*10^93062-13)/9 93063 Robert Price 09/2015 8407 (2^309138+1794)/2 93060 Stefano Morozzi 01/2021 8408 2^309131+1869383 93058 Enzo Doria 05/2016 8409 (2^309114+3610)/2 93053 Stefano Morozzi 09/2020 8410 2^309066-93 93039 Lelio R Paula 11/2012 8411 2^309063-113269 93038 Enzo Doria 07/2014 8412 3^194965+16 93022 Robert Price 10/2013 8413 (89*10^93019-737)/9 93020 Robert Price 01/2022 8414 2^308979+1869143 93012 Enzo Doria 05/2016 8415 5^133064+54 93008 Lelio R Paula 04/2016 8416 (2^308947+2750)/2 93003 Stefano Morozzi 01/2021 8417 (2^308905-509203)/119 92988 Lelio R Paula 06/2013 8418 (94*10^92981-49)/99 92981 Ray Chandler 07/2011 8419 (2*10^92976-17)/3 92976 Robert Price 08/2014 8420 24783^5642+5642^24783 92972 Hans Havermann 08/2020 8421 (472489^16384+1)/2 92969 Richard Fischer 01/2021 8422 2^308809+37967 92961 Phil Moore 03/2008 8423 (3^194825+5)/11656 92952 Lelio R Paula 04/2013 8424 (2^308679+5)/1573 92919 Lelio R Paula 06/2013 8425 2^308650+513 92913 Lelio R Paula 02/2016 8426 5*7^109936+6 92908 Lelio R Paula 10/2014 8427 2*10^92897+89 92898 Robert Price 07/2016 8428 (2^308585+3182)/2 92894 Stefano Morozzi 09/2020 8429 (467307^16384+1)/2 92891 Richard Fischer 01/2021 8430 12^86073-29 92889 Lelio R Paula 06/2016 8431 2^308566-117 92888 Lelio R Paula 11/2012 8432 11594^22851-22851^11594 92872 Norbert Schneider 03/2022 8433 (17*10^92869-11)/3 92870 Robert Price 07/2015 8434 2^308459+75431 92856 Enzo Doria 04/2016 8435 2^308426-1866377 92846 Enzo Doria 03/2016 8436 24810^5521+5521^24810 92840 Hans Havermann 09/2020 8437 (96^46831-1)/95 92830 Paul Bourdelais 09/2017 8438 2^308349-112111 92823 Enzo Doria 06/2014 8439 9*10^92821+19 92822 Robert Price 05/2016 8440 2^308337-75 92819 Lelio R Paula 11/2012 8441 4*3^194508+7 92805 Lelio R Paula 08/2014 8442 22*25^66379-113 92796 Curtis Bright 05/2015 8443 24538^6047+6047^24538 92792 Hans Havermann 09/2020 8444 11^89101-1080 92790 Enzo Doria 12/2012 8445 2^308236-1867859 92789 Enzo Doria 04/2016 8446 12^85963+25 92770 Lelio R Paula 06/2016 8447 23692^8221+8221^23692 92753 Hans Havermann 08/2020 8448 7^109750-66 92750 Lelio R Paula 04/2016 8449 9*10^92742+11 92743 Robert Kinser 01/2017 8450 (2^308054+778)/2 92734 Stefano Morozzi 09/2020 8451 (21*2^308046-1)/8857 92729 Lelio R Paula 02/2014 8452 2^307997-110655 92717 Enzo Doria 05/2014 8453 L(443609) 92709 Renaud Lifchitz 11/2003 8454 10^92691+9 92692 Robert Price 03/2011 8455 10^92691-252291 92691 Patrick De Geest 08/2013 8456 (2^307883+3506)/2 92682 Stefano Morozzi 09/2020 8457 2^307879-2521 92681 Yves Minet 07/2014 8458 21269^21412+21412^21269 92666 Norbert Schneider 04/2020 8459 (2^307780-7)/19959669 92644 Lelio R Paula 06/2013 8460 14^80831+47 92643 Lelio R Paula 06/2016 8461 15^78744+92 92611 Lelio R Paula 07/2016 8462 65^51083-64 92610 Norbert Schneider 11/2014 8463 (2^307639+506)/2 92609 Stefano Morozzi 09/2020 8464 131^43737-130 92604 Norbert Schneider 02/2019 8465 6^118996-16943 92597 Enzo Doria 02/2013 8466 (16*10^92591+41)/3 92592 Robert Price 10/2017 8467 (2^307566+3094)/2 92587 Stefano Morozzi 09/2020 8468 (2^307528+1578)/2 92575 Stefano Morozzi 09/2020 8469 9*10^92573+83 92574 Robert Price 11/2020 8470 (3^194014-7)/2 92568 Lelio R Paula 04/2013 8471 (2^307498+570)/2 92566 Stefano Morozzi 09/2020 8472 (63^51439+1)/64 92555 Paul Bourdelais 08/2017 8473 (26*10^92546-77)/3 92547 Robert Price 02/2017 8474 3^193954+340 92540 Lelio R Paula 04/2016 8475 2^307407-307407^2 92539 Henri Lifchitz 05/2005 8476 24299^6430+6430^24299 92536 Hans Havermann 08/2020 8478 (17*10^92513-11)/3 92514 Robert Price 07/2015 8477 2^307322-399071 92514 Harrison Mesh 06/2022 8479 2^307318-4211 92512 Yves Minet 06/2011 8480 2^307280+193 92501 Lelio R Paula 11/2012 8481 20^71075-33 92471 Lelio R Paula 05/2016 8482 2^307126-78795 92455 Lelio R Paula 02/2016 8483 2^307125-49789 92454 Henri Lifchitz 08/2005 8484 2^307099+23 92447 Lelio R Paula 11/2012 8485 129^43798+128 92440 Norbert Schneider 01/2019 8486 21826^17181+17181^21826 92435 Hans Havermann 09/2020 8487 Phi(277314,10)/3327769 92430 Makoto Kamada 05/2019 8488 (2^307022+1038)/2 92423 Stefano Morozzi 09/2020 8489 7*10^92414-69 92415 Robert Price 01/2017 8490 (9787*2^306975-1)/2129155 92407 Lelio R Paula 04/2015 8491 22280^14037+14037^22280 92402 Hans Havermann 09/2020 8492 2^306915+1873373 92391 Enzo Doria 06/2016 8493 2^306908+12915 92389 Lelio R Paula 02/2016 8494 21620^18759+18759^21620 92387 Hans Havermann 09/2020 8495 (2^306897+1142)/2 92385 Stefano Morozzi 09/2020 8496 19^72244-80 92383 Lelio R Paula 06/2016 8498 2^306849+75 92371 Lelio R Paula 11/2012 8497 (397*10^92369+53)/9 92371 Robert Price 11/2017 8499 2^306813-869688105 92360 Lelio R Paula 08/2016 8500 (2^306797+2694)/2 92355 Stefano Morozzi 09/2020

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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