## PRP Records

### Probable Primes Top 10000

#### (224660 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 (> 30000) Who ? When ? 7251 (27*2^219760-1)/227 66154 Lelio R Paula 01/2014 7253 (11^63521-4^63521)/7 66150 Robert Price 03/2013 7252 5*7^78274-6 66150 Lelio R Paula 09/2014 7254 (-lucasV(1,2,439441)-2)/(3*11927*81359) 66134 Mike Oakes 04/2017 7255 2^219679-112015 66130 Enzo Doria 05/2014 7256 2^219653+15015*219653 66123 Henri Lifchitz 04/2005 7257 15445^15782-15782^15445 66108 Norbert Schneider 08/2018 7258 2^219600+76561 66107 Enzo Doria 05/2016 7259 2^219594+255255 66105 Lelio R Paula 10/2011 7260 4*7^78210-3 66096 Lelio R Paula 09/2014 7261 (15185*2^219557-1)/63 66096 Lelio R Paula 04/2015 7262 (19*2^219499-1)/13 66076 Lelio R Paula 01/2014 7263 2^219496+66615 66075 Lelio R Paula 10/2011 7264 (F(79021)^5-F(79020)^5)/F(79019) 66057 Wayne Halsdorf 03/2012 7265 (2^219414+7)/443657 66045 Lelio R Paula 04/2012 7266 (115*10^66043-1)/3 66045 Serge Batalov 12/2014 7267 10^66033+19 66034 Robert Price 01/2011 7268 10^66033-78309 66033 Patrick De Geest 05/2013 7269 (lucasV(1,2,438701)+2)/7599419 66025 Mike Oakes 04/2017 7270 2^219304+454245 66018 Henri Lifchitz 03/2007 7271 (27*2^219293+1)/9145 66012 Lelio R Paula 08/2012 7272 2^219273-112635 66008 Enzo Doria 06/2014 7273 2^219250+25 66001 Lelio R Paula 08/2011 7274 132^31123+131 65999 Norbert Schneider 03/2015 7275 V(319871) 65987 Serge Batalov 03/2015 7276 2^219189-195 65983 Lelio R Paula 08/2011 7277 (7*2^219143-1)/55 65968 Lelio R Paula 01/2014 7278 (73^35401-1)/72 65962 Paul Bourdelais 08/2017 7279 2^219112-17009 65960 Enzo Doria 05/2013 7280 2^219093-111201 65954 Enzo Doria 05/2014 7281 2^219089-112099 65953 Enzo Doria 06/2014 7282 46714!3+81 65950 Robert Price 09/2014 7283 (11*10^65944-131)/3 65945 Robert Price 02/2017 7284 2^219021-3553 65932 Yves Minet 03/2017 7285 Pell-LucasQ(172243)/2 65931 Eric W. Weisstein 01/2007 7286 2^218990+73519 65923 Enzo Doria 04/2016 7287 58^37378-57 65914 Norbert Schneider 09/2014 7289 (2^218945-7)/1675 65906 Lelio R Paula 04/2012 7288 5*10^65905+81 65906 Robert Price 08/2017 7290 3*10^65899-13 65900 Robert Price 11/2017 7291 (-lucasV(1,2,437845)-2)/1679917 65896 Mike Oakes 04/2017 7292 127^31322-2 65896 Lelio R Paula 10/2017 7293 2^218897-111889 65895 Enzo Doria 05/2014 7294 2^218896+1869451 65895 Enzo Doria 05/2016 7295 63^36616+2 65885 Lelio R Paula 05/2013 7296 (3*2^218822-1)/11 65872 Lelio R Paula 01/2014 7297 2^218796-113297 65865 Enzo Doria 07/2014 7298 2^218797+73727 65865 Enzo Doria 04/2016 7299 3^138040-110 65862 Lelio R Paula 06/2013 7300 11^63240-1950 65858 Enzo Doria 12/2012 7301 2^218764-111873 65855 Enzo Doria 05/2014 7302 (34*10^65839-7)/9/37 65839 Makoto Morimoto 04/2016 7303 3^137988+26 65838 Lelio R Paula 06/2013 7304 2^218680-719 65830 Yves Minet 05/2012 7305 18^52424+17 65807 Lelio R Paula 08/2013 7306 (2*15683^15683+1)/732384425 65789 David Broadhurst 09/2010 7307 (23*2^218517+1)/19003 65778 Lelio R Paula 07/2012 7308 (5*10^65773+1)/3 65774 Erik Branger 12/2013 7309 2^218457-17329 65763 Enzo Doria 05/2013 7310 151703#+223381 65759 Nicolas PALAU 10/2016 7311 2^218436+40755 65756 Lelio R Paula 10/2011 7312 (F(44)^7433-F(43)^7433)/F(42) 65744 Wayne Halsdorf 03/2012 7313 157^29934+29934^157 65733 Serge Batalov 05/2014 7314 211^28273-2 65715 Lelio R Paula 09/2013 7315 (59*10^65712+31)/9 65713 Robert Price 09/2015 7316 611^23586+23586^611 65712 Norbert Schneider 08/2016 7317 p(13991)#/2+32 65712 Robert Price 12/2016 7318 2^218282-18485 65710 Enzo Doria 05/2013 7319 2^218274-111251 65708 Enzo Doria 05/2014 7320 2*F(314335)-1 65693 Henri Lifchitz 12/2009 7321 2^218200+427 65685 Henri Lifchitz 01/2005 7322 (10199^16384+10197^16384)/2 65676 Jeppe Stig Nielsen 04/2018 7323 (10199^(2^14)+(10197)^(2^14))/2 65676 Robert Price 05/2018 7324 46532!3+3 65667 Robert Price 10/2014 7325 2^218120-147 65661 Lelio R Paula 08/2011 7326 452^24729+24729^452 65659 Norbert Schneider 09/2016 7327 2^218102-114893 65656 Enzo Doria 05/2015 7328 (15*2^218083-1)/17 65650 Lelio R Paula 01/2014 7329 (15*2^218081+1)/18941 65646 Lelio R Paula 08/2012 7330 (306^26407-1)/305 65638 Eric Chen 09/2017 7331 19^51326+36 65634 Lelio R Paula 08/2013 7332 (21*2^218045-1)/451583 65634 Lelio R Paula 01/2014 7333 2^217989-33 65622 Lelio R Paula 08/2011 7334 (13*2^217961+1)/3 65614 Lelio R Paula 06/2012 7335 4*6^84315-5 65611 Lelio R Paula 09/2014 7336 (315047^11933+1)/315048 65607 Faysal YAtim 06/2008 7337 6^84303+55 65601 Lelio R Paula 07/2013 7338 (-lucasV(1,2,435857)+2)/(173*859*8017) 65595 Mike Oakes 04/2017 7339 (9787*2^217873-1)/37 65589 Lelio R Paula 04/2015 7340 5*2^217858+3 65583 Lelio R Paula 04/2014 7341 (19*10^65572+119)/3 65573 Robert Price 02/2017 7342 20^50399+51 65571 Lelio R Paula 08/2013 7343 7162^17009+17009^7162 65571 Norbert Schneider 07/2018 7344 11^62946-5670 65552 Enzo Doria 01/2013 7345 2^217742-3911 65547 Yves Minet 08/2009 7346 (19*10^65545+77)/3 65546 Robert Price 08/2016 7347 2^217731+131 65544 Lelio R Paula 08/2011 7348 2^217720-111287 65541 Enzo Doria 05/2014 7349 (365^25579+1)/366 65539 Eric Chen 10/2017 7350 10^65537+27 65538 Robert Price 01/2011 7351 10^65537-76859 65537 Patrick De Geest 05/2013 7352 (28*10^65532+359)/9 65533 Robert Price 11/2017 7353 (10223*2^217676+1)/3 65531 Lelio R Paula 06/2014 7354 PadovanNumber[536485] 65518 Eric W. Weisstein 05/2009 7355 5*10^65509+23 65510 Robert Price 11/2017 7356 (8*10^65507-83)/3 65508 Robert Price 10/2017 7357 7*10^65492-47 65493 Robert Price 02/2017 7358 2^217547-1868407 65489 Enzo Doria 04/2016 7359 2^217531-111769 65484 Enzo Doria 05/2014 7360 7^77484-18 65482 Lelio R Paula 06/2013 7361 2^217488-113285 65471 Enzo Doria 07/2014 7362 151153#/30-30 65468 Henri Lifchitz 12/2011 7363 2^217466+4257 65464 Lelio R Paula 10/2011 7364 46396!3-81 65455 Robert Price 09/2014 7365 2^217421-113185 65451 Enzo Doria 07/2014 7366 (6883*2^217440-1)/1061193295893 65448 Lelio R Paula 04/2015 7367 2^217408-2145 65447 Lelio R Paula 10/2011 7368 2^217398-16947 65444 Enzo Doria 05/2013 7369 8*5^93613+3 65434 Lelio R Paula 09/2014 7370 11^62828-5310 65429 Enzo Doria 01/2013 7371 10^65426+13 65427 Robert Price 01/2011 7372 2^217341-6555 65427 Lelio R Paula 10/2011 7373 10^65426-54849 65426 Patrick De Geest 05/2013 7374 (21*2^217363-1)/56003626667 65424 Lelio R Paula 01/2014 7375 30011^14608-108 65405 Enzo Doria 07/2012 7376 119^31504-2 65389 Lelio R Paula 10/2017 7377 (43^40031-1)/42 65388 Robert Price 04/2014 7378 2^217190+94395 65381 Henri Lifchitz 02/2005 7379 15^55587+46 65376 Lelio R Paula 08/2013 7380 2^217088-111833 65350 Enzo Doria 05/2014 7381 (13*2^217069-1)/1682945 65340 Lelio R Paula 01/2014 7382 (10^65340+47)/3 65340 Robert Price 11/2017 7383 (62*10^65331+1)/9 65332 Serge Batalov 11/2010 7384 2^216947-111351 65308 Enzo Doria 05/2014 7385 -E(18022)/775201845682685322943949235068359 65307 Thomas Ritschel 02/2017 7386 (13*10^65297+83)/3 65298 Robert Price 09/2016 7387 5^93400-8 65284 Lelio R Paula 06/2013 7388 2^216802-165 65264 Lelio R Paula 08/2011 7389 2^216799-28635 65264 Lelio R Paula 10/2011 7390 5*10^65255+51 65256 Robert Price 01/2017 7391 2^216762-167 65252 Lelio R Paula 08/2011 7392 11^62657-5790 65251 Enzo Doria 01/2013 7393 3^136756-112880 65250 Enzo Doria 06/2014 7394 2^216752+21 65249 Lelio R Paula 08/2011 7395 3*10^65247+11 65248 Robert Price 11/2017 7396 11^62651-2700 65245 Enzo Doria 12/2012 7397 15130^15609-15609^15130 65244 Norbert Schneider 07/2018 7399 Pell-LucasQ(170413)/2 65230 Eric W. Weisstein 12/2006 7398 gcd(V(790525),5*F(158105)*(F(158105)+1)+1) 65230 Serge Batalov 04/2015 7400 (2^216676-1017)/637 65224 Lelio R Paula 04/2012 7401 2^216652-2327 65219 Yves Minet 10/2013 7402 (9179*2^216648-1)/4667 65218 Lelio R Paula 04/2015 7403 (5*10^65203-119)/3 65204 Robert Price 04/2016 7404 2^216555-113269 65190 Enzo Doria 07/2014 7405 (9513^16384+1)/2 65181 Henri Lifchitz 02/2007 7406 2^216474+12915 65166 Lelio R Paula 02/2013 7407 19^50958-32 65163 Lelio R Paula 08/2013 7408 2^216442-112133 65156 Enzo Doria 06/2014 7409 2^216437-112213 65155 Enzo Doria 06/2014 7410 2^216435-112767 65154 Enzo Doria 06/2014 7411 2^216420+12705 65149 Lelio R Paula 02/2013 7412 8*3^136507-7 65132 Lelio R Paula 04/2014 7413 (-lucasV(1,2,432719)-2)/(5*461) 65128 Mike Oakes 03/2017 7414 15132^15575-15575^15132 65102 Norbert Schneider 07/2018 7415 5*10^65086-51 65087 Robert Price 10/2017 7416 2^216197-111769 65082 Enzo Doria 05/2014 7418 6^83631-79 65078 Lelio R Paula 07/2013 7417 572^23601+23601^572 65078 Norbert Schneider 08/2016 7419 (3^136399-7)/544220 65074 Lelio R Paula 04/2012 7420 2^216154-1421 65069 Yves Minet 01/2013 7421 2^216145-112663 65067 Enzo Doria 06/2014 7422 (7*10^65064+53)/3 65065 Robert Price 10/2017 7423 132013*10^65050+2^216091-1 65056 Gilbert Mozzo 01/2014 7424 132019*10^65050+2^216091-1 65056 Gilbert Mozzo 01/2014 7425 148918*10^65050+2^216091-1 65056 Gilbert Mozzo 02/2014 7426 194014*10^65050+2^216091-1 65056 Gilbert Mozzo 02/2014 7427 223864*10^65050+2^216091-1 65056 Gilbert Mozzo 04/2014 7430 82090*10^65050+2^216091-1 65055 Gilbert Mozzo 07/2012 7429 95133*10^65050+2^216091-1 65055 Gilbert Mozzo 12/2013 7428 98142*10^65050+2^216091-1 65055 Gilbert Mozzo 12/2013 7431 ((2^216091-1)*34009-48)/25 65054 Serge Batalov 01/2012 7432 5977*10^65050+2^216091-1 65054 Gilbert Mozzo 03/2012 7433 7*2^216091+2^298-13 65051 Peter Lesala 03/2007 7434 2^216091+2*29208-1 65050 Makoto Morimoto 10/2013 7435 (10^(2*32521+1)-6*10^32521-1)/3 65043 Robert Price 02/2016 7436 p(13861)#/2+256 65039 Robert Price 05/2017 7437 (2^216091-2096)/(2^4*3*2918437*5220283) 65036 Makoto Morimoto 10/2017 7438 11^62439-4380 65024 Enzo Doria 01/2013 7439 3^136244+2 65005 Mike Oakes 11/2009 7440 13^58343-50 64991 Lelio R Paula 07/2013 7441 331^25791-10002 64989 Enzo Doria 07/2012 7442 2^215877+131 64986 Lelio R Paula 08/2011 7443 4*5^92959+9 64977 Lelio R Paula 09/2014 7444 2^215789-18825 64959 Lelio R Paula 09/2011 7445 (2^215801-509203)/41327 64958 Lelio R Paula 05/2012 7446 U(315311) 64954 Serge Batalov 03/2015 7447 46072!3-59049 64951 Robert Price 12/2015 7448 2^215750-5955 64948 Lelio R Paula 09/2011 7449 13^58281+46 64922 Lelio R Paula 07/2013 7450 2^215623+183 64909 Lelio R Paula 08/2011 7451 (46*10^64904+521)/9 64905 Robert Price 08/2017 7452 (3^136043-2^136043)/(19862279*33466579) 64895 Mike Oakes 12/2016 7453 5*2^215554+3 64889 Lelio R Paula 04/2014 7454 2^215541-112075 64885 Enzo Doria 06/2014 7455 2*10^64882-3 64883 Dmitry Domanov 11/2010 7456 10^64862+342339 64863 Patrick De Geest 05/2013 7457 10^64862-47 64862 Robert Price 05/2011 7458 19^50718-84 64856 Lelio R Paula 08/2013 7459 (3045*2^215471-1)/(17*1151*27067*173473) 64853 Jens K. Andersen 09/2007 7460 86413!6-12 64846 Robert Price 08/2018 7461 10^64843+4278697839 64844 Robert Price 05/2015 7462 10^64843+21967 64844 Patrick De Geest 03/2016 7463 10^64843-340073 64843 Patrick De Geest 03/2016 7464 11^62254+70 64831 Lelio R Paula 07/2013 7465 2^215351-111925 64828 Enzo Doria 05/2014 7466 2^215310-117 64815 Lelio R Paula 08/2011 7467 124^30958-123 64809 Norbert Schneider 02/2015 7468 (7*10^64807+17)/3 64808 Erik Branger 03/2014 7469 (7*10^(2*32400+1)-27*10^32400-7)/9 64801 Robert Price 11/2015 7470 2^215243-15949 64795 Enzo Doria 04/2013 7471 23^47581-22^47581 64793 Robert Price 08/2012 7472 (62*10^64783-17)/9 64784 Robert Price 09/2015 7473 5*3^135747-4 64769 Lelio R Paula 04/2014 7474 (59*10^64767-41)/9 64768 Robert Price 09/2015 7476 (2^215140+3)/19 64763 Lelio R Paula 04/2012 7475 2^215135-17169 64763 Enzo Doria 05/2013 7477 2^215115-111277 64757 Enzo Doria 05/2014 7478 9*5^92641+2 64755 Lelio R Paula 09/2014 7479 (lucasV(1,2,430086)-2)/(7*1033) 64731 Mike Oakes 03/2017 7480 (5*10^64715-23)/9 64715 Robert Price 11/2014 7481 2^214938-1781 64703 Yves Minet 03/2013 7482 11^62111-420 64682 Enzo Doria 08/2012 7483 5^92525+42 64673 Lelio R Paula 06/2013 7484 2^214824+71893 64669 Enzo Doria 04/2016 7485 2^214799-2221 64661 Yves Minet 08/2013 7486 (21*2^214688+1)/293 64627 Lelio R Paula 08/2012 7487 92^32907+32907^92 64623 Serge Batalov 05/2014 7488 (89*10^64608-539)/9 64609 Robert Price 11/2017 7489 6^83013+101 64597 Lelio R Paula 07/2013 7490 p(13775)#/2+8 64594 Robert Price 01/2017 7491 (7*10^64568-43)/9 64568 Robert Price 10/2014 7492 Pell-LucasQ(168677)/2 64566 Eric W. Weisstein 11/2006 7493 (24737*2^214476+1)/2877 64565 Lelio R Paula 06/2014 7494 (47*2^214463+1)/7 64561 Lelio R Paula 04/2015 7495 2^214458+54615 64559 Lelio R Paula 10/2011 7496 (3^135322+7)/122911408 64557 Lelio R Paula 04/2012 7497 2^214389-683113 64538 Paul Bourdelais 03/2013 7498 (76*10^64534+113)/9 64535 Robert Price 11/2017 7499 2^214369-111241 64532 Enzo Doria 05/2014 7500 (19^50461+3^50461)/22 64526 Robert Price 07/2013

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 15 2018 21:33 (Time in France)

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