PRP Records

Probable Primes Top 10000

(252675 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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 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 ? 7501 19^52265+52 66835 Lelio R Paula 08/2013 7502 2*10^66826-27 66827 Robert Price 02/2017 7503 4*6^85867+5 66819 Lelio R Paula 09/2014 7504 11955^16384+2 66807 Matt Stath 12/2018 7505 15^56800+8 66802 Lelio R Paula 08/2013 7506 (2^221891-2^110946+1)/5 66796 11/2006 7507 10^66793+69441 66794 Patrick De Geest 05/2013 7508 10^66793-63 66793 Robert Price 05/2011 7509 35^43256-1704 66791 Enzo Doria 03/2013 7510 3^139976+2^(139976-1) 66786 Robert Price 05/2016 7511 88769!6-48 66786 Robert Price 08/2018 7512 7^79023-54 66783 Lelio R Paula 06/2013 7513 104^33109-103 66782 Norbert Schneider 11/2016 7514 (34*10^66778-7)/9/37/358901 66772 Makoto Morimoto 04/2016 7515 (-lucasV(1,2,443622)+2)/(7*281*487) 66766 Mike Oakes 04/2017 7516 2^221768+183 66759 Lelio R Paula 02/2012 7517 gcd(V(1197915),5*F(239583)*(F(239583)+1)+1) 66759 Serge Batalov 04/2015 7518 (154*10^66755-1)/9 66757 Serge Batalov 12/2014 7519 11^64097+48 66751 Lelio R Paula 07/2013 7520 (lucasV(1,2,443547)-2)/(7*13*79*1327*221773) 66749 Mike Oakes 04/2017 7521 (19*10^66748+413)/9 66749 Robert Price 10/2017 7522 (3*2^221696-1)/13 66737 Lelio R Paula 01/2014 7523 8*6^85758-7 66734 Lelio R Paula 09/2014 7524 135^31325+2 66733 Lelio R Paula 05/2013 7525 (49*10^66729+41)/9 66730 Robert Price 07/2015 7526 (349*10^66720-7)/9 66722 Robert Price 03/2017 7527 (-lucasV(1,2,443285)+2)/(3^2*307) 66718 Mike Oakes 04/2017 7528 (25*10^66714+71)/3 66715 Robert Price 01/2017 7529 11^64061-780 66713 Enzo Doria 11/2012 7530 7^78929+4 66703 Lelio R Paula 06/2013 7531 11^64048-930 66700 Enzo Doria 11/2012 7532 120^32079-119 66699 Norbert Schneider 09/2018 7533 2*7^78921+5 66697 Lelio R Paula 09/2014 7534 (25*2^221526+1)/409 66685 Lelio R Paula 08/2012 7535 (2^221509-1)/292391881 66673 Jens K. Andersen 02/2009 7536 2^221479+72953 66672 Enzo Doria 04/2016 7537 10^66666+275403 66667 Patrick De Geest 03/2010 7538 10^66666-115521 66666 Patrick De Geest 03/2010 7539 (18*10^66657-81)/99 66657 Ray Chandler 01/2011 7540 4*10^66653+21 66654 Robert Price 08/2016 7541 (10^66650+149)/3 66650 Serge Batalov 12/2014 7542 9^69842+3*8^69842-2*4^69842-3*2^69842 66647 Mike Oakes 12/2010 7543 2^221391-2145 66646 Lelio R Paula 04/2012 7544 (5*10^66613-119)/3 66614 Robert Price 04/2016 7545 2^221273-113233 66610 Enzo Doria 07/2014 7546 3^139571-46 66593 Lelio R Paula 06/2013 7547 (4*10^(2*33295)-2*(10^33295)+1)/3 66591 Robert Price 04/2018 7548 2^221181-869688105 66583 Lelio R Paula 02/2016 7549 (61*10^66575-7)/9 66576 Ray Chandler 02/2012 7550 2^221126+133 66566 Lelio R Paula 02/2012 7551 12^61680+91 66564 Lelio R Paula 07/2013 7552 (lucasV(1,2,442258)+2)/103 66564 Mike Oakes 04/2017 7553 (13*10^66551-73)/3 66552 Robert Price 12/2016 7554 11^63901-1590 66547 Enzo Doria 12/2012 7555 11^63901-1500 66547 Enzo Doria 12/2012 7556 6^85517+23 66546 Lelio R Paula 07/2013 7557 17^54069-40 66530 Lelio R Paula 08/2013 7558 (2^110503+4725)^2+(2^110503+4725)+41 66530 Makoto Morimoto 05/2016 7559 (2^110503+8099)^2+(2^110503+8099)+41 66530 Makoto Morimoto 05/2016 7560 (2^221008-1017)/78533 66526 Lelio R Paula 04/2012 7561 3^139432+26 66526 Lelio R Paula 06/2013 7562 ((2^110503+5139)^2+(2^110503+5139)+41)/20865797 66523 Makoto Morimoto 05/2016 7563 ((2^110503+6647)^2+(2^110503+6647)+41)/197/17327 66523 Makoto Morimoto 05/2016 7564 6^85481+85481 66518 Henri Lifchitz 08/2014 7565 (9179*2^220913-1)/399 66503 Lelio R Paula 04/2015 7566 13^59687+66 66488 Lelio R Paula 07/2013 7567 (49*10^66485-31)/9 66486 Robert Price 07/2015 7568 (46*10^66469+17)/9 66470 Robert Price 06/2015 7569 2^220790+97 66465 Lelio R Paula 02/2012 7570 (23*2^220790+1)/807 66463 Lelio R Paula 06/2012 7571 40009^14441-102 66460 Enzo Doria 07/2012 7572 2^220736-143 66449 Lelio R Paula 02/2012 7573 (79*10^66447-97)/99 66447 Ray Chandler 01/2011 7574 2^220675+69 66430 Lelio R Paula 02/2012 7575 88323!6-16 66419 Robert Price 08/2018 7576 2^220633-111381 66418 Enzo Doria 05/2014 7577 (2^220625-509203)/4000321 66409 Lelio R Paula 05/2012 7578 2^220596-15813 66407 Enzo Doria 04/2013 7579 (5*10^66394-17)/3 66395 Serge Batalov 05/2009 7580 2^220549-1859173 66392 Enzo Doria 04/2016 7581 2^220478-161 66371 Lelio R Paula 02/2012 7582 5^94938-14636 66359 Enzo Doria 02/2013 7583 (F(67)^4861-F(66)^4861)/F(65) 66353 Wayne Halsdorf 03/2012 7584 15444^15839-15839^15444 66346 Norbert Schneider 08/2018 7585 2^220253-114871 66303 Enzo Doria 05/2015 7586 12^61432+95 66297 Lelio R Paula 07/2013 7587 2^220192-111563 66285 Enzo Doria 05/2014 7588 2^220188-111449 66284 Enzo Doria 05/2014 7589 (4*10^66284+23)/9 66284 Robert Price 11/2014 7590 32501!2+2 66266 Robert Price 01/2015 7591 (8*10^66261-101)/3 66262 Robert Price 10/2017 7592 1530*10^66254+R(66254) 66258 Patrick De Geest 05/2016 7593 (47^39623-1)/46 66252 Robert Price 06/2014 7594 2^220044-97305 66240 Lelio R Paula 04/2012 7595 (77*10^66237-257)/9 66238 Robert Price 10/2017 7596 29^45285+2 66225 Ray Chandler 08/2011 7597 15^56289+38 66202 Lelio R Paula 08/2013 7598 3^138749+98 66201 Lelio R Paula 06/2013 7599 (21*2^219912-1)/5 66201 Lelio R Paula 01/2014 7600 2^219904-16995 66198 Lelio R Paula 10/2011 7601 (3^138712-2)/5297 66179 Lelio R Paula 04/2012 7602 Phi(198552,10) 66177 Ray Chandler 07/2010 7603 4*6^85041+7 66176 Lelio R Paula 09/2014 7604 2^219812-3149 66171 Yves Minet 10/2009 7605 2^219795-611167 66165 Paul Bourdelais 03/2013 7606 32455!2+512 66162 Robert Price 02/2015 7607 (27*2^219760-1)/227 66154 Lelio R Paula 01/2014 7609 (11^63521-4^63521)/7 66150 Robert Price 03/2013 7608 5*7^78274-6 66150 Lelio R Paula 09/2014 7610 (-lucasV(1,2,439441)-2)/(3*11927*81359) 66134 Mike Oakes 04/2017 7611 2^219679-112015 66130 Enzo Doria 05/2014 7612 2^219653+15015*219653 66123 Henri Lifchitz 04/2005 7613 15445^15782-15782^15445 66108 Norbert Schneider 08/2018 7614 2^219600+76561 66107 Enzo Doria 05/2016 7615 2^219594+255255 66105 Lelio R Paula 10/2011 7616 4*7^78210-3 66096 Lelio R Paula 09/2014 7617 (15185*2^219557-1)/63 66096 Lelio R Paula 04/2015 7618 (19*2^219499-1)/13 66076 Lelio R Paula 01/2014 7619 2^219496+66615 66075 Lelio R Paula 10/2011 7620 (F(79021)^5-F(79020)^5)/F(79019) 66057 Wayne Halsdorf 03/2012 7621 (2^219414+7)/443657 66045 Lelio R Paula 04/2012 7622 (115*10^66043-1)/3 66045 Serge Batalov 12/2014 7623 10^66033+19 66034 Robert Price 01/2011 7624 10^66033-78309 66033 Patrick De Geest 05/2013 7625 (lucasV(1,2,438701)+2)/7599419 66025 Mike Oakes 04/2017 7626 2^219304+454245 66018 Henri Lifchitz 03/2007 7627 (27*2^219293+1)/9145 66012 Lelio R Paula 08/2012 7628 2^219273-112635 66008 Enzo Doria 06/2014 7629 2^219250+25 66001 Lelio R Paula 08/2011 7630 132^31123+131 65999 Norbert Schneider 03/2015 7631 V(319871) 65987 Serge Batalov 03/2015 7632 2^219189-195 65983 Lelio R Paula 08/2011 7633 (7*2^219143-1)/55 65968 Lelio R Paula 01/2014 7634 (73^35401-1)/72 65962 Paul Bourdelais 08/2017 7635 2^219112-17009 65960 Enzo Doria 05/2013 7636 2^219093-111201 65954 Enzo Doria 05/2014 7637 2^219089-112099 65953 Enzo Doria 06/2014 7638 46714!3+81 65950 Robert Price 09/2014 7639 (11*10^65944-131)/3 65945 Robert Price 02/2017 7640 2^219021-3553 65932 Yves Minet 03/2017 7641 Pell-LucasQ(172243)/2 65931 Eric W. Weisstein 01/2007 7642 2^218990+73519 65923 Enzo Doria 04/2016 7643 58^37378-57 65914 Norbert Schneider 09/2014 7645 (2^218945-7)/1675 65906 Lelio R Paula 04/2012 7644 5*10^65905+81 65906 Robert Price 08/2017 7646 3*10^65899-13 65900 Robert Price 11/2017 7647 (-lucasV(1,2,437845)-2)/1679917 65896 Mike Oakes 04/2017 7648 127^31322-2 65896 Lelio R Paula 10/2017 7649 2^218897-111889 65895 Enzo Doria 05/2014 7650 2^218896+1869451 65895 Enzo Doria 05/2016 7651 63^36616+2 65885 Lelio R Paula 05/2013 7652 (3*2^218822-1)/11 65872 Lelio R Paula 01/2014 7653 2^218796-113297 65865 Enzo Doria 07/2014 7654 2^218797+73727 65865 Enzo Doria 04/2016 7655 3^138040-110 65862 Lelio R Paula 06/2013 7656 11^63240-1950 65858 Enzo Doria 12/2012 7657 2^218764-111873 65855 Enzo Doria 05/2014 7658 (34*10^65839-7)/9/37 65839 Makoto Morimoto 04/2016 7659 3^137988+26 65838 Lelio R Paula 06/2013 7660 2^218680-719 65830 Yves Minet 05/2012 7661 18^52424+17 65807 Lelio R Paula 08/2013 7662 (2*15683^15683+1)/732384425 65789 David Broadhurst 09/2010 7663 (23*2^218517+1)/19003 65778 Lelio R Paula 07/2012 7664 (5*10^65773+1)/3 65774 Erik Branger 12/2013 7665 160^29839-159 65769 Norbert Schneider 12/2018 7666 2^218457-17329 65763 Enzo Doria 05/2013 7667 151703#+223381 65759 Nicolas PALAU 10/2016 7668 2^218436+40755 65756 Lelio R Paula 10/2011 7669 (F(44)^7433-F(43)^7433)/F(42) 65744 Wayne Halsdorf 03/2012 7670 157^29934+29934^157 65733 Serge Batalov 05/2014 7671 211^28273-2 65715 Lelio R Paula 09/2013 7672 (59*10^65712+31)/9 65713 Robert Price 09/2015 7673 611^23586+23586^611 65712 Norbert Schneider 08/2016 7674 p(13991)#/2+32 65712 Robert Price 12/2016 7675 2^218282-18485 65710 Enzo Doria 05/2013 7676 2^218274-111251 65708 Enzo Doria 05/2014 7677 2*F(314335)-1 65693 Henri Lifchitz 12/2009 7678 2^218200+427 65685 Henri Lifchitz 01/2005 7679 (10199^16384+10197^16384)/2 65676 Jeppe Stig Nielsen 04/2018 7680 (10199^(2^14)+(10197)^(2^14))/2 65676 Robert Price 05/2018 7681 46532!3+3 65667 Robert Price 10/2014 7682 2^218120-147 65661 Lelio R Paula 08/2011 7683 452^24729+24729^452 65659 Norbert Schneider 09/2016 7684 2^218102-114893 65656 Enzo Doria 05/2015 7685 (15*2^218083-1)/17 65650 Lelio R Paula 01/2014 7686 (15*2^218081+1)/18941 65646 Lelio R Paula 08/2012 7687 (306^26407-1)/305 65638 Eric Chen 09/2017 7689 19^51326+36 65634 Lelio R Paula 08/2013 7688 (21*2^218045-1)/451583 65634 Lelio R Paula 01/2014 7690 2^217989-33 65622 Lelio R Paula 08/2011 7691 (13*2^217961+1)/3 65614 Lelio R Paula 06/2012 7692 4*6^84315-5 65611 Lelio R Paula 09/2014 7693 (315047^11933+1)/315048 65607 Faysal YAtim 06/2008 7694 6^84303+55 65601 Lelio R Paula 07/2013 7695 (-lucasV(1,2,435857)+2)/(173*859*8017) 65595 Mike Oakes 04/2017 7696 (9787*2^217873-1)/37 65589 Lelio R Paula 04/2015 7697 5*2^217858+3 65583 Lelio R Paula 04/2014 7698 (19*10^65572+119)/3 65573 Robert Price 02/2017 7700 20^50399+51 65571 Lelio R Paula 08/2013 7699 7162^17009+17009^7162 65571 Norbert Schneider 07/2018 7701 11^62946-5670 65552 Enzo Doria 01/2013 7702 2^217742-3911 65547 Yves Minet 08/2009 7703 (19*10^65545+77)/3 65546 Robert Price 08/2016 7704 2^217731+131 65544 Lelio R Paula 08/2011 7705 2^217720-111287 65541 Enzo Doria 05/2014 7706 (365^25579+1)/366 65539 Eric Chen 10/2017 7707 10^65537+27 65538 Robert Price 01/2011 7708 10^65537-76859 65537 Patrick De Geest 05/2013 7709 (28*10^65532+359)/9 65533 Robert Price 11/2017 7710 (10223*2^217676+1)/3 65531 Lelio R Paula 06/2014 7711 PadovanNumber[536485] 65518 Eric W. Weisstein 05/2009 7712 5*10^65509+23 65510 Robert Price 11/2017 7713 (8*10^65507-83)/3 65508 Robert Price 10/2017 7714 7*10^65492-47 65493 Robert Price 02/2017 7715 2^217547-1868407 65489 Enzo Doria 04/2016 7716 2^217531-111769 65484 Enzo Doria 05/2014 7717 7^77484-18 65482 Lelio R Paula 06/2013 7718 2^217488-113285 65471 Enzo Doria 07/2014 7719 151153#/30-30 65468 Henri Lifchitz 12/2011 7720 2^217466+4257 65464 Lelio R Paula 10/2011 7721 46396!3-81 65455 Robert Price 09/2014 7722 2^217421-113185 65451 Enzo Doria 07/2014 7723 (6883*2^217440-1)/1061193295893 65448 Lelio R Paula 04/2015 7724 2^217408-2145 65447 Lelio R Paula 10/2011 7725 2^217398-16947 65444 Enzo Doria 05/2013 7726 8*5^93613+3 65434 Lelio R Paula 09/2014 7727 11^62828-5310 65429 Enzo Doria 01/2013 7728 10^65426+13 65427 Robert Price 01/2011 7729 2^217341-6555 65427 Lelio R Paula 10/2011 7730 10^65426-54849 65426 Patrick De Geest 05/2013 7731 (21*2^217363-1)/56003626667 65424 Lelio R Paula 01/2014 7732 30011^14608-108 65405 Enzo Doria 07/2012 7733 119^31504-2 65389 Lelio R Paula 10/2017 7734 (43^40031-1)/42 65388 Robert Price 04/2014 7735 2^217190+94395 65381 Henri Lifchitz 02/2005 7736 15^55587+46 65376 Lelio R Paula 08/2013 7737 2^217088-111833 65350 Enzo Doria 05/2014 7738 (13*2^217069-1)/1682945 65340 Lelio R Paula 01/2014 7739 (10^65340+47)/3 65340 Robert Price 11/2017 7740 (62*10^65331+1)/9 65332 Serge Batalov 11/2010 7741 2^216947-111351 65308 Enzo Doria 05/2014 7742 -E(18022)/775201845682685322943949235068359 65307 Thomas Ritschel 02/2017 7743 (13*10^65297+83)/3 65298 Robert Price 09/2016 7744 5^93400-8 65284 Lelio R Paula 06/2013 7745 2^216802-165 65264 Lelio R Paula 08/2011 7746 2^216799-28635 65264 Lelio R Paula 10/2011 7747 5*10^65255+51 65256 Robert Price 01/2017 7748 2^216762-167 65252 Lelio R Paula 08/2011 7749 11^62657-5790 65251 Enzo Doria 01/2013 7750 3^136756-112880 65250 Enzo Doria 06/2014

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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